 Come you to your first session of, I still have the wrong tagging, of your basic statistics for human sciences. Here we're going to deal with content related to the site three, seven, or four module. However, because this is not a tutorial, I'm going to explain the whole process at a later stage just now as well. Oh, sorry before I continue. Please make sure that every week you come in into the session. Please make sure that you complete the register that will be placed on the chat. If you have any technical issues for some reason, you can sign in, you can log in. Please send an email to cityandtact at unisa.ac.zda. Send me an email only if it is content related. If it's anything relating to your site three, seven, or four content and you want assistant, then you need to send an email to me and CC or copy cityandtact at unisa.ac.zda. Now I'm going to expose myself here. Okay, so like I said, welcome to your basic statistics for human science. Today is our first day. So I'm going to do things a little bit so that then you understand the purpose of this session. We will do introductions. My name is Elizabeth Boyd and I will be your tutor for the rest of the semester until you go write the exam. I'm here to support you. I'm here to help you with anything related to your module as well. I hope at some point in time you will unmute yourself and you will have a discussion with me so that I know that there are people behind the screen as well. So I'm also not the only person who is constantly. Are you now able to hear me perfectly? The network did cut off. Thank you. So in the next two weeks remaining for August, this is the session plan that we're going to follow. So today we're just doing orientation and the introduction to the statistical literacies relating to your module. We're not going to go into detailed and because I'm not a psychological research person, I'm a pure statistician. So I'm going to stay away from explaining in detail things that are outside of my view in terms of the things that I know. So if we have some discussions, it will reflect as well because I will want to hear from you how you understand certain things because some of these things I've never done them before. I just went through your study module and I'm trying to unpack it then make sure that you guys understand the content. So if there might be some slight challenges there and there, especially when it comes to things that are related to research. So next week we will start looking at how we calculate the z-scores and the mean and the standard deviation. And the last week we will look at how we calculate the basic probabilities. And after that, then we can go into statistical inferences and start looking at how we calculate certain things. But then now, just to introduce you to the academic literacies because this is not a tutorial class and I'm not the lecturer, I'm just the facilitator contracted by UNISA. My job, it's easier. It's just to make sure that we unpack some of the difficult concepts and make it easier for you to understand. That is my job. I'm not here to explain any, like I said, explain any content relating to your psych 3704 because I don't know anything about that. So we're going to learn about skills, how to answer certain things. And this is just my bio in terms of who I am and the type of skills and experience that I have. I'm not gonna go through all of them. It's not of much interest to everyone who is young. The statistical literacy focuses on skills, like I said. So we're going to unpack the statistical skills and concepts and try and find different questions and use that and do different exercises week in, week out to unpack the content so that you are able to understand the concepts. I'm going to provide you with a whole range of strategies in terms of how to do this, how to answer a question, how to look at the table, how to identify things and how the process of answering the question. And sometimes the process might be something that or a skill that you're going to learn and you can apply in other modules as well. And the sections, we assume that you already went through your module. You understand the content. We just hear to explain certain things that are not clear to you as well. So one of the skills that I'm going to empower you with is the skills of how to answer questions or how to solve problems. And we're going to use the Newman prompt. Newman prompt is an easy, easy, easy step-by-step problem-solving technique that if you apply it, even if it's not for this module, but for other module, you will never go wrong. With this skill, it's that by asking you to read the question and make sure that you understand the question in the language that you speak. So it means interpreting the question the way you understand it to yourself. You can even, if you speak closer, tell yourself in closer, what did you understand the question is asking you to do? Because we want you to be able to say, I've read this question and I now know and I a little bit understand what the question is trying to tell me. Once you have read the question and you understand the question and you are able, then you will be able now to identify the kind of things that the question is asking you. For example, if you're gonna ask yourself, what does this question is asking me to do? Does it ask me to, is it asking you to calculate? Is it asking you to describe? Is it asking you to measure? Is it asking you to manipulate? All those things you need to be able to identify. What is it that the question is asking you to do? Are they asking you to calculate the probability? Are they asking you to find the critical value? Are they asking you to make a decision? Those are the kind of things that you need to make sure that from the statement that they gave you and the question, you are able to identify. Also, you need to make sure that you are able to identify the important facts. Before you do any calculation, identify and write the important facts and the facts here we're talking about because statistics is more about math, it's about numbers, it's about things. Highlight them, write them. If they gave you the average, write in there that this is an average and it's equals to 50 or it's the standard deviation, it's equals to 70, things like that. You need to make sure that you'll write them. The other thing that you can use is drawing a picture. Sometimes it's easier to understand the question by mapping out what the question is asking you. So with this method, we say, feel free to draw something relating to what the question is asking you. If they're asking you that it moves from here to there, write it as if like it's moving from one spot at a point A to point B. If it's about making decisions, draw the care, the