 Thank you for that. I forgot. I totally forgot about it. I'm not going to start there. I hope you made notes. So I'll just do a revision. So population, fine arts. So that it's recorded on the fine arts. And this would have been your sample from a specific, because this is all of the fine art students. Then option question 34, because they say better it, which means greater than, which means superior than. Then we say visual artists have a superior ability for perception than general population. We're not talking about the relationship between, because when we talk about the relationship, we either looking at the linear or we can do a high square test. So we're not looking at that. And they are not asking about the relationship yet that exists. They say one is better than the other. Okay. It's question 35. We chose option two because also with superior meaning greater than. So therefore it means the alternative will have a greater than. And it's said also the population mean is five. So it should be greater than five. The reason why option one is not correct is because when we talk about the superior or greater than or more than. Then it means the alternative should have a greater than five. Number three, why is not correct is because in your old, in your null hypothesis, in your null hypothesis always has an equal side. Other you can write it as an equal or greater than or equal or less than or equal. Or you can have it as less than or equal only in the null hypothesis, but never a not equal. Okay. Moving on. Now we are back. Which is the correct value of the standard deviation of the sampling distribution of the mean. So we need to go back to our data. And did you write we have our mean. We're not actually looking for the mean because the question was asking what is the standard era. So remember our standard era is our population standard deviation divide by the square root of N. So our population standard deviation. In this instance, because we do not have a population standard deviation, we're going to use the sample standard deviation. So, so our sample standard deviation is 1.7 and our and our sample size is 100. So we're not going to use the population. We're going to use as divided by the square root of N. Because we're not given. This is unknown, but we are given the sample. I forgot the value now was 1.7. 1.7 divide by 100. Calculate. Should be 2. 1.7 divide by 10, not divide by 100. Is it divided by 10? What was the sum? The square root of 100. I forgot that. Oh, thank you very much. So some people are still awake. So divide by the square root of 100. Which is 1.7 divide by 10. Which is number 3. 0.17. It's 0.17. Which is the appropriate statistic to calculate. For our data now. I've already gave you some hints. There is one of the hints that I've given you. And because we're dealing with the sample and the mean. Which test statistics are we dealing about? Are we talking about? So let's go back there. So remember this. What we have here. Very important. So you need to ask yourself, is the population standard deviation given? Let me give you the answers. Is it known? Z. Is it unknown? We use a T. Oh, come on. Since it's unknown, we're going to use number one. So I've already given the answer. And based on the null hypothesis as well. As long as you don't see things like the mean one is equal to the mean two. If you don't see this, this is one group. And this is. Two groups. You must remember that also depending. So whether it's one group or two groups. If your population standard deviation is known. We use. The Z. If it's unknown. If it's unknown. We use a T test. So this is for one group. So let's look at the question. What is the appropriate test statistic? This is for the T test for the mean for single group. Because the population standard deviation is unknown. It's not a search. And this says. For two independent for two dependent groups that is not correct. So the only answer that is correct is option. One two population mean. Means are compared. The P value is calculated to represent the probability of. Observing a specific. Difference. Between the sample means given. When two population means are compared. The P value is calculated to represent the probability of. Of observing a specific difference between the sample means. Given that. Given that. Dot dot dot. I would say three. I want to say two. The alternative is true. If the alternative is true. Wouldn't that mean the null is false? I want to think so. Because. When two groups are compared. The P value is calculated to represent the probability of. Observing the specific difference. So what is the null? What the alternative hypothesis would have said. We would have said that. It's either there's a. Less than. Or a greater than. In numerical. So your alternative hypothesis is also always saying that it is equals. So it's either there's a there's no effect between the two. So now here we are checking the difference. That's why I'm thinking. The alternative is true. I don't know. I stand to be corrected. So always to remember that the null hypothesis you always say. There is a difference between. The sample. Remember that. Because. Oh, sorry, there is no difference. Always say it's equal. So we say the mean of this group is equals to the mean of that group. Or we say the mean difference. Is null. Is equals to two. Sorry, it's equals to zero. It's null. That is the null hypothesis we stated in that manner. We say there is. No difference between the mean or what. The two. There's no difference between the significance. We stated in two ways. You need to go to the two sample groups. So. There's the one sample sample to sample. So we state always the null hypothesis and the alternative. Okay, so. To develop a test for the difference between the mean. We need to know something about the distribution. So we say. There is no difference because they are the same. There is no difference. They are different. So. In that instance. Then what would be the P value? No. We can look at it this way. Anyway. When two populations are compared the P value is calculated to represent the probability of observing a specific difference between the mean. Given that. Given that H naught is true