 and go through with that as well. Let me see if I got all the screenshots. There is one that I'm unable to copy. I don't know what's wrong with this. I see. I copied half of the question. Let me copy the rest of it because I think I only copied question 21, not the table as well. It's important to have all the information. I hope it will be visible. Let me just also check if the email came through. I am so sorry for this, but thank you. I have your tutorial letter 101, so it's fine. We can use that as well. Let me just double check. There are no tables on the tutorial letter 101. That is why I need the study guide. The one that has tables will assist. Because when we go look for the p-value, we need to use the table. The challenge I have is in my previous encounters, everything was on my hard drive and my hard drive. When I reformatted my hard drive, I lost everything so I don't have cow information. Everything I have to do, it means I have to start from scratch. I'm going to share one of the other things that I think. I will share with you in the chat as well. You can download it. I will paste it there. It's the document that I'm going to use now with you. I must just apologize again for all this. Next time we meet, it will be fine. We will, how do I attach something on the chat? I cannot attach a document on the chat. Anyway, let's start. Last thing, I just need to check if the email came through. Thank you, the email came through. Thank you, guys. One last email, and I think this is. I'm going to assume, let me go back to the presentation mode. I'm going to assume this was taken from a tutorial letter, tutorial letter 101, and this, we ever gave me access to this. I'm going to go out and share the. Now we can start. Somebody started recording this session. I don't know who started. Maybe it's one of the people from UNICEF. When it comes to your module, since they already started the recording, I don't have to start from the beginning. When it comes to your module, you just need to know how to do the hypothesis testing. I'm going to email or put this somewhere on the chat, if I can find a way to put it on the chat and share with everyone, or I will post it under the notes section on my UNICEF. There is a link where you can access the notes as well. This will guide you in terms of what kind of a test you need to be doing. You need to ask yourself certain questions as well. Am I doing a hypothesis looking at the difference between two groups or one group? Or am I doing between two variables? You need to ask yourself those kind of a question. Let's say we're looking at the pink section. We only concentrate on the pink side where we ask ourselves if we're calculating or we're doing a hypothesis on two groups. When you do for two groups, you have to ask yourself two questions. Is my population standard deviation given in the question? Remember the population standard deviation? Either they will say population standard deviation, or they will give it to you as sigma like this. If they give it to you as sigma in a symbol, this is sigma tells you population standard deviation. If they have told you that it is 3.5 or it's 10 or it's 1.3, then you know that it is given, and when it is given, we're going to use this as a test. The most important thing is the population standard deviation for group between a group. That is the formula that you will use to standardize your scores or your mean scores. Which is the sample mean minus your population standard deviation or population mean divided by the standard error. Remember this is a standard error, and the standard error here is population standard deviation divided by the square root of n, and they would have given you the population standard deviation. You must remember that. If the population standard deviation is not known, then it means they wouldn't have given you the population standard deviation, but they would have given you a sample standard deviation, which is represented by an S, symbol S. If they give you S is equals to 1.3, 1.4, or they say sample standard deviation, then you know that they haven't given you the population standard deviation, so your sigma is unknown, and when it is unknown, then you're going to use the t-test, which also is your sample mean minus the population mean divided by the standard error. You can see that the standard error here uses the sample standard deviation and the square root of n. That is if you're doing a hypothesis testing for a group. This one is for one group. Let's say they give you one group and they say, you're going to test the marks for students who are doing site 307. It's only one group. Only one group, then it means you're going to check whether are they giving you the population standard deviation or are they giving you a sample standard deviation. If they give you the population standard deviation, we use the z-test. If they're giving you the sample standard deviation, we're going to do a t-test. Excuse me, can you repeat that again because that is very important there? Okay. It is very, very important. That's how to just know when to use what test. Can you repeat that again for me? One group, meaning they say, test the hypothesis for the scores that students who wrote site 303. You need to prove that the mean is different to the population, something like that. The sample mean is different to the population mean. It's from one group of students. If they give you the population standard deviation and they say, the population standard deviation is this, then you're going to use a z-test from that one group. One group, meaning one. Let me look for an example from your study guide or from, let's see, from the questions that they are asking here. It needs to be, for example, like this one, it's only the exam marks so they can ask you to calculate this and they say the exam mark is more than, sorry, it's more than 30 percent. You need to go back there or we can use another one. We can use this. Let's use this one. Let's use this question here. I hope we can use this question. You can see that on this question, they're only talking about the depression score. They are not saying two groups, they're not giving you two different groups. They are only giving you one group of patients who were diagnosed, and then they give you the depression score and they say, you need to test that the clinical depression score is greater than 120. It's one group, it's not multiple groups that they did, only one group, and they're asking you to test the hypothesis. I'm not going to go into the hypothesis just to understand what you need to look out for in order to know which one you need to use. Yeah, they say she uses a random sample of 64 drawn from a population of diagnosed patient with the mean, which that bar should have been on top of the X with the mean of 127 and S of 24. Remember that? They didn't give you Sigma. So this is not Sigma, this is S. Let's go back to our paper. If they give you S, we use t-test. You see that? It means the population standard deviation is not known. If they would have given us Sigma, then we will use the Z-test. So coming back here, therefore it means this question, when we answer the hypothesis, if we were going to have to test the hypothesis on this, we were going to use t-test. But for this one, they just want you to calculate the standard error, which is your standard error on this. If you go back to the t-test formula, remember everything underneath there is your standard error. We can also call this SX bar. That is your standard error. So they just want you to calculate SX bar, SX bar, which is your sample standard deviation divided