normal distribution care that will help you to make a decision much better. Then once you have identified all of this, then now you are going to find the things that will help you answer the question. What I mean by the things? So they've asked you to calculate the probability. They've given you the mean, they've given you the standard deviation. You need to know that now I need to find the formula for Z so that I can calculate my Z score and then go to the table to find my probability. So you need to be able to identify the correct formula. And that correct formula will be based on the important facts that you already highlighted because when you have all your important facts, you are able to go through the formulas and say, but this is the formula that I need to be using. And because you're going to get a lot, a lot, a lot of formulas, you need to make sure that you understand your important facts to identify the right formula. Once you are done with that, then you can start substituting into that formula and then do the calculation. And here, feel free to pick up your calculator because you're going to be calculating certain things. Take your calculator and start calculating if you need to calculate. If it's not something that you needed to calculate, then find the answer based on the information that you are given. And once you have your answer, you're going to reflect back on that answer and receive feedback at this point because we're working in a team, in a group, we're going to give feedback to one another. When you are working on your own, there is no other person who is going to give you feedback. The only feedback you will get is if you go back and recheck what you have done. So it means you need to go back and look at all the steps that you have done and check and validate and say, maybe I made a mistake here, I need to fix it and then fix and get the correct answer. And this is the process that we're going to follow, week in, week out. I might not say, let's now answer this question using Newman prompt, no. I will give you him to say, what is it that we are given in this question? And then you can tell me that they're giving us this and this and this and I'm like, okay, then what is the formula that we need to be using? And as you can see that it will be covering the important facts, then we go to, how are we going to answer this question by identifying the formulas? And I might say also, do we need to draw a diagram that depicts the picture, that shows the picture that the question is trying to create? And if so, then we draw it and then we can then substitute the values and then do the calculation. And then we come back and we do the rechecking and we get the answers, we get feedback and we move on to the next one. But it's not something that I'm gonna say, now let's use Newman's prompt. So it's something that will come as we go along. So that is the process and that is the academic literacies. It's not a tutorial session. Are there any questions, comments? I know that I talk a lot, but are there any questions, comments, anything that you need clarity on? You need something to be clarified? Remember, you are more than welcome to unmute. And I am low-shading. If I'm not audible enough, you must just let me know. Guys, are you all going to be very quiet? Even if you don't have a question, you can just tell me. You don't have a question. So that I know that there are people on this other side. It's very lonely. All good, thank you very much. Yes, it's very lonely if I don't get this conversation going. If I ask a question and nobody responds and I'm thinking, oh, maybe you guys don't even like me. Why are you here? Or maybe you are very cross with me because I told you that it's not a psych session right now. But anyway, we're going to continue since you don't have any question. If you don't have any question, my slides don't want to move. Okay, so we're going to start looking at introduction to the basic literacies for human sciences, which touches more or less the same concepts as your psych 3704. Now, those who joined late, I explained, I am not from a psych background. I am from a statistics background. So some of the themes, some of the concepts, I might not elaborate even more on them because I'm not familiar with them, but I just included them in this presentation so that we have a holistic view of your module. And maybe it might be very helpful, who knows? Okay, so by the end of the session, in the next hour, we're going to learn the basic concepts of your quantitative research. We're going to learn the difference between descriptive statistics and inferential statistics. What is the population versus sample and the type of sampling methods? And then lastly, we're going to learn what and how to use hypothesis testing. It's very important that we learn all these things now so that by the time we start working on the concept, we have already ironed out some definitions and some concepts that builds up to the work that we're going to be doing because if I think about hypothesis testing, I think about population and sample. It's something that we're going to be constantly working on until we get to hypothesis testings and test the relationships and all that. We are using hypothesis testing. We are going to talk about population. We are going to talk about samples as well. So we need to iron them out right now. Okay, so some of the basic concepts that you need to be aware of and you need to know how to define them are as follows. We have what we call a construct and a construct is a concept that acts as an explanation for a phenomena or an event and a behavior and are abstracted from an observation. For example, because it explains an event. So if I have stress, stress is an event which culminates from maybe something, a behavior that happened or someone will be looking at me but then you cannot see it but it's there and I'm stressed but you can't see it. So and hence the reason why it is an abstracted from an observation because then it's something that is not very visible but it's there. When you have constructs and you want to explain something then we're going to build up what we call theories and a theory is a frame of reference for the facts that attempts to account for why things are happening. So for example, since I said I've got a stress, why do I have stress? Theories will be able to help in explaining why I have stress. So a theory is a culmination of things that will help explain a construct. Okay, out of all the constructs, can I ask that you constantly mute yourself when you join the sessions unless if you have a question? Thank you. And of a construct, you can measure a construct, right? And when you measure a construct, you are creating a numerical