because that's what we want to prove. We want to prove what the researcher wants to prove is always in your null hypothesis. So we want to test if this is true. The null hypothesis is true. And that's what you always want as a researcher. To prove the null hypothesis and then we create an alternative to test against what you wanted to prove. And that is why also when we make a decision we always make it in relation to the null hypothesis. We reject the null hypothesis because we say in the null hypothesis not true or is true. So we make it. In relation to that. What should a researcher do if a sample difference between two means based on a large sample is found to differ significantly. To determine whether the outcome is of practical importance. A psychologically unimportant results may turn out to be statistically significant if the researcher dot dot. And this is one of those areas that we need to consult the book. So practical importance. An unimportant results. May turn out to be statistically significant. If the researcher set the level of significance low determines the power of a statistical test. Let's go see the power of a statistical test. Okay. So all the effect size. So let's see what that's that mean. Okay. Given that a particular direction is of a right it is necessary to perform a statistical test to see whether the result is significant. A large significant or a large effect can fail to be significant if the sample is too small. What did it say there? Nothing to do with the sample. Okay. The smaller the sample the greater the probability of finding the result that appears to be significant purely by chance. This relates to the issue like the power of a test and the effect size. So we need to go to section 3.3.2. 3.3.2. Page 77. Page 70. We must look there because when I search 77 I don't find them. 80. The effect size. There is the effect size. What does it say? The major determinant of a sensitivity or power of statistical test is the sample size. When the sample is larger the smaller effect will have the statistical significance. The reason is that the larger the sample the lesser the variance. This is due to law of large numbers. This implies that when the sample size is larger even the small, even the sample effect that seems insignificant can produce small p-value leading to a rejecting of the null hypothesis. Let's go back and refresh on what they're asking. So what should the researcher do if a small difference between the means based on the large sample is found to differ significantly to determine whether the outcome is of practical importance. The psychologically or a psychologically unimportant result may turn out to be significantly or statistically significant if the researcher set the level, set the lower level of significance or determine the power of the statistical test or calculate the effect size. So what are we looking at? The effect size. So what are we talking about? The effect size. So let's go to 3.33 if that exists. So very tricky. So this is the effect size. So the implication is that we have carefully interpreted the result. The p-value is smaller chosen. Improbable that the effect we see in our observation is purely due to chance. One way that statisticians have suggested to deal with the problem is by notion of effect size. Oh, tricky, tricky, tricky. This size is giving us problems. Because I know that they, so in this case, the sample of 64 would conclude that even though Uniswast didn't exceed the population, the IQ to greater extent than expected by chance, the difference is not very large. So the larger. Okay, the power of the test is calculated by subtracting type two error. So let's see what does that mean? The power of the test is related to how sensitive the test should be. See section 3.4 on effect size below as well as the sample size and that you are going to use. Not reassuring, not giving me the answer that I'm looking for. There are a few things that could be done. Namely, one increase the sample size to decrease the error of the sampling error. That. Influence the power of the procedure by our choice of the statistic. Can I suggest something though? Yes, let's have a look at the answers. If we set a lower level of significance, what would the implication be? If we determine the power of statistical test, what would the implication be? And then I think if we look at the unimportant results, some of things there, which may turn out to be significant. If we sort of. Understand what those things do. I think we may come up with something that you know we may be closer to the answer, if not the answer itself. Yes, I was actually going to put a question back here and I will say let's come back to it tomorrow. I still guess number one. I still guess number one. If you do lower the level of significance, then it is more likely that you will. It will, it will be more statistically significant. Not necessarily. Okay. My guide says if you take a larger sample, which is the larger number than the lower, you are likely to, to be more statistically significant. Yes, because if you increase your sample size, yes, you are likely towards that. Remember your level of significance. This is the error margin that you are setting as a researcher. It's not saying whether you are increasing it or decreasing it. You will get a, you will get a better chance of being significant. So that won't help you, but between this two, between either determining your power of a statistical test or the effect size, because with the effect size also it talks about increasing your, your sample size. So I'm leaning towards the effect size, which is number three because it implies that when the sample size are larger, then the sample effect will be insignificant as to produce the PVN that would lead to a rejection. So that's why I'm saying I'm going to put a question mark there and then come back to it tomorrow when I've read it, because at the moment my mind is not even moving. It's not the area that I am familiar with. You're taking all this time in one question in an exam. Yes. So in the exam, you just pick it, pick it my Bellani. Sala, Sala, gentlemen, pick your, your, your T and then you sign, that is the after. We'll, we'll