by the square root of n. You are given all the information there is your n and there is your standard deviation. You should be able to calculate that. Okay. So that is when the population standard deviation is unknown for one group. Now, if you have two groups, if they say test for math and test for physical science, two groups of test or maybe they can say test English and math, test if the scores are different or something like that, then you have two groups. You no longer have one group, you have two groups that you need to test from. Now you need to ask yourself the following question. When you have two groups, where you have to test the difference between two groups, you ask yourself this question. One, are the groups independent or the groups dependent? How do I even know? That's what I'm going to ask yourself. How am I going to know whether the groups are dependent and independent? Okay. The two groups will be independent if they don't come from the same population. Then it means one group doesn't affect the other one. But if they come from the same population, let's say, maybe I used the wrong example when I chose math and English. So let's say we test Limpopo people and Western Cape people. So they both come from different groups. Then the two groups are independent from one another. So the other does not influence the other. So if we take from two groups and you want to test, let's see what two groups can be. Okay. I'll still have to go back to the math and the English. So there are still two groups of information that you need to test. The English and the math. You need to test the difference between those two groups. But those two groups come from almost similar population. So it means they depend on one another. So if you didn't study for math, you will not do well in math anyway. So, and if you concentrated more on the English side, so, or let's even use another example. The pre and the post. So if one, you do one test before and another test after. So those two groups are dependent, independent. And that's how you will know which one is dependent and independent. So for example, if the two groups are independent, then you will take the difference between mean one and mean two when you calculate divided by the standard error. And the standard error will be the standard deviation of one divided by not the standard deviation, the variance. The variance from group one divided by the sample size of group one plus the variance of group two divided by the sample size of group two. That is if the two groups are independent. If the two groups are dependent, so it means they come from the same, the pre and the post. So then that one, you take the difference of the match pay. So they have to be from the same. So it has to be, so you take a test before and a test after. So you take the difference of that and you're going to find the standard deviation of the two, the difference between the two. And I think the reason the other person was asking, how do we find the standard deviation? It's in relation to this, because sometimes they don't give you the standard deviation of the difference. You need to calculate that standard deviation of the difference divided by the square root of n. And this is the standard error for those difference. With, okay. The other thing that you need to also remember with the two, whether the one is independent or the other. So the two groups for independent, if we have n one, it does not have to be equals to n two. So n one can be eight and n two can be 10. But for dependent groups, n one should, if it's 10, if it's equals to 10, therefore n two as well needs to be equals to 10. Because they need to be matched. Okay, let's look at an example from here. Where do, oh, how do you determine which one is independent and which one is not? So, okay. So this is the T one, so not here. Okay, there we go. So this one, now here we have a statement that says an educational psychologist wants to establish if raised expectation has an effect on how students do in mathematics test. Select 100 students at random, oh, she selects 100 students at random. Half of the students from a control group refer to group one, and we're told that they have to do 20 meds problem. But that is just an exercise to practice their skill. The remaining 50 attempted, I told to complete the same problem, but this is called group two, which is our treatment. But their maths will count towards their final maths. She decides to use a T test to compare the results. Which of these two tests is she using? Let's go back. I want the answer from you now. Remember where I wrote with the red pen? Two independent groups, two dependent groups. Independent groups, they do not have to be equal. Dependent groups, they have to be the same. Independent group, one does not influence the other because one does not depend on the other. Dependent group, one depends on the other. Remember that. Reading the statement, we have 100 students, 20, we're given the meds problem, and 50, we're also given the meds problem. The first question you need to ask yourself. Can I also ask, I know that I didn't start the session properly by introduce there's a grid line that I always like. Please mute yourself, please switch off the video, and always participate in class. So can I ask in order for the bandwidth and all that everybody when they joined the class to switch off their videos. Thank you. Okay, so while I was busy talking, I hope you reflected on this question. Is this an independent or dependent? Ms. Elizabeth, I think it is dependent because it's coming from the same group. Am I correct there? Even though they come from the same group, does one influence the other? Does one depend on the other? Okay, so that makes them independent because it doesn't affect each other. Thank you. You need to ask yourself that question. It's very, very important. Even though they come from the same group, because they can still come from the same group, like I said, from the same group, it will be mathematics, but you do a pre-test because now you know what the questions looks like. Pre, you do that, you fail, then you take the post-test, the same question again. So already because you were exposed to the first, the second one is dependent on how well did you do on the other one? Because if you did well on the other one, you will do much even better on the second one. Because it's the same thing. One depends on the other. So on this one, there are two distinct groups and one does not depend on the other one. They are both independent because whatever group one does, does not influence what group two does. You understand the independence? That makes sense. Thank you, Mrs. So then if this is independent, which one are you going to be choosing? Option one, option two or option three? Let's go back. You must pay attention to the formulas as well when you work through your questions. They give you option one, option two and option three. So this is one, this is two, this is three. Which one are you taking? Option two. It will be option two. Okay. This will be if you had to calculate the test statistic, you will choose that test statistic to solve your problem. Okay. So those are the things that you need to keep at the back of your mind as well. When you answer the questions, try and read it through again and again and again. So probably next time when we do things properly, we will go into how do we solve problems? How do we read the statistics questions and understand and unpack them? Because today just the hijack section. Okay, so let's see. So we've covered the green part. So now let's go and cover the