value for it and there are different ways you can measure a construct. You can build a survey or a tool or a psychometric test or something that will help you to measure the level of stress that a person has, right? And because the score that you will get will be a numerical value, which means it will be a quantified measure that you have. So a measurement will be a process where you are allocating numbers according to a rule in order to quantify a construct. And in order to measure something, a way must be found to operationalize it. I'm always struggling with this long way to operationalize it in a way because if you have surveys that you run on a quarterly basis or maybe after every three years or you run psychometric tests for all new employees that comes through or new applicants that applies for jobs in your company, then you can make sure that that becomes part of your process of how you're going to measure that construct, right? Other concepts that you need to know about in your module are your variables. So a construct is also somehow a variable and one thing I looked at your module and I feel like I'm confused a little bit in terms of how they explain a construct and how they explain a variable. But in a way, a variable is a characteristic that represent an item or an individual. So now, since a construct is not an object, it's not an individual and it's not probably it is an item because it's something that is happening even though it's not visible, but it's there, right? So we can assume that it is also part of an item. So a variable can also be a construct. So a variable, it is a construct that we measured and are represented by numbers, right? Because we know that if we measure the construct from what we've learned previously about the measurement is that if I have that psychometric test, I will have a score and with that score, I can then determine whether what type of a construct it is, right? So sometimes a construct, when it is or a variable, not a construct is second because construct can be visible as things that might not be visible to the naked eye. But a variable can be visible and can also be invisible. When a variable, because, okay, let me break track. Remember I said variables can also be construct because constructs are variables anyway, but there are variables that are visible. Like for example, you are able to see that that person has brown eye or black eyes or blue eyes or green eyes. Those are things that are visible, clearly visible that you can account for them, right? When a variable it's visible, we call it a manifest variable because you are able to see it, you are able to observe it. When it is invisible, we call it a latent variable because it's not something that you can just open your eyes and you are able to see that it is there. For example, if someone has cancer, you can see cancer, but you will know that it's there unless if the person has been diagnosed with that or if I have anxiety or I have depression, you can't see those things. So they are invisible and we call them the latent variables. Now, when we talk about a variable, since I said it is a characteristic and I explained about also looking at the eyes, color of the eyes of an individual. When I talk about a color and I specify that color and I say this is blue, this is brown, this is green, then I'm referring to a data, which is a point, right? I'm referring to a data and in most cases, a variable and a data. Sometimes we use them interchangeably because a data point is a measure, okay? It's a measure of a variable. Or if we don't say a measure, we can say it is a value of a variable. Like for example, a variable gender you can have values which we call them data that the person can either be male, female and others, right? That is the values. Male and female and others will be your values and those we call them the data. And we use data for the analysis but you also need to understand the type of variables you have in order for you to be able to know the type of techniques that are applicable for you to use to answer your questions. And we will touch on the types of variables later on as the sessions progresses because for numerical variables which are number variables, there are certain inferential statistics techniques that you can apply. For nominal or categorical variables, there are also different techniques that you can apply. So we're going to discuss that at the later stage. So when data values are meaningless unless their variable has operational definition universally and accepted meaning that are clear to all associated values, then we call those things operational definitions. Okay, now, reason why you need to learn all this, it's because when you know the type of data you know all your values, right? You need to be able to know how to summarize them, how to manipulate them and how to visualize them. So when you manipulate the data and you just doing simple things like summarizing by putting it in tables and graphs or describing it by manipulating it in terms of calculating the average, the standard deviation and others, that we call the process or the method that you are doing. We call it a descriptive statistic because you just collect the data and by collecting the data it can come from surveys, it can come from systems, it can come from voice recordings and all that. That is the information or data that you collected. And then you take that data and you summarize it by visualizing it by means of creating summary tables or histograms or graphs or pie charts or you can analyze them by just describing the data by means of calculating what you call the average or the means and the standard deviation and the mode and all the other measures. When we take the data and we make inferences about that data, we make conclusions about that data then we are creating inferential statistics. So that is the process or it's the method. We call that method of drawing conclusion about the population based on the sample and we're going to explain what I mean by sample based on the sample and we draw conclusion about this population we are doing inferential statistic. And the type of inferential statistics that exists are estimations. I don't think in your module you do cover estimation but you do cover hypothesis testing in detail because we do hypothesis testing for independent groups, dependent groups and also for the relationship. And we're going to discuss that just now. Some of the key statistics measures. So we spoke about the variable, the data but where do those things comes from? As a researcher, when you want to study something you need to define certain things. For example, you need to define your population which is the element of interest of your research. All right? And