have a look, we'll have a look at that one. I will make note of it. Before I go to sleep, I will, I will Google, Google search the answer, the correct answer for you. Question 89. So that we don't spend more time on it. If we can't find it now in the study guide, then it will take us forever. So let's move on and look at the one so you will hit the problem. So make note, you will hit a problem when you get to some way on question 39 in your exam. I think a few more as well. Okay. So let's look at 40. The mean score of a sample of research participant is compared with the population mean of 24 that particular. The following hypothesis is to be tested. So since they say they are comparing the mean population of 20 for a particular question. So what will be the correct answer? Let's finish the sentence. The following hypothesis is to be tested. The null hypothesis states that the mean is 20, then alternative states that the mean is not 20. So we know that we're doing a non-directional test. A researcher draws a sample of 50. So that is our end, our sample of 50 and obtains the mean of 25. So this, we need to remember that that is the sample mean of 25. And this previously they gave us the population mean and the standard deviation of four because this is a sample. This is S and the standard deviation of four on this questionnaire. If the null hypothesis is true, what would you expect the probable value of the mean of the sample to be, to have been? Three. Option two. Option three because it's non-directional so it can be greater than or it can be smaller than 20. Yeah, this one is also another tricky one. So if the null hypothesis is true, which says the null hypothesis is 20, what would you expect the probable mean of the sample to have been? Remember now they're talking about the sample, not the population. And yeah, they told us that the sample mean score is 25 with a standard deviation of four. So if we're not rejecting the null hypothesis, so what would be the probable sample? I don't even know which is called. I also don't know which is that, but I think what we can do because it's non-directional, let me just double check something here. So I have all the values that I need to calculate my probability. So let's see because then it will tell me I'm going to reject my null hypothesis. So let's calculate this value first. So we have 25 minus 20 divided by 4 divided by the square root of 50. What do you get? 7.07, I don't know, square root of 50. Square root of 50 is 7.07. Square root of 4 is 0, square root of 7 is 7. So 25 minus 20 is 5 divided by 4 divided by the square root of 7.0. So I'm just still waking out 0s. I'm going to keep 4 decimal 0s, 7 0s, 7 1 1. I can't write. It's 8.83. 5 divided by 4. So we have 5 divided by 4 divided by the square root of 0.57. 4 divided by 0.57. I mean 5 divided by 0.57. The answer is 8.88, yes. Okay. So if I go to, I don't even think we do have the Z score that goes to the 8 values. So we can't even go there. If the null hypothesis is true, what would you expect the probable value of the mean of the sample have to be? Will it be wrong to say not equal to 10, 20? I guess number 3 can be correct because when we use 25, we're not getting 8.83. And I don't think we have a Z score of that much. It ends up also double check on. But Leslie, they already tell us the mean score of the sample is 25. Yeah, I'm also thinking it might be as straightforward as that. The answer is option 2. Yes, it's like a trick question of a whole lot of story around it. Around the answer. Yes. Can I just ask Ms. Boye, does Z score do they end at 4 or is there another table that continues? I think there is a table that continues. I just wanted to open this, that's one. Just check. But I think they end at, they end at 3 or 4 because this one also you see it ends at minus 3. So you won't get like 8 and so forth. Stretching it. Yeah. So it's only three standard deviation away because what is the Z score of 8? It means there is a huge difference between your values as well. Remember that your Z score also determine how far away from the mean of 0. So if it's 8 standard deviation away. So you can just imagine. So if this is your mean, that means how the difference that's there. So when it is 1 is closer. When it's 2, at least it's closer as well. But when it's 8 standard deviation, that is why you can calculate those probabilities as well. So I'm going to assume that maybe the answer is just in front of us is 2. Because the mean they gave us is 25. Can we also put the question here for tomorrow as well? So that's why I said we hit a brick wall. Oops, sorry. We hit a brick wall when you reach to this question. In the exam, don't stress too much. Don't stay there for too long because time will be ticking. So if you spend more than two minutes on one question, know that you are not going to finish your exam. But how can we, if questions are this tricky? Yeah. When two means are compared, the p-value expresses the probability that a difference which is observed between the means in the sample of measurement. It looks like we have already answered this question. Didn't we? When two means are compared, the p-value expresses the probability that the difference which is observed between the means in a sample of measurement will be significant. Is due to the alternative hypothesis? Is due to the chance or the sampling error? Oh, yes. This one I can help you with. Okay, so we have the null hypothesis and we also have the alternative hypothesis. The null hypothesis always have an equal, whereas the alternative has the not equal less than or greater than. When we go and look for the p-value, we look at the sign that is relating to the alternative. So to find the p-value, because the p-value is the probability that whatever you are testing, either is related or there is a difference will be observed between the means in the sample as a measurement which is due to the alternative hypothesis because that is what we use either to test whether it's a one directional, it will be due to looking at that and saying this is a one directional or two directional or non directional, whether it's left or right. That is option number two. Which symbol is