Complete the sentence; We use the analysis cfvariance (ANOVA) to tes: whetner mcre sampi means are equa whether or mcre populazion variances areall equal; whetner m...

In a one-way ANOVA, explain what it means to reject the statement in the null hypothesis if three treatment groups are being compared.

What's up, stat Cats. So in this video, we're gonna be talking about the differences between the chef and Tukey Post Hawk tests. The so these are gonna be used after we have a significant unova one way and over test. So the chef test is more general of the test, so it's less powerful, but we can use it when we don't have the best sample sizes or the best data. We can also use it when we have uneven sample sizes. So on evil ends on evil sample sizes. And then the test statistic is f sub s, which is gonna be equal. Teoh Thea Differences and Means square over means square within groups multiplied by one over sample size one plus one over sample size to and for the two key test. It's a more powerful test, so we're gonna have more statistical power when we're using this test. But we need even sample sizes, and the test statistic for this test is lower case Q. And it's equal to the differences and means over square root of mean square within groups over and And there's on Lee one value for end because we on Lee are you using groups with the same sample sizes? Alright, guys, that's it for this video. I hope you enjoyed it. I'll see you next time.

So there are three hypotheses for a two way in nova and usually just see the null hypothesis. And I'm gonna write down the alternative. It's really just the opposite of what the knoll would be, but I'll write the null hypotheses. I'll just call this h not one, and they're all pretty much the same thing. At least the first two are, it says for the first one, it's there is uh no difference in group means at any level of the first independent variable. That's the first knoll. The second knoll is almost exactly the same. I'm going to write it as a church, not two, and it says there is no difference in groups. In group means at any level of the second independent variable. And then the third null hypothesis is a little bit different, and that talks about effect. So, the way we were there, this when it says the effect of one independent variable does not depend on the effect of the other independent variable or in other words, no interaction effect. Now, usually you'll just see the knoll because the alternative is just the opposite. But just for clarity, I'll go ahead and write the alternative hypothesis, I'm gonna write the whole thing. But basically the first one is saying that there is a difference, there is a difference between or at at least one level of the first independent variable and then the second alternative same thing, there is a difference. But this time for the second independent variable, and then the third hypothesis would again just be the opposite. There is an interaction, there is and interaction effect between the two independent variables. Okay, so again, typically there are three. There will be three, but generally just written as the null hypothesis. So those are the ones to know, you know, for sure.

Okay, So this question asks us to analyze the differences between one way and two way and over to start. I thought I'd just make sure that we have a clear understanding of what an Innova is. All in a nova is is analysis of variance, right. This is a short way of saying analysis of variance eso to dive right in one way and over or one way analysis of variance is a hypothesis in which only one category categorical variable or single factor is considered. Um, these air, based on the following assumptions, right in order for in order to use a one way and over these assumptions have toe hold true, you have to have normal, uh, normal distribution of the population from which samples air drawn. You have to have independence of samples in the variance of the population has to be humble genius. Right. So, by contrast, the two way in over or two way analysis of variance, um is the classifications. Classifications of data based on two factors. An example. A good example of this is a sales firm classifying the sales made by the firm first by the sales made by different salesman and second by sales in various regions. So, for two way, you're looking at each one, Uh, first local, second regional in a one way you would just be looking at one of those sets. You would not be making the jump between the second. The assumptions that you have to include for two way, um are normal distribution of population, independence of observations and not samples. Uh, homogeneity. Uh, the variance of the population once again has to be the home jeans. So I hope this helped. Please let me know if you have anybody.

What's up, stat? Cats in this video, we're gonna talk about post talk test for a one way in, over. So after we have a no hypothesis that is rejected for a one way and over what sort of tests can we her form to figure out which means are significant from each other. So two tests we can do our the chef test and the two key test. So the test statistic for the chef test is up sub us. And in the numerator, we're gonna have the differences of the means squared and in the denominator, we're gonna have the mean squared of within groups multiplied by one over the sample size of our first sample, plus one over sample size of our second sample. Okay? And then if our if our f calculated if this test statistic is greater than our s critical then we reject are no hypothesis. So that means our means are significant from each other. So now for two key test, the test statistic is que and it's gonna equal the difference of the means in the numerator not going to square it over the square root of the mean square within groups divided by sample size. So for two key test, we only want to do to key test when all of our sample sizes are equal. And that's why there is only one value for end. All right, guys, those were the two tests that we can do following a significant one way and over. That's it for this video. I'll see you next time.