other part, which is there when you are given two variables. So with hypothesis testing as well, you can test two variables. So yeah, we can test whether late coming and cold weather goes together. So we can say late coming and weather. And is there a relationship between? So when they ask you things like is there a relation? Now we're moving away from the difference. We're talking about is there a relationship between the two variables? When they ask in that manner, if they ask you to test whether there is a different, or let me not put the difference, because then when you do the difference, you might think of the other part that we just covered. So when they ask you to test whether there is a relationship between two variables, then you need to ask yourself, the variables, are they numeric or are they categorical? Two things. Am I testing numerical variables? Are they numbers? Or am I testing the categorical, where there are categories, like gender, like race, like school type, like what else? And others. And then numerical like scores, if they ask you to test the scores of certain or depression scores or outcomes, then you need to ask those questions. If they ask you to test the relationship between two variables, and I think here where they say there is a difference, I think here we need to change this to a relationship, because here we're talking about are they two related, two variables related to one another. So for numerical variables, then whether it's interval or ratio, for numerical variable, as long as it's numerical, then we use Pearson R, which is Pearson coefficient of correlation score, which also is called R. And the formula we use, that complex formula, that's the one that you need to use. I am not sure if you are expected to use the formula, but if you have a calculator, you can calculate R using your calculator. It's just that now, we don't have a lot of time, I can show you how to calculate the R on your calculator. We will see how far we get. The session is up to seven o'clock now. We might get time, we have an hour left. Okay, so if it's numerical variable, we use R, coefficient of correlation or the correlation coefficient. If it is categorical variables, which are categories or labels, we can call them that, which are like your nominal scales or ordinal scales. Then we use chi-square, or they call it Pearson chi-square. We use chi-square and with chi-square, we use the formula, the sum of your observed value minus your expected value squared divided by your expected value. And I can show you how to calculate those expected values. So, let's find an example of when do we use any of those. Okay, so this, actually you might not even be doing the R-square, I'm not sure, do you do R-square? Or am I introducing you to, yes, you do chi-square, there we go. So, where you see this, it's a chi-square and also coefficient of correlations. So, you need to read the question. So, on this question, yes. This question, a researcher ask a statistician to help her with to determine whether there is a significant relationship between two variables, gender and color. The statistician points out that both variables are nominal level of measure. Therefore, what kind of a test are you going to do? Numerical, we use PSNR, categorical, we use chi-square. If you don't know how to pronounce chi-square, you can just tell me that one or two, which one or three is the third one. Number one. That will be number one because they are categorical. If this was a score for math test and this was a score for another variable, then we'll use PSN correlation. If we go to the bottom one, they say you must calculate coefficient of correlation. So, they're asking you to calculate R on this. Do you guys have calculators? Can I get an indication of what type of calculators do you have? You can unmute or you can type in the chat because I've got multiple calculators, different calculators. Mr. Elizabeth. Yes. At the previous question, question 64, it says there the statistician points out that both variables are nominal level. Am I correct if I say the moment I read the words nominal, I already know that it would be the chi-square. Yes. Okay, so I can just use that as my reference. Yes. Thank you. Calculators, you can unmute and tell me so that I can open one calculator. I'll show you how to calculate the R. I'm trying to get to my calculators just now. Or do you have calculators, guys? Let's see the chat. I use my laptop, my guys. Hey, if you were going to seek for an exam, were you going to use your laptop and your phone? You need the proper calculator. You must go, Kim, you must go by either a sharp calculator or a cashier, the one that Lizette has posted at the bottom there. I will show you how to use it. Should it be a scientific? Yeah, since this is the record, you can come back to this and use that. So let me open the calculator. Ways, I didn't think that I will show you new the calculator. Sorry, ma'am, should we use scientific calculators? Yes, you are allowed to use a scientific calculator. Okay, because I tried to use one, but it was complicated for me. I just put it aside. I don't know how. Huh, don't worry, because you never had me. It was too complicated, I just can't figure it out. Yes, now you have me, so don't worry about it. Okay, so I was trying to open all my calculators so that I have them ready to help you to show you. So my screen will be a mess right now because I'm going to share my entire screen. So that's my screen. Let's go back to our question. So how do we calculate this? So this is because it's only one, two, three, four, five. Five, so it's easy. So I'm gonna start with the case show. If you look at my case show and you look at your case show, you will see that it looks exactly the same as the one that you have in front of you. And it's the same as the one that Lizette has posted. It's just that this one is an online one. So to capture the data, you do the following. So you can come back and watch the recording time and again and again and again. You need to put your calculator to state mode. By pressing the mode function, there is the mode. So when you press mode, it will give you a menu. We're putting it to a state mode. So we're going to press whatever the button that relates depending on the type of a calculator you are using as well. Depending on the number that the state is linked with, you're going to press that. On my one is three, so I'm going to press three. Then it shows me one, which is one minus var and two, which is a plus b. Only keep to those two. This we're gonna use it later on when I show you how to calculate the standard deviations, right? This is when you want to calculate the coefficient of correlation. You will choose a plus bx, where it says two. So we press two and it gives us the table. As you can see, I also have x and y and the table also is x and y. So to capture the data, we're going to press the equal sign and the value. So we just say two equal. And that's how you capture the data. And we're only going to capture x values the way they appear. And we also going to capture the y values the way they appear. Do not mix them up. So you just press two equal. Then the next one is seven equal. It will, and you can see that the black line moves as well to the next row to the next row. Then four equal and five equal and one equal. Now I've captured all five because there are one, two, three, four, five. So I've captured all of them. To capture the y values, I need to go to the right side. By using the arrows, you have those arrows. So if I press the left or not the left right arrow, it will take me to the right