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| Name | t Test vs ANOVA with Two Groups - P-Values Compared |
| Video Uploader | Video From Quantitative Specialists |
| Upload Date | This Video Uploaded At 31-08-2015 15:00:04 |
| Video Discription | In this video, we compare the t test in SPSS with the ANOVA. You might be surprised what you find! t test ANOVA P-Value Video Transcript: In this video I want to take a look at the relationship between the independent samples t-test and the one-way ANOVA. Now it may seem that these tests are quite different, it may look like that on the surface, after all they're located in different chapters in intro stats texts and so on, but we'll take a look today at how these tests are actually very similar. So let's go and start with this example here on your screen. Here we have a two group problem where we have volume, where we have 1 and 2, where this corresponds to either a no music condition, or no volume condition, and a high-volume condition. So in this hypothetical study we had 20 people, 10 were randomly assigned to study for an exam with no music, and then 10 were randomly assigned to study for an exam under high volume. And then the dependent variable here is the exam scores. So our independent variable is type of volume, where we have none or high, and then our dependent is exam scores. So let's start by running an independent samples t test. So do that we go to Analyze, Compare Means and then select Independent- Samples T Test. Here we'll move our dependent variable, exam scores, into the Test Variable(s) box. We'll move volume into the Grouping Variable box. And, as we can see here, we have 1s and 2s, so under Define Groups, group 1 was assigned a 1 and group 2 was assigned a 2. Click Continue and then OK. And then here's the results for the independent samples t test. Before we take a look at that, let's go back and now run the One-Way ANOVA. So we'll go to Analyze, Compare Means and then One-Way ANOVA. This time we move exam scores into what's called the Dependent List, and volume into the Factor box, factor standing for the independent variable. Go ahead and click OK. And then now here's the ANOVA results. Now the first thing here that I want you to notice is the p-value. Look at the p-value for the Independent Samples T Test under Equal variances assumed, we have a p-value of .014. Now here, in the ANOVA results, if you look at this p-value, notice what it is. It's the exact same, .014. And just to make sure, let's go ahead and double-click on this table here, double-click on the p-value and we can see it's .013996, and then we'll do the same here for the ANOVA table, and this is also .013996. Well, if the p-values are the exact same, that indicates that we're really running the same test here. So the first thing we can see is that we get the exact same p-value running our two groups under the independent t as we do when we run our two groups under the one way ANOVA. But there's something else here. You might notice here you see a t of 2.722 and an F of 7.407. Well, despite the p-values looking the same, we can see here that t and F definitely are not equal. So, in summary, we had an F of 7.407 and a t of 2.722. Well, while those are not equal, if we square the t, we would actually get the value for F, within rounding error, it's off by a couple one-thousandths of a place just because SPSS rounded. But this relationship does hold: F is equal to t- squared, within rounding error. Or in other words, when we have two groups, F is equal to t-squared. So we saw that the p-values were the same in SPSS and now we can see that F is equal to t-squared. So therefore we could summarize the results as follows here, the one-way ANOVA and t test are equivalent With two groups. They will provide the same answer or decision in terms of the hypothesis test (as they produce the exact same p value). So, in other words, if you reject the null with the ANOVA, you will reject the null with the t test. However, this property only applies with two groups. So, for example, if we had three groups and we ran the ANOVA we got a p-value is let's say .003, for example. If we have three groups and we run the ANOVA, that would require that we run three separate independent samples t tests, group 1 vs. 2, group 1 vs. 3, and group 2 vs. 3. Now if our p-value for the ANOVA was .003, that doesn't mean in any way, shape, or form, that the p-value for any or all of those t-tests will be .003. So the relationship, once again, only holds when there's two groups. But with two groups, we can run the independent samples t, or we can run the one-way ANOVA, as they produce the exact same p value, meaning you'll draw the same conclusion about the hypothesis test. And once again the relationship between F and t is that F equals t-squared with two groups. This concludes the video for looking at the relationship between the independent t and the ANOVA with two groups. Thanks for watching. YouTube Channel: Quantitative Specialists https://www.youtube.com/user/statisticsinstructor Subscribe today! |
| Category | Education |
| Tags | Student's T-test | Analysis Of Variance | Statistics (Field Of Study) | T test | ANOVA | t test or ANOVA | test on means | p-value | P Value | t test | ANOVA F | F = t-squared | how to do a t test | how to do an ANOVA in SPSS | SPSS p-value | t test vs analysis of variance | t test vs ANOVA two groups | t test vs f | P-Value | how to run a t test | how to run an ANOVA | anova and t | inferential statistics |