conventionally used to indicate the value of the maximum probability that an error would be made if the null hypothesis is rejected, which is particularly a researcher is willing to allow. So actually, they're asking you what is the level of significance? What will be that's one, that will be one because that is the alpha and alpha represent the level of significance and that represent the maximum value that the researcher would want to set or the risk that he's willing to take. Now we go to the effect side size co-hens d refers to the difference score when the two means from the dependent samples are compared the effect size or the power of test. Number two. It's number two because we all we also did look at it. What is it? Co-head size is your effect size which is number two. The effect size is calculated to determine one whether an effect is statistically significant or not to the ability of the statistical test to test to detect a significant relationship between variables such as the relationship does not in fact exist or three whether a significant effect is meaningful from the practical point of view irrespective of the sample size. See the challenge with this is the effect size can be calculated also with the correlation. I would say number two. What page is that in the text book Lizzie around what page are you? Page 87. So if you check on your let's go to effect size so that is one two. Proceed to determine of the results. So is there whether the end effect is statistically significant or not the ability of a statistical test to detect a significant relationship between variables when such relationship does not in fact exist whether a significant effect is meaningful from a practical point of view irrespective of the sample size. On page 86 by effect size it says the on the second the second sentence when the sample is large even smaller effects will have statistical significance as the measurement of statistical to see whether how significant the page 86 yes I'm on page 86 and page 90 let's see page 94 says something that helps you. We are on page 94 which line on question I might be using the wrong study guide that says 2012. The study guide that would be okay let me just quickly read it says here one way that statisticians have suggested to deal with this problem is by the notion of effect size different procedures exist to determine the effect size of a result in the case of a comparison between means one way of calculating this is by the use of reference D. Come back and read the sentence yeah it says whether an effect is statistically significant or not number three whether a significant effect is meaningful from a practical view irrespective of the sample size so I'm going to assume that this will be incorrect based on page 84 that's where you read it Are we not at at 40 what's the at 43 are we already beyond 43 44 which 43 now yes no 3 we already answered in call hands D refers to the effect size we are on 44 we are trying to answer what effect size might be because call hands size it says D is calculated by means of the mean difference I think divided by the standard deviation difference or standard deviation what divided by the estimated standard deviation so based on the P value the difference between the mean is quite impressive however that the T test is sensitive to the sample size and the sample size if a smaller effect would be significant to evaluate and that is the call hands D see the challenge here is finding the correct definition of the effect size what is the effect anyway the different procedure exists to determine the effect size of a result in cases of a comparison between the means one way of calculating this is to use call hands D and we do this by expressing the mean difference that we observed relative to the standard deviation a result of the effect size greater than one would imply a difference of greater than one standard deviation between the means which is quite large which doesn't help in interpreting the question so when we calculate the effect size are we calculating it to test whether the effect is significant or not so let's start there so the implication is that we have to be carefully or to be careful how to interpret the significant result a P value of smaller than our chosen level of significance implies that relative to this sample it is improbable that the effect we see in our observation is purely due to chance it does not imply that the effect is big or important this is something that we have to decide by looking at what the data means and they have suggested that we can be solved by using the effect size what does that mean we calculate the effect size for the relationship let's see we do calculate the effect size for the correlations as well as I could remember as well so let's go to next know how to calculate the effect size for the correlation so we should however be careful as to how one interprets the significant results to clarify this consider the relationship between the calculated significance the P value and the sample size but all of this talks about the R and the P value not about the effect size where do they talk about the effect okay so the effect size in terms of this let's see so they say R squared okay so that is why maybe I'm getting lost with this on the correlation side of things instead this we call it coefficient of determination not the effect size so here coefficient of determination means the proportion of the variance in one variable can be determined by the relationship of how much the variance have in common it can also be used to indicate the size of the effect which is what they use so here we can say how much of an effect one variable has on the other how does it influence the other one so do they talk about influence here the ability of a statistical test to detect a significant relationship between variables when such relationship does not in fact exist so if you have a correlation of R of 65 then your R squared will be 0.42 that implies that two variables share 42% of the variance and this can be interpreted as a very large of large effect yeah this is one of those areas okay bringing to number two on this one because in terms of the relationship R