side, but I need to go to the top of the table to capture the values. So you just use the up, up, up until you get to one. Where am I now? Okay, up, up, up three, two, one, there. So where x is two, I must start there. Two equal, seven equal. Four equal, five equal, one equal. I've captured all of them. If you want to check, you just go up and see if all the values cross bonds. And once you are done, you can go AC, AC. Your data is stored in the memory of the calculator. What you're not panic is that if you want to get your data and see how it looks, you can press the shift button. You press shift, and to press button number one, where it says stat, S-T-A-T, it's number one. And if I want to go and see the data, there is number two. I can go and press two, it will give me my table. But we're not interested in seeing the data. We're interested in calculating R. So we'll go back to the calculator, AC, and you press shift, we'll go back to one. And you will see that we have type. This will tell you the type of data that you have. You have the data, we've looked at it. You have the sum. If I come back here, remember we had these values like sum X, Y, sum X, sum, if I make this bigger so that you can see what I'm referring to. Sum X, Y, which is sum X times Y. Sum X is the summation of X, which means it's the sum of all the X values. Sum of Y is the sum of all the Y values. Sum X, Y is the sum of all the values of X times Y. Sum X, Y, and so forth. On your calculator, you can calculate them. When you click on the sum, you will see all these values that you can use to come back and substitute into the formula if you want. There is your sum X, which is that value. Sum X, Y, which is that value. Sum X, so this is not sum X, sum Y. It's sum of X times Y. So that is number five is that value. So you can see that all these values, you can calculate them and come here and substitute, but we don't want to go through that. So I was just showing you on your calculator. We go back, shift, start. The var is to find the standard deviation of the X and the standard deviation of the Y value. You can look at that. You press button number four. As you can see there, that is the mean of X, there is the mean of Y, that is the population standard deviation for X, that is the sample standard deviation for X, that is the population standard deviation for Y, and the sample standard deviation of Y. I don't know where you're gonna use that, but I'm just showing you that the possibilities are there. Okay, we're not looking for that, we're looking for R. Okay, shift, start. When we click on the reg, the reg calculates the regression. Remember the regression line, it's Y is equals to AX plus B, that will calculate that. So you click on five because reg corresponds to five and that is where we're going to find the R as well. So there is your coefficient of correlation. This is if we want to estimate the value of X and if we want to estimate the value of Y and this is the slope at A plus BX. So this is the intersect and this is the slope. Okay, we're looking for R, so you just press three and equal. Instead of doing this whole calculation the very long way, you can find the answer as quickly as possible. Sometimes, and your R is one. And I can check if R is actually one by pressing shift and going back to reg and pressing B. The value of B is two, if B is negative therefore it means R will also be negative. So the B value is one, so it's positive. So it's also there. I've got the right value of R because on your calculator, if you remember when we did the state mode, it was A plus BX. You remember that? We pressed the button that looks like this. So where B is your slope and A is your intercept. Okay, so you can calculate the value of your coefficient of correlation without stressing about the long formula. Okay, so that is one calculator. The other calculator, which is the Casio, not Casio, sharp, depending on also your sharp calculator, some sharp calculators have all the information you need on here. So if you look here, you have your X bar, you have your SX, which is the standard deviation for, the sample standard deviation, the population standard deviation for Y, for X. This whole row is for X, that one is for the Y. The sum, remember those sum X, Y, the sum X and the sum X squared, sum XY, sum sum, and the N. So you also have all of them in front because they are written in green on a sharp calculator, you're going to press the alpha button to reach those button. But like everything else, you need to first know your values by putting your calculator to state mode. So you press mode. You can see there, state corresponds to one. You press one, and you have SD. SD will help us when we do the calculation for the standard deviation, for the mean, and so forth, because we'll be working with one variable. So now we're working with two. We're going to use the one that says line. So line is for the regression line. So it corresponds to button number one, and then our calculator is ready. It's on state mode one. So once it's on state mode one, it means we are ready to calculate the regression questions. So if I go back because my values are hidden, I know it's two, seven, four, five, one. You must help me if I get lost. So on this calculator, we're going to use M plus and store. So those two buttons are very important to us. If you are using a financial calculator, those who have a financial calculator, you still follow the same steps. But on your calculator, you will have a data change there, not an M plus, but a data change. But everything else looks almost exactly the same. So you will have store and data change. It will look like this. And then I think it's written change. I don't know how to write. I was never good at writing as good. So mind my handwriting. I was that kid that was always getting beaten because the teachers can read what I wrote. Maybe probably I should have been a doctor. So but it's written data, data change. Somewhere there. It's got the arrows at the bottom and at the top. Okay, so, but we're using this one. So we're going to press store and press the M plus. So let's, and on this one, we do both of them at the same time. So it means we're going to do seven, what? It's two and two, seven and seven, four and four and five and five and one and one. So we're going to press that and then press M plus and then press the value and press S-T-O and we continue like that. So we say two, store, I've got them the other way around. So we press two first and then we say store. So it will be store, two store and then two M plus. That's how, that's the logic. Two store, two M plus. And then it will say dataset one. So it captured that line. Now we move on and capture the whole, until it says dataset five. So then it will be seven store, seven M plus. Four store, S-T-O, four store, S-T-O M plus, five S-T-O, five M plus. Those who are using the financial calculator way, I'm saying M plus, you're going to say data change. The last one, one store, one data change or M plus. And it will say dataset five and then it means I've captured all of the data. Here you cannot go and find the table because the table doesn't exist. You need to be sure that you have captured the right values onto your calculator. If you make a mistake, it's fine. You can clear your calculator, there is a CA. So you press second function, CA, it will clear your calculator and then you can start capturing again the data. Okay, so once you have captured your data, you can go on and off your calculator and we can answer any of the questions that we need to answer. Now we need to do R. So R is here on the division