your population needs to be exhaustive. It needs to be a huge population for you to be able to make sense of the information and if you also want to make generalization of the information, you need to take everyone. When you have your population and you calculate certain things like you calculate the mean, the standard deviation you create some measures out of the data that you have. The measures that you are creating, you call them parameters. And in a later stage somewhere when we deal with activities you're going to learn that the parameters which are the measures that comes from a population we always use Greek letters to represent them. They will always use Greek letters. For example, like if I need to calculate the mean that is for the sample, I am writing the wrong thing teaching you wrong things. So the mean will look like that. That will be the mean which we call this symbol mu. M, U, mu, mu, mu, mu, mu, mu. That's the mean. The standard deviation, it's sigma. Sigma, it's your standard deviation. That will be your population standard deviation. And the mean is the average is the sum of everything divided by how many there are. The standard deviation tells you how far apart your data points or your data values are away from the mean. It gives you the dispassion of your data points. The larger your standard deviation, it means your data is scattered around the mean. It's far apart from the mean. The smaller your standard deviation, it means your data is scattered closer to the mean. And that's the two measures. And we've got other measures. I'm just only going to share those two. When your population, especially when you're doing research, when the population is too huge, huge, you mangas, it's big. Like if you define your population and say, I want to study South Africa, you cannot study South Africa because the population is too huge. You're gonna take the whole year. Unless if you have a lot and a lot of money, like study South Africa and employ field workers. So it's gonna take you long to study the rest of South Africa. So the population is huge. Even if you want to study UNICEF, let's take even not South Africa, let's take UNICEF where it has about 100 and 200,000 students registered at UNICEF or maybe even close to a half a million students. It's going to be very, very difficult for you to study everybody who studies at UNICEF. And if your population of study you define it as everybody who is at UNICEF, then it even works because you also include the lectures, the contract staff, unless you specify certain criteria. So that when the population is huge, then we take a subset which will be a representative of your population and create what we call a sample. So we go into your population, we select different individuals and we include them in this group that we call a sample and we're going to do our survey or our research on them. And when we done with that survey and the research, then we can infer back the results back to the population and say, based on the information that we just analyzed, this we can say about the population of our interest. Now, the measures that we will collect or calculate from the sample we call those statistic, hence the statistic language subject is named statistic because everywhere we do, most of the time we use statistics to draw conclusions about the population. So for the sample, we're going to use Roman letters, which means we're using standard letters that you and I understand and know. For example, the mean is X bar, it's X with the bar at the top. That refers to the mean, the standard deviation is S. That is just the standard deviation, is it right? So for sample, we use the Roman letters for population because it's big, we use complicated letters that we don't even know how to pronounce. You and Sigma. For the sample, we use simple letters that we are able to pronounce like X bar and S. Please stop me if I am going too far and you are, I'm leaving you behind. Okay, so we spoke about the process that if our population is huge, we take a sample. That process of selecting the sample, it's very, very important because if your sample is not a true representative of your population, then you cannot infer back the result to the population. Also, if you do not use probability sampling methods, the possibilities are, you might not infer back the result to the population, but you can only interpret the result and infer them back to the group of people that you just studied from. So in your module, you are expected to know the probability sampling methods, not the non-probability sampling methods like your convenience and others. So you're going to learn about the four. And I think I only included three on this, but it's fine. So you need to learn four probability sampling methods. The first one is called a simple random sampling method and a simple random sampling method, it is when you select or it's when every person in the population has an equal chance of being selected to be part of the sample. So everyone has an equal chance. How do you do a simple random sample? You know, probably at some point when you were at school or somewhere, you had this thing where they will say, let's put all the names in the head and shake, shake, shake and draw one head. Oh, a good example. A good example it is when you're selecting balls out of for round robin games and all that, then you put all the balls in there. Everyone who is in that box has an equal chance of being selected first or second or third. So that is simple random sampling. So you're applying a process of sampling then, right? Unless if, but because now you're picking all of them it's not like you're doing a proper sampling. But yeah, the process works the same. You put all the names and you want to draw a winner. That process, everyone who's number is in their head has an equal chance of being selected. That is simple random sampling. We also have what we call a systematic random sample. I don't have it here and I'm just gonna write it. Systematic random sample. What a systematic random sample is, is that? I'm gonna use street, house street, like house numbers in the streets. You know that in most locations there are street lines and straight street lines, right? The houses are in a straight line. So when you do what we call a systematic random sampling it means you need to select the first point that you're going to start with and then you're going to also determine that from that one point you are going to select the KM or the AM number, the 10th number or the fifth number. So if you have a street, I'm gonna use my street name it's Glenhaven. If I'm staying in Glenhaven it's a very, very long street, right? It's got almost 30 houses. And I want to do a survey along my 30 houses, 