Distance Between Pupils The following table lists distances (m...

Question

Distance Between Pupils The following table lists distances (mm) between pupils of randomly selected U.S. Army personnel collected as part of the ANSUR II study. Results from two-way analysis of variance are also shown. Use the displayed results and use a 0.05 significance level. What do you conclude? Are the results as you would expect?

Table of pupil distances by gender and handedness with ANOVA results, including F-statistics and p-values.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In a study on reaction time, a two-way ANOVA is performed with the factors being caffeine intake, yes, no. And sleep duration, short, long, the P values from the ANOVAR as follows, caffeine 0.12, sleep duration 0.004, and caffeine and sleep duration interaction 0.33. Using a 0.05 significance level, which conclusions are correct? Awesome. So it appears for this particular prompt, we're asked to take all the information that is provided to us by the prom itself, and we're asked to use a 0.05 significance level to determine which of our multiple choice answers state that that conclusion or those conclusions are correct. So with that in mind, noting. That ANOVA means analysis of variants. So once again, ANOVA means analysis of variance. So, now that we know what we're solving for, and we're, we have been reminded what ANOVA means, let's read off our multiple choice answers to see what our final answer might be. So A is caffeine has a significant effect on reaction time. B is sleep duration has a significant effect on reaction time. is there is no significant interaction between caffeine intake and sleep duration on reaction time, and is there is no significant effect of sleep duration on reaction time. Awesome. So first off, in order to solve this particular problem, let us note that caffeine, which I'll call C for short, We're told that P, in this case is going to be equal to 0.12. Awesome. So once again, the P value for caffeine, which we're told that the P value for caffeine in this case is 0.12, to be specific, and 0.12, and let's not make a note of this. So 0.12 is greater than 0.05, which let's make a note. In blue that our significance, which is denoted by alpha, is equal to 0.05, and because 0.12 is greater than 0.05, this will mean that we fail to reject the null hypothesis for caffeine. In other words, there is no significant main effect. Of caffeine intake on reaction time at the significance level of 0.05. Awesome. So with that in mind, our next step is we need to focus our attention on the sleep duration, which I'll call SD for short, and for the sleep duration, let us know that our P value is equal to 0.004. And let us note that the P value for sleep duration is less than 0.05, so 0.004 is less than 0.05, and because this is the case, that will mean, as a result, as we should recall, that we reject the null hypothesis for sleep duration. And that will mean as a result, there is a significant main effect of sleep duration on reaction time. Our third step is we need to focus our attention on caffeine and sleep duration interaction, which I'll just simply call I for interaction. And as we should recall, P for this case is gonna be equal to 0.33, and the P value for the interaction is greater than our significance. So, once again, 0.33 is greater than 0.05, and because this is the case, this will mean that we fail to reject the null hypothesis for the interaction, and as a result, there is no significant interaction between caffeine intake and sleep duration on reaction time. So, with that in mind, we can make the following conclusions. There is no significant effect of caffeine. On reaction time. So once again, there is no significant effect of caffeine on reaction time, and we can also note that there is a significant effect of sleep duration on reaction time, and finally, There is no significant interaction between caffeine and sleep duration, and considering these elements, these pieces of information, our final answer without a doubt has to be multiple choice answer letter B, which states that sleep duration has a significant effect on reaction time, and that is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Two-Way ANOVA

F-Statistic

P-Value

Watch next