side. Look on your calculator and see if you can identify where R is on your sharp calculator because some sharp calculators don't look like this. So if you bought the latest sharp calculator, there is another sharp calculator way. Not all the values are written in green here. The STA is written somewhere at the top here and it's written in orange. Pay attention to your calculator. If you need more help, I don't have a WhatsApp link. I will share with you the WhatsApp link before the end of the session so that you can join that and then we can have discussions as well offline. Okay, now we're ready to answer the question, which is the R. If we were doing the equation of a straight line like we had with this way, it says A plus BX, you can also answer it because there is your A and there is your B. There is your intercept and there is your slope. And if you want to estimate the value, there is the value to estimate the value of X. This is to estimate the value of Y. But we are interested in R. So we just press the green button, which is alpha and then we press division, which is R, as you can see. But you also have to press the equal sign to read the answer that you're looking for. And there is your R. As you can see, it's the same as what we had from the previous one. And that's how you use your calculator to calculate coefficients of R without doing the complex formula, which is this, which is time consuming. Then you need to know how to interpret the R values anyway. Okay, so that is how you test the question, all the information. Okay, let's go down with question and some of the things here are just like things that you need to know. Okay, so here is another one. It's about the coefficient of correlation. You need to also know how to interpret the coefficient of correlation that zero means there is no relationship. One means there is a positive strong relationship or a perfect strong relationship. Negative one means there is a strong negative relationship, perfect relationship. You need to also know how to interpret it in terms of the other values. Like in between like 50%, what is 0.5 mean? And what 0.2 mean? And what 0.8 mean, whether it's negative or positive? Strong relationship, weak relationship, you need to know how to do that, how to interpret it. You also need to know, because I can see here, I'm not sure if anyone doesn't know how to answer questions 61 because I already gave you the answer. So questions like this, you need to know the following with this. So you know that you have two types of variables. You know that you have a numerical variable, and you have categorical variable. You need to know that for categorical variables, because it's variables that you can put into categories, what type of visualizations you can do when you have categorical variable. And they are very limited only, only two visualizations you can, oh, one visualization, oh no, three visualization and a table. You can do a summary table, you can do a contingency table, which remember contingency category one, and category two, yeah, where you can do that. Summary table is just to summarize your categories into table where it has your frequencies and your percentages, where it's your categories here. One, two, three, four, five, six, seven, whatever, Coke sprite, like that. That is a summary table. So you just need to know that. In terms of other visualizations, which are not tables, and this is where I don't like writing on a PDF, it takes forever to write. So you can do those as tables. Then you can also summarize it in terms of bar chart or pie chart. So those are the things that you can do. This is a bar chart. Like I said, please ignore my handwriting. Maybe in my next life, I will become a doctor so I can write scripts. Okay, so that's how you summarize categorical data. Summarizing numerical data, we use what we call a frequency distribution, which is a table that summarizes your frequency distribution. We use frequency distribution. And from the frequency distribution, because you take your numerical data, you put it into categories, what we call the class intervals. You group your data into different classes and those becomes your category and then you can do your frequencies, your percentages, your cumulative frequencies and so forth. That's what we call a frequency distribution. Numerical data, you can do a scatter plot. You can do a histogram. I am sure that you know what I'm talking about when I talk about a scatter plot. Remember scatter plot is that one way you have all the values for your X and your Y scatter plot. A histogram is a bar chart for numerical values and you can develop it from a frequency distribution and with the difference between a histogram and a bar chart is a bar chart, the bars will never touch. On a histogram, the bars when one ends, the other one starts. That's an histogram. This is a histogram, a scatter plot. What else can you do? You can do a cumulative polygon, a frequency polygon. You can do an all give. You can do a box plot. What else? That's all I can think of right now. In terms of this information that you are given on question number, what is the question? Question 66, it says, the number of psychiatric patients are classified into four categories. So already you should already jump up and down and say, oh, this one, how many marks do you get for each question? They don't give you the marks, so that you know how much you are scoring here. So you should be jumping up and down and say, oh, they say categories, categories. You should already know by then which graph you're going to be using. Which one of the following is suitable for cross-classifying and also even they say that cross-classifying this information against gender? Which one can you use to cross-classify? A contingency? It's a contingency table because you have category, what happened? You have, oh, sorry, you have category one, which will be your category of schizophrenia and category two will be your gender. That will be that. So psych is not that difficult. So I guess those who are writing, you will get it right. So let's see what else I can help you with to understand. I'm trying to look at the questions where we can use a table. And remember what I just said, if they ask you relationship, if they ask you about the relationship, you must think of chi-square and PSNR. You must ask yourself, is it the numerical or is it the categorical? You must think of that because yeah, they say what is the relationship that exists between gender and type of work and they give you T test, chi-square and coefficient of correlation. Do you know which one you're going to be using? The first question you ask yourself is, I'm looking at the relationship, ask yourself is gender and type of work, is it at the numeric? Because already test is not an option. Test of two independent sample is not an option for the answer. T test is not an option for a question where they ask you to find the relationship. So gender type of work, is it numeric or is it categorical? That's the first question you ask yourself. Is it categorical? It's categorical, and if it's categorical, you, chi-square, so you will have your answer there and there, so you will know that you is in number two. Oh, sorry, I haven't been looking at my, what do you call that? My check, and I know that some of you have been posting. Sorry to take you back, is there a recording after this lesson? Oh, yes, the session is recorded. Somebody has started the recording. Recording has started. Unfortunately, one needs a scientific calculator because normal calculator does not have the functions. Yes, normal calculator