15 on the other side and 15 on the other side, right? So I want to do a conduct a survey. So I'm going to start at my first house at the corner house, the first corner house. And I'm going to say all the houses I'm going to count every fourth house in the street. I'm going to select and use it in my sample. So I'm going to start at number one and I'm going to start counting. One, two, three, four, I include that one into the sample. One, two, three, four, I include the other house into the sample. One, two, until I've exhausted the whole population and I have created my sample that is systematic random sample. Then we have a stratified random sample. Stratified random sample is when you group your population into mutually exclusive subsets. So for example, you take mutually exclusive, it means they cannot exist at the same time. So you create this mutually exclusive sample. So you put males there, females there, or if you are using race, you put all the races in different groups. And then from there, you're going to take one, one, one or two, two, two, two out of those groups that you have created. And we call those group stratas or subsets. And then you do a random sampling from those subgroups. And the random sampling, you remember, it is everyone has an equal chance of being included in the sample. Because if there were 10, 20, 20, 30, you're still going to select from the 10, you're going to speak one. And whoever gets selected, everyone in that group had an equal chance of being selected to be part of the sample. The last one is cluster sample. A cluster sample, it is a simple random sample of groups or clusters of elements. So yeah, the clusters needs to be a true representative of your population. So for example, if your population is structured in a way that they were 20 males, 10 females, but there are 20 males of those 20 males, five of them are black, three of them are white, two of them like that, you will need to make sure that in your strat, or your clusters, your groups, you take the proportions of the population. They are true representative of the population in all their groups. And then you can go and do your random sample from all those clusters. And those are the methods of doing a sampling method of the samples from the population. Unless if there is a question, feel free to ask. We're almost closer to the end because I didn't prepare a lot of things. I just wanted to give you a brief background and introduce myself. Okay, so in your module later on, you're going to use hypothesis testing to do lots and lots of or anti-lots and lots of questions. So you need to understand the steps that you need in order for you to do hypothesis testing and what I've realized is sometimes you need to know all four steps because you most likely are going to write multiple choice questions and in that likelihood, sometimes questions, they ask you all four of them as an option and you need to at least choose one which is correct or which one fills the blank or something like that. So you need to be able to know how to do a proper hypothesis testing and to do hypothesis testing, we have four, actually we actually have five steps because I've consolidated some of the steps here. So we have four steps that we're going to go through now but when we do the work, we're going to split it so that it makes sense. But this is in general the steps that you need to know and remember. So the first step of everything, when you're doing hypothesis testing, you are going to state what the researcher wants and this will be in two statements. One statement that is called a non-hypothesis which is what the researcher wants to do and an alternative hypothesis which will be the opposite and we call those the complement of the other and your alternative and your non-hypothesis. So when you do hypothesis testing, it's that phenomenon where you say you are guilty until proven, you have innocent until proven guilty. That is what non-hypothesis is. You go into test the scenarios and test by calculating and finding the critical values and finding the P values and then making the decision to see if the non-hypothesis is true or is false. And usually the hypothesis concerns with the value of your population parameter. So therefore it means when we state the non-hypothesis and the alternative hypothesis and usually we use subscript. So we say the non-hypothesis, we always use H naught. We always state it using the population parameter. So we will use the mean or you will use the proportion but for you will use the mean. So we will always have the mean but there are also other things that you need to be aware of. In your non-hypothesis, there are only one or three signs that needs to be there but usually there is only one sign which is the equal sign. There is always an equal sign to your non-hypothesis. Or if you don't want to use the equal sign you can use a less than or equal or greater than or equal. Now, the reason why I'm not interested that much on this too is because that thing that you place on your non-hypothesis you will use unless you make a decision. So whether you put less than or equal or greater than or equal, it doesn't make any difference. What makes difference? It is what you will put in the alternative which sometimes they use a subscript one, some they use subscript A. So depending they all refer to your alternative hypothesis. So in your alternative hypothesis you will state that they mean because this is the alternative which is something that needs to prove otherwise from the non-hypothesis. You will say it is not equal or it's either greater than or less than, very, very important because the sign you put on your alternative hypothesis has the repercussion for the steps to follow. It tells you how you're going to make a decision. It tells you how, oh, sorry, how you're going to find the critical value and how you're going to make a decision. That is very, very important. So now, when it is not equal, we say it is a non-directional test, right? Probably you have heard of it or you friend about it somewhere. It's called a non-directional test. We also refer to it as a two-tail test. This will be a two-tail test because when we come to step number two you will have two regions of rejection, one region this side and the other region that side because then your critical values will be on there. So if it's either Z, T, Z or T critical value and this side will be negative, will either be there. That is for not equal. When is greater than or less than this two, we call them directional tests. Or we can call them one-sided test because when you make a decision, so this one is not equal, when you make a decision for a greater than it will be on this side. So your critical value will be from the