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F statistic is 1.18 The p-value is 0.317

Now try one for yourself.

Learn By Doing: One-Way ANOVA –Flicker Frequency ( Non-Interactive Version – Spoiler Alert )

The ANOVA F-test does not provide any insight into why H 0 was rejected; it does not tell us in what wayμ1,μ2,μ3…,μk are not all equal. We would like to know which pairs of ’s are not equal. As an exploratory (or visual) aid to get that insight, we may take a look at the confidence intervals for group population meansμ1,μ2,μ3…,μk that appears in the output. More specifically, we should look at the position of the confidence intervals and overlap/no overlap between them.

* If the confidence interval for, say,μi overlaps with the confidence interval forμj , thenμi andμj share some plausible values, which means that based on the data we have no evidence that these two ’s are different.

* If the confidence interval forμi does not overlap with the confidence interval forμj , thenμi andμj do not share plausible values, which means that the data suggest that these two ’s are different.

Furthermore, if like in the figure above the confidence interval (set of plausible values) forμi lies entirely below the confidence interval (set of plausible values) forμj, then the data suggest thatμi is smaller thanμj.

EXAMPLE

Consider our first example on the level of academic frustration.

Based on the small p-value, we rejected Hand concluded that not all four frustration level means are equal, or in other words that frustration level