does not have a function to do the standard deviation. You need the square root to calculate some of the things, some normal calculators, you will struggle to do that. So please, before you go right, go invest, skip if you like eating KFC, chicken again, pizza, McDonald, all those, you're going to starve yourself just to get a calculator in order for you to pass stats. Oh, psych, invest in that. Okay, so let's go back to, wait, wait, wait, okay, we are here. So some of the questions, they're not really my, what do you call that? My specialty in terms of your psych questions. Sometimes I notice that you also talk about things that I don't cover in stats. So, but doesn't mean I cannot help in unpicking some of them. So we can start at the top. I'm not going to do all of them because some of them I think they are straightforward. For example, like psychological research, you know how to define your psychological research questions like this, I cannot assist you with that one. So in statistics, we have, let's see what time is it? We are on half past six. We have 30 minutes. Statistics has two branches or research, or I can call it statistics because that's what we do. Statistics has two branches. We have inferential statistics, we have descriptive statistics. Descriptive statistics describes your data in terms of where your data is located. Inferential statistics tells you how dispense your data is. Now, I have a problem with the question that they post to you here. Only those are part of the inferential statistics, but we use the mean as part of calculating the variance and the standard deviation, but it does not mean the mean needs to be part of the variance, the variance, and the standard deviation. The mean is part of descriptive statistics, which also includes the mean, the median. They tell you where your data is located. They give you the locality of your data. That's why they are called the measures of central location or the measures of central tendencies. They are there to describe your data. And they can also give you the shape of your data because they describe your data. The standard deviation, the variance, the range, the quartiles, the percenta, they give you how dispense is your data. They give you the spread of your data. How far apart are your data from the mean? And those we call them the... Oh, sorry. They are also part of the... I'm now in cloud nine. Sorry, let me take you back. Sorry, I know. Instead, we have two branches. I'm already in cloud nine myself. Sorry, sorry for confusing you. I need to come back. We have two branches. Oh, yeah, right. Oh, yeah, right. These are also part of the descriptive statistics. They are all part of descriptive statistics. There is no problem with this question. Let me come back to Earth now. So, two branches of statistics, descriptive statistics and inferential statistics. Descriptive statistics describes your data in terms of the locality, the shape, the spread. That's what it does. The locality, which is central measures of central tendency, they mean the more the median. The spread in terms of the standard deviation, the range, the variance. The shape in terms of whether it's positively skewed or negatively skewed. And we can describe it also in terms of tables and charts. That is descriptive statistics, just describes your data. Inferential statistics, on the other hand, it's about inferring the information or making conclusions about the population based on the sample information that you collected from the population. So, I nearly confused you right there. So, they mean the variance, the standard deviation, then they form part of, is it inferential or is it descriptive? So, some of the example for inferential statistics is everything that we have been doing here. All this form part of what we call inferential statistics because yeah, we take the sample we infer and make conclusion about the population. That's what we have been doing with this. So, you need to know what the mean, the range, the variance and standard deviation are the inferential statistics or descriptive statistics. Variables are characteristics that describes your population or your sample of interest. For example, a variable is like gender, race, and so forth. So, in this regard with this question too, your answer will be option. Your answer will be option two, sorry. I see that Catherine and Lisa have answered that. I nearly got you lost right there, so it would have been option two. So, like I said, some of the information, I'm not gonna be able to help you with and this is one of them, question three, I cannot help you with that. Question four, I can help you with question four because with question four, when the population is big and because it's time consuming to analyze, we select from there and we create a smaller subset. So, if this is the population, what will make the other one? A sample, so we create a sample, a population, and a sample and the process that we are doing when we create a sample and the name sample comes from that process as well. It's called what, that's what the question is asking you. Am I doing a triangulation? Am I doing operationalization? Am I doing a sampling? And yes, someone posted. The message disappeared quickly before I could read. Yes, we're doing a sampling, sampling. Okay, empirical knowledge, that one I'm sorry I cannot help you with that, so you will just have to, some of the things are more psychological research linked than my statistics background and also you must know that I come from a pure state, I don't come from a research states. So, the ones that I can help you with, I will skip, like describing what the latent variable is, you need to know what the latent variables are and what the constructs are, you can just, those I'm going to skip. In terms of dependent and independent, I'm going to skip it because we already have explained what dependent and independent are. For example, if we have an X and Y, we always say X influences Y. So if X influence Y, we say XY is dependent on X. So X becomes our independent and Y becomes our dependent. And usually dependent are also what we call outcome. So reading that statement, if you want to know whether that statement is it, whatever they are referring to a learner's test, is it dependent or independent or manifest? I don't know what manifest is in terms of your research, you just need to know to understand what manifest is. I only know the dependent and independent and this is, I can explain it up to so far. I cannot in relation to the manifest one. You will need to sort that one out yourself. You will need to know how to define a scientific study that should be easy to do. I'm not gonna worry myself there. We explain what the population is. Okay, so because we said the population is big, this is our population. And we take out from that population a small annular sample. So this will be our population and this is our sample. So when we take this population and calculate not X bar, when we calculate the mean, the standard deviation, the variant, all this, we call them parameters. There are parameters. When we calculate the mean, the sample, the standard deviation, we call this statistics or statistic. Statistics when there are so many because there are many. So I can just call them individually, they are called statistic. So it means the measures that comes from a population are called parameters. The measures that comes from a sample are called statistic. So you will just need to know how to define all those things right there in there to answer the question that question number 12. So population is called while the measure that