greatest side which will be your Z or your T. When it's less than your region of rejection will be on the less than side because always remember that in the middle on this normal distribution it's always distributed with the mean of zero. So at the big middle, yeah, it's always zero. So that's why the side is negative, that side is positive. So this will have a negative Z of T because it is less than. And when we come to hypothesis testing do not stress a lot about this that I'm explaining now because I will make it easier for you. But that is very, very important especially the sign that you put on your hypothesis testing. Now you're going to ask if in my hypothesis testing and I know that my null hypothesis is what the researcher wants to prove and if the researcher say they are less than, why can't I put it in the hypothesis testing? You cannot put it in your null hypothesis testing. You are going to create a false null hypothesis and put your researcher's statement in your alternative hypothesis. Now, when we come to the end and make a decision I'm going to explain about the type errors. And next time when we do hypothesis testing in detail we will explain about the type errors. Okay, so I've already covered step number two to some extent, but in step number two here we want to make sure that you are able to find your region of rejection. And your region of rejection is based on different things. Different tests that you're going to be doing in your hypothesis testing will determine whether you're going to do a Z test or a T test. Therefore it means it will determine whether you are going to find the critical value on the Z table or you're going to find the critical value on the T table. Now, there are certain things but we will explain them just now. I will explain all those things just now. All what you need to remember is that for step number two we need to be able to find the regions of rejection that will help us to make the decision at a later stage. Because once we have calculated, once we have the critical values which defines our regions of rejection then we're going to calculate the test statistic and also the test statistic will be different. It will either be the test statistic for Z or the test statistic for T but I'm also covering a portion of it because I haven't now even included when we look at eucalyptus weight. I'm not going to confuse you right now with that. Let's stick to those two because we're going to explain in detail just now. So we're going to calculate the Z test statistic either for Z or T, the test statistic. And once you have the answer from the Z test you can then find where the Z value or T value falls. Does it fall in the red shaded area which is your rejection area? Anywhere where you see the red shaded is the rejection area. Where you see the white area it is the non-rejection area. So if your Z test statistics falls in the red area then you're going to reject your null hypothesis. And because you would have said there is no difference in your null hypothesis when you reject it it means there is a difference between the two groups or there is a difference between the variables. And then once you have found where does it fall if it's not, if you're not rejecting or you are rejecting then you need to make a decision and making a decision you will need to compare your data with the hypothesis that you made about the population in the beginning. And you will usually use your null hypothesis statement to make this conclusion or you will usually compare the value of your test statistic from the sample data with the hypothesis value and refer back to your hypothesized value at the beginning. And my battery is running low on my PC and I'm still low on chatting, can't believe this. Let's double check how far I still left with, I'm left with 20 minutes. Should take us to the, let me reduce the light from my PC, sorry, not the volume, the light. And I'm not gonna see a thing, okay. So then once you have done your hypothesis testing and you have made your decision and you are done and that is the stats that you need to know about hypothesis testing. Unless if they are questions, the questions, comments, I've said a lot to you, nonstop. Hi everybody, I think from my side, we are with you but I think after the session we'll also just need to go back and just remind ourselves and revise and go through the work, I guess, but more slower but yeah, we are still with you. Okay, cool, because I'm not expecting you to do any exercises or anything today. Next week then we will start engaging and then start doing a lot of exercises and doing some check-ins and all that, so I understand. So today I'm just explaining the concepts to you. Okay, all right, so let's move on to the last slide. Yeah, now I want to show you the different types of hypothesis testing that you're going to have to do in your module, right? You need to be able to know how to answer there or identify and answer your questions when asked. So there are three different tests that you can run but in a way, not only three, there are six. So it means you need to be able to identify from the question given, what is it that they're asking you in terms of the six tests that you have because they are all different tests. The first test that you're going to do is to check or do a hypothesis, looking at whether there are differences between one group. The other thing I forgot to mention, when we were talking about the variable, now it comes to my mind, especially now when we are here. Yeah, I'm just gonna go back to variables. I forgot and I didn't include it on the slides as well. We spoke about whether the variables are manifest or invisible and visible. The one thing that I forgot to mention here, which we will mention now is if we're going to do some tests, there is always going to be two variables that we're going to test. One variable, which is your X variable will always be your independent, independent variable, and your Y will be your dependent variable. And when we do some tests, right? When we do some tests, we are going to use our independent variable to make the dependent variable. Or we're going to check whether are there relationships between your dependent variable and your independent variable. That is one thing that is going to be achieved. Or you need to know about. And you always constantly need to remember that, that your X variable is your independent variable and your Y variable is your dependent variable. And X can influence Y. Okay, so coming back to our decision tree. So there are three different types of tests that you can run. So the first one, you can do a hypothesis testing to check whether there are differences between one group. Yeah, we are talking about the difference within