squared and I'm lazy 44 41 then 40 the list is growing 40 and question 40 44 I don't know how many marks are they issued on question 45 a random sample of 100 people are tested to see how many items they can recall from a list with pictures of items the distribution of the results is found to be or more or less normal with the mean of 7 the sample mean of 7 and the standard deviation of 2 but is the probability that a specific person is chosen at the random and I think we are also running out of time from a general population will remember 10 or more items from the list a random sample of 12 people how many items they can recall from a list with pictures of 12 items the distribution of the results is found to be more or less normal with a mean of 7 and the standard deviation of 2 what is the probability that the person chosen at the random from the population will remember 10 or more from the list the tricky part with this question of theirs is they didn't give us the population mean but they gave us the sample mean and the sample standard deviation and they give us our X observation to say we need to know or find out the probability that it's more than so it's greater than our X is greater than 10 or more so it's greater than or equals to 10 we are given our sample size oh sorry our sample size which is N of 100 we are given the mean of 7 and the standard deviation of 2 if we use the Z formula then we need to X minus the mean divided by the standard deviation at the moment we are given the sample standard deviation oh yes because they gave us S bar and X bar who am I I guess until 45 it's 8 o'clock what time must we finish until 8 it's 3 hours done I don't know how to answer this question just maybe out of my head here you said when we were not given what a mean when you're not giving the population standard deviation so yeah we're not giving the population mean population mean so the X bar there of 7 is what mean is that that is the sample mean okay a random sample a random sample is your sample size you get a population and then you select from a population a random sample which is a subset of the population and from there they checked whether those people how many they will remember more or less like your number of pictures the average they calculated was from that sample so the 7 people so 7 out of 100 oh no people could remember on average 7 items out of 12 out of 12 yes that is average and that is the standard deviation so between the individual people how far apart were they from that mean so they are to standard deviation away from the mean so now they want you to calculate what is the probability that a specific person chosen at the random from the general population will remember 10 or more items miss point something yes can I just ask is not a question of cumulative probability maybe the challenge with the cumulative probability on this one is we not given the frequency distribution or the probability for a person selecting only one item 2 items 3 items 4 items 5 items so it's not and because they say they are less alternatively what we can do as well is use what information we are given so in state of using the population because we don't have the everything population but we have the sample so we can use the sample X bar and the S which is our sample standard deviation and substitute the values so our X is 10 because it's there minus our sample which is 7 divide by our standard deviation which is 2 and then we just 1.5 which is 1.5 1.5 so now because it's greater than now we need to go back to remember we are looking for the probability right so it's greater than so it will be on this side and since it's greater than remember if it's positive if it's plus we go to the smaller side if it's negative we would have went to the larger side so it's positive 1.5 let's go 1.5 positive 1.5 go go go into the smallest portion 1.5 1.5 1.5 smaller portion 0.0668 0.0668 0.0668 0.0668 0.0668 so if I round off this looking at the value to the right 0.1 so it says the probability of getting greater than item on the list will be greater than 0.1 because the sign said it's more than that's the only way that you can get to the answer based on the information that you are given and that is 8 o'clock not much I can do now so so let's take the miss boy I guess on every scenario we will not add on but use what we are given isn't it yes so you will have to read the question and look at what else are you given can you use that to and that will also guide you because are they asking you to calculate the basic probabilities or are they asking you to calculate the discrete probabilities or the frequency distribution probabilities or are they asking you to calculate normal distribution probabilities quick question yes since this is going to be an open book exam can we open these videos here and refer when we get lost or something like that I don't think the videos are allowed but if it's an open book you should have all your papers written some way because how are you going to go through the videos how long is your exam is it 2 hours or 3 hours no that's what I am saying specifically because I know if I have gone through this I know roughly where to get what yeah so this one had how many questions which we still needed to go through 70 questions so we still had about 30 left because we are still on 40 something this doesn't require only one day session of 30 hours Ivan and then Vanessa please get okay so and our session ends right here thank you very much good thank you Niazee thank you so much I will go through thank you Niazee thank you thank you so much so tomorrow I will be giving another session so tomorrow yes you will have we will have another session so how can I get the link because I was just sent someone assisted me this is the first time I am joining so someone someone will give you the link for tomorrow because tomorrow's link will come from Unisa unless if already they already sent out the links for Saturday then I will send you the link I will send the link on the WhatsApp group and then everybody can share with others I am not on the WhatsApp group how do I join the WhatsApp group let's do this just wait there let me stop for a minute okay