describes the same aspect of a sample is called option one, two, and three. Will you be able to know how to answer that? Let's see. I see answers, answers, light and hidden. Okay. I will remember that option two because I already gave you the answer as well. Okay. Then I'm not sure, you never said anything about probability. So I'm going to assume that you know how to answer the probability questions. Remember probabilities to calculate the probability of a value, no, sorry, to calculate the probability of a value. It's always going to be the number satisfying that divide by n. And you're going to count how many numbers satisfy this. So you have a jar containing five red, eight blue, three green, four yellow. What is the probability that a blindfolded person would choose green marble? So how many are they in the jar? Because when they go into the jar, they will, and how many in the jar are green? So the number satisfying the green divide by the total of them. That will give you your answer. So you need to add all of the marbles that you have. And you need to divide the number of green marbles by how many marbles you have. And that will give you your answer that you are looking for. How many marbles do you have? Which is your total? There are three marbles in the jar that are green. How many in total do you have? Eight plus five is, okay, I see there. I have an answer. Let's see. Oh, you're giving me an answer. You're not giving me the total number. I was expecting the number 20. There are 20 marbles. Which is zero comma one five, which is option one. Okay. So you need to know that the total, which is N, is also called a sample, a sample space, because it's all of them. It's all of them. If I have a deck of cut and the deck of cut have 18 cuts in them in the box. So all 18 from part of a sample space. If I have a die with all the six sides, all six sides of a die form part of a sample space. Question 14, you should be able to answer question 14 because I also just gave you the answer. Let's see. It asks, a list of all outcomes that are possible in a statistical experiment is called. I don't have to ask you that question because I just gave you the answer. Okay. Okay, this one you need to go ahead and read as well. It talks to when you increase or decrease the sample size, what happens? Is this a law of large number? Anyway, instead, we don't even talk about that. So you should know that some of the things that you're not familiar with, you can just say, that is not correct. Then you are left with two. Is it a central limit theorem, or is it the effect size? So it's not gonna be the law of large numbers. Okay. Now, a test for a short-term memory capacity is normally distributed with the mean of 100, the standard deviation of 10. What is the probability that a person chosen at random will have a score of X more than? Okay. So here we're talking about. Elizabeth? Yes. I just reminded that the students need to complete the attendance register. Yes. We did post it. I did mention it. I will mention it again. So you have posted it. Thank you. I will remind them again as well before we leave today. Okay. So this question is asking, will a score of X equals 125 or more? This is a question that you need to solve using the Z score. Not the one with the standard error, the normal Z score and go and use a table to find the probability because that's what we want. We want the probability that a person is chosen at random will have a score of more than 125. So we need to calculate the probability that a score will be more than 125. So I'm going to give it to you, give to you the formula, which we know that the formula for Z is X minus the mean divided by the standard deviation. Based on the question, you are given the mean, you are given the standard deviation. You are also given your X value. Substitute into the formula and calculate. That's all what you need to do. Substitute the values and calculate. Are you winning? You have an answer or are you lost? Talk to me. I'm not getting it. You're not getting it. So your X is what you are given in the question. So it's 125, your mean it's given to you there, which is 100 divided by your standard deviation which is 10. When you answer questions, please do them step by step. So 125 minus 100, if I use my calculator here. So it's 125 minus 100 and then equal, that gives me 25 divide by 10 equal, that gives me 2.25 and so here is 2.25. Remember our question is to go find the probability. I hope in this, we do have tables. So this is where you need to use a table. So you need to go to the probability, normal distribution table and they also give you formulas in the exam. So we need to come here. Oh, your module is that one where we talk about the larger and the smaller. Oh, Christian. This is a question I had, unless we draw the diagrams to look at the portion, the grade section, how do we know? Yes, yes, yes, yes. Sorry, I also keep the calculation. I got 2.5, not 2.25. What do I get? 2.5, did I write 2.25? Yeah. Oh, sorry. Let's blame it on the night. It's a long day. We will blame it on a long day because on the calculator it says 2.5. I don't know where I got 2.25. Okay. Maybe two is my lucky number. Okay, so, hey. You know the difficulty with your module is I need to always refresh my mind in terms of the larger and the smaller. So this says greater than. In order for me to know how to assist you as well, let me, I must open my, because I don't want to give you wrong information. No, let's go to. Don't I have a, there we go. Because your table looks different to the one I'm used to. So I'm going to use the one that I'm used to and then I'm going to go and guide you in terms of your one. So the answer I got was 2.25. So on this one, it's easy to use because this table tells me that the table I'm looking at looks at the smaller than. So it contains all probabilities that Z is smaller than any value. And I can use this. So let's see what value I get. The value that I will get here because now I'm looking for the PZ of greater than. What do we looking for? 2.5. That's what we're looking for. 2.5. So then I must say one minus the value I find on the table and the value I will find on the table will be 2.5 is 0.9938. 0.9938. So I must say one minus 0.9938. Oh, come on. That's one. So the answer I get is 0 comma. Just want the number 0 comma 0062. 0062. So that is the answer that we need. So coming back to your question, we go to your table. We, okay. So because we're looking for the larger portion. So if I look at the question was like, we need to find Z greater than. So therefore greater than 2.5. So this is zero. 2.5 is somewhere here. So we're looking for this area here. So this area is the smaller area. It's not the greater area. It is the smaller area. So we need to go to Z because this site is greater. We're looking for the smaller site. So 2.5. So you need to go look where it says Z. That's what we need. Z 2.5. So it will be 2.50. 2.50. That is 5.5. So it needs to be right at the bottom. 2.50. As you can see, we are looking for the smaller than site. So 2.5, we're looking for this site. This is the larger site. This is the smaller site. So the answer is 0.62. So the answer is 0.62. Because we're looking at the smaller site. And you are right. We just need to draw a picture in order to understand this. I always need to understand from the table that I'm used to in order for me to help you as well. So as you can see from that one, because the table contains the less than, we're looking for the greater than. If we look for the greater than, we say 1 minus the area, the bigger area. And that gives us 0.0062. So on your table, we're looking for the smaller area because they say small portion and large portion. So we need to go to the small portion. We use the Z value to locate the answer. So happy that we tie. So that is, we are left with five minutes. So the answer here is option number three. And that's how you answer the question. So let's see, have I answered all the things that you wanted? Let's see. What happened to this, to the presentation? And the things I wrote, they disappeared. So, but you said you wanted to know what the test is. You wanted to know how to calculate. Oh, how to do the test for the means. We did look at those. You said you wanted to learn how to calculate the standard deviation. We didn't cover that. Okay, we must look for a question that does that, standard deviation. You also had, so we did that, we did that. You also wanted to learn how to use the table for Q. Where do we use Q? Okay, let's see. Do we have anywhere where we use Q? I think Q we use it for the non-parametric methods. So let's see, do we have Q here? So unfortunately for those ones who are writing on the second, there's not much I can do to help you. But those who are writing in November, we will have more sessions, I think every second week. Okay, you only have one table. So you don't have a lot of tables. So, okay, let's look for one last question. So how to use the table? We've read that. So it means, if they say, let's say you calculated the Z. Let's go down, down, down, down. Let's say you calculated Z. Because that table you will use it so many times. You will use it also when you answer the hypothesis testing questions as well. So let's say they said to calculate the probability that the value is less than some value. Let's say some value. And we find that when we calculate Z, and that Z is minus 1.25. So let's not do one minus 1.25 because it will be on the smaller side. Let's do that. Let's draw that. So when you draw it, this will be your zero. It's always zero in the middle because we know that the area underneath the curve is always going to be equals to one. And in the middle, it will be zero. So if it's minus 1.25, that will be minus 1.25 there. So it means we're looking for, and they say less than, it means we're looking for this area. This is the smaller area. Regardless of where you are, that's the smaller area. This is the bigger area. If it was 1.25, let's say, if the answer here was 1.25, positive 1.25, then zero will be there. And 1.25 will be somewhere here. So we'll be looking at this. This is the larger area. So you need to remember that when you go to the table. Draw yourself a picture, visualize. What is it that you want to find? If it's a less than, you draw the less than. Less than, greater than. You must always remember that current, left current, right current means bigger. It's not like when I say left current, I'm saying all people who use right hand are superior than those who use left. But I mean like, right is most dominant, left is the less one. You must always remember that. How you draw those, greater than and less than. Okay, so the other one, this other one, I think it's just a general. You just need to know how to calculate some of the probabilities here using the information that you are provided. Because the first one, suppose over a thousand students wrote exams in psych and 6,000 of them passed. So thousand wrote, 6,000 passed. What is the percentage of passed from there? So you just- 10,000, another thousand. Yeah, of which 300 obtain exactly 50%. This means that randomly selected students, the probability of obtaining at least 50 is, then you need to know what will be the 50% of those who passed, while the probability of obtaining more than 50% will be. So this says you need to calculate the probability of exactly, this means obtaining the probability of more than. You use the same. Exactly, it will mean when you go to the table, remember the table has three columns, has mean to Z, a larger portion and smaller portion. Mean to Z, this will be the probability of exactly. This will be the probability, then you can use for more than, less than, whichever one is it in the large portion of the graph. Is it the large portion when you draw? Is it this large portion or is this the smaller portion? You choose that. Okay. What else is there? Time to see if we can find somewhere where we can calculate. The mean, there is no way where we calculate the mean, the standard deviation. I guess the reason why they don't want you to calculate the mean and the standard deviation is it's time consuming to calculate the standard deviation. Okay, so they don't give you questions to calculate standard deviation. Yeah, this is a contingency table. You need to know how to do the contingency table, how to calculate the expected values and the observed values. That's that. Okay, and that concludes today's session. Before you leave, those who are writing good luck, those who are not writing, hopefully Jack will send formal communication again in terms of when we're going to have another session. And I guess that session, we will follow a session plan where we would have a proper notes and we will discuss certain topics. I did create the session, but yeah, I'm not gonna go into that detail, but we had a session plan developed and I think we will start with those sessions maybe probably in July. And since you're writing exams, I hope the same number of people that are here, except those who are writing and feel that they would have done successfully in their exam, we will continue having our sessions. I think on Tuesdays, same time, but I prefer to do them later in the evening from six o'clock because I don't want to rush. After my work, I rush to join the MS teams and so at least the six I have some time because I knock off at five. So for today, it works because we're still waking from home. I'm not sure in July whether they will say come back to the office and then I have to rush to get to assist you. So, but anyway, thank you. I'm going to share with you. Please make sure that you complete the register. I'm going to share with you now a WhatsApp group where we can discuss outside of this. And also for those ones who are writing on the second, if you have any question, Elizabeth, you can use the WhatsApp group to discuss. Lizzie, I want to ask, should I change it from 1800 hours to six? Yeah, from six o'clock until what time? Since you want me to do two hours till the two hour. I'm not saying that you must do two hours. It's fine until eight. So it will be, yeah, until eight. Just let's start them at six because, yeah. I might have challenges with five because sometimes my meetings run up until exactly five. Okay, perfect. Perfect. Elizabeth, thank you. Yes. So I will share the WhatsApp. The WhatsApp just now so that you can join the WhatsApp and just to assist those who are writing, you can ask any question and we can also use it for administration papers to when the classes are canceled or something or there is load shedding and we can't and we can use it to quickly share. And you must know when you join my WhatsApp group, I'm very strict. We don't post meanies or what do you call those meanies? We don't post the good morning. How are you? It's not a show shall. We talk psych on that group. So please, I don't want to remove anyone. I will also post the rules of the group so that everybody who joins the group understand that we're there to help one another with school work and not socializing. I've just posted in the chat, you can join and we are off on a good start. Let's see, am I still recording? Okay, and we can stop the recording. Any question?