this one group, but two different variables. Oh, sorry, not two different, but yeah, we're talking about one group. So we're going to be using one group, not two groups, one group. So we're going to check if there are differences between one group. However, when you test for those differences, there are some assumptions that needs to be made or made. One of those assumption is that populations that are deviation should be given. And if it's not given, then you're going to be doing something else. So when the populations done at deviation is known, which means it is given in the question, then you're going to use the Z test. Then it means you're going to find the critical value on the Z table. And then we're going to make decisions based on that. Very, very important to know that. Now, when we talk about the Z test, we're talking about the test statistic and the formula that we're going to be using, it's for your Z score. It's Z is equals to the sample mean minus the population sampled mean divided by the standard error. So this value here at the bottom is called the standard error. And this is the same as your standard error is the same as your population standard deviation divided by the square root of F. Do not panic, scratch your head, thinking, how am I going to answer this? This looks so complicated. Do not worry. I will show you on your calculators whether you have a financial calculator, whether you have a scientific calculator, any calculator you have, we're going to work it out together. You're going to learn how to use your calculator to be able to answer questions like this, where your standard error is your population standard deviation divided by the square root of N. And what happens when you are not given the population standard deviation, you will be given the sample standard deviation. And when you are given the sample standard deviation, the formula is almost exactly the same because now we're using the T test. And it means when we do hypothesis testing, we're going to find the critical value on the T table. And when we calculate the test statistic, we're going to use this formula, which tells the same as the mean test. The sample mean minus the population divided by the standard error, which is your sample standard deviation divided by the square root of N, which is the same thing. And that is when you are testing for one population group. Now, you can also be asked to do a hypothesis testing to test when you have two groups. And now, these two groups can come from the same population. The assumption will be in terms of the hypothesis testing. If the two groups are independent, it means one does not influence the other, which ones will be independent. Your age and your salary are independent from one another. How? Because there are two variables that do not even influence any one of them. So when the two variables or two groups, the two groups, when they are independent of one another, then you can apply the test for independence where you are looking at the differences between two means of those variables. And the formula will be the test statistic will always be, so when we test for two groups, we're always going to use the T test. So your test statistic here will be the difference between your mean from the variable one minus the mean of the variable two, divide by the standard error, which will be the square root of your standard. This one will not be the standard deviation, but we call it the variance, but you can call it the standard deviation squared because it's the variance which will be the standard deviation squared divide by your sample size for one plus your standard deviation for two squared divide by your sample size. And that will be the test you do for two independent. So what happens when you have two groups, but they come from the same group? So doing a test on this group of students, giving them a test in the morning before the class ask them to write and then give a lesson and then at the end of the lesson ask them to write similar test. Again, this is what we call the before and the after. Then it means A is dependent on B or B is dependent on A. So those two are dependent. So those will be two groups that are dependent on each other. And we call those matched pair because we can do before and after. As long as you are able to clearly see that this was before and this was the after, then you know that you need to use this formula. You will have to use the test statistics of a D mean difference. What do we mean by D mean difference? So it will be the difference mean. So you take the difference of every group and then sum and apply the average on the differences. And that will be your D. It's your differences between your ex, your before and after. So you look for those gaps between before and after score and once you have the answer of the differences then you calculate the mean. Like you will calculate the mean by the sum of your Ds divided by N. That will give you the mean because for all the gaps that exist you will be able to calculate the difference. That will be, the test statistic will be given by your difference mean divided by the standard error of the differences, which means you're going to also be able to calculate the standard deviation of the differences divided by N because your N is one. Before and after from the same group of students if there were 10, your N will just be 10 but we will have 10 before, 10 after reports but it's one sample size. And that is testing the difference between groups. When the population standard deviation is unknown, oh yeah, the dot should be a sigma. When the population standard deviation is unknown and whether you're testing for independent groups or dependent groups. Now, the last type of a hypothesis testing that you need to do is to test the relationship between variables. Now here you need to pay attention. Remember our variables. We said they can be measured for constructs, right? And then we said for others where we cannot measure what we can observe, those can be like your categorical variables, right? So when you test the difference between the variables you need to be able to know and be able to identify that this is a numerical variable and this is a categorical variable and a categorical variable is those that you observe like gender, race, color of your eyes and all that. As long as it does not have a number and numerical number linked to it, it is a categorical field and it can be a nominal variable as well in terms of the scale of measurement. So for your numerical variable which can take any scale of measurement, whether it's a ratio or interval, you will be able to calculate what we call a Pearson R or a coefficient of correlation. And a coefficient of correlation tells you whether or it gives you the direction and the strength of that relationship. Tells you whether is it strong, moderate, weak or is it negative or positive? It gives you the direction by means of negative or positive answer. It gives you the strength in terms of whether is it weak relationship when it is between 0.3 and 0 or negative 0.3 and negative 0.35 and negative 0.35. 0.35 and negative 0.35. If it's between negative 0.5 and negative 0.3 and 0.35 and 0.5, we say it is moderate. When it is above, we say it is strong. When it is close to one or it's equals to one, we say it's a perfect relationship. You will learn about all this and how to interpret them. When we get to that, don't worry too much about it, but it's just today I'm giving you those kind of information. Don't also worry about squinching your eyes to look at that formula. When we get to correlations, you will get the formula to understand how to calculate it. The last one, which looks at categorical data, there we use what we call a chi-square, a cheek. Chi-square or chi-square, whichever way you feel comfortable of saying it. English is not my first language. I don't care how I pronounce it at this point, but feel free to know how you differentiate certain things. So chi-square tells you the relationship between categorical data. We're going to use what we call a contingency table for it to calculate this. We're going to have to calculate the expected value of those contingency observation values from the, sorry, of the observations from the contingency table. And a contingency table, it is where you have two categorical values, one in the rows and one in the column. So it's like your summary table like that. So maybe at the top, you will have your maid and female and yeah, you will have primary school, secondary school and high school. I don't know if they are possible like that, things like that. And that is what we call a contingency table. And you use that to answer the question. But like I said, this is the skills development session. I'm going to give you all the tools you need to go and write your exam and be able to know how to answer this question. Even if you don't use your calculator and the formulas, I will give you everything you need. And that concludes today's session. Are there any questions, comments, query? Happiness? Are you happy? Are you good or are you all right? We are left with seven minutes to the time. Before we leave, can you please also make sure that you complete the register, especially those who came in late? I'm gonna put it on there in the chat right now. Please make sure that you complete the register. And before you leave, we just don't go as yet. Are there any questions? Thank you very much. This is helpful. Thank you. If there are no questions, don't leave. Seems like there are no questions. Okay. So the other person, oh, they just said they wanted to leave early. They are excused. I can't hear you. Not sure if, okay, I don't know. Maybe it was when I lost the connection. Sorry, I'm reading your comments from the chat. Okay. If there are no questions, I'm going to stop the recording. Oh, before I stop the recording because I want this to be part of the recording. I'm going to just stop sharing my slide and then you can do a recap with the slides not on. I just want to show you where to find the notes, but I don't have it as yet on there. I will upload them. Just want, just give me a second. Just want to open. Just do. And I want to share my screen right now. I hope you are able to see my screen. So every week, in order for you to join the session, they might not be sending you emails every now and then to remind you about the classes because they already send you the notification. Now you know where you have the email with all the information, right? Then when you come to this link on the thing that they send you, on the email, there is a button that you use to join the session. And then there is the button, yeah, which says notes and recording. So when you click on notes and recording, I'm not sure if your one is set up correctly. Okay, it comes to this. So these are tutorials. If you have any module that has tutorials, you feel free to go and check and also attend those modules. They are very helpful. If you're doing any writing, English, you can also join some of the session or you can come and watch the recordings. We are under the numeracy center. Oh, the other thing, when you complete the register as well, make sure that you select the correct link. So you can see that we are under the numeracy center and your link is basic statistics in human sciences like 3704, which makes it easier for you to identify and be able to know which one to use. So you're going to click on that and it will open this. At the moment, the recordings are not there because today's our first session. So you will find all the recordings on here. Whether you attend the session or not, the recordings, if the session was recorded, it will be uploaded here. And usually it takes about 72 hours or something like that. So please be patient or be patient with UNISA. They will eventually post them at some point or the other. But if you see that a week has passed and there are no videos on this, please let me know so that I can follow up as well. For the notes, you will find them. You will find the notes on here. Just give me a second because the notes are not there. I just want to give you the notes to just show you where you're going to find them. I couldn't upload them earlier, it's still not there. But the notes will be there. I see, it's still thinking it's not... It is not saving my thingy. Anyway, let's go back. So you will be able to see also the session plan for today, for August, and also you'll be able to see what we've planned for September. Now, depending on when you're going to have your exams, we will also make time and provisions for exam preparations probably. If you're not writing in the first week of October, then we will use the second week of October to do your exam preparations. If you're writing only in November, then we can also make some arrangement in terms of how we can help you prepare for the exam. But I'm hoping that by September we should have completed everything related to what you need to learn and know for you to go to enable you to go write the exam. Okay, so let's see. I'm going to try for the last time. If you don't want to load, then I don't know. It's frozen. I can see there, it says uploading. Okay, there it is. So there are the notes for today. You will find them there. Then I'll load it. Okay, so, and that concludes. I'll stop presenting. Just give me a second again. Don't go when you is yet. I'm going to stop the recording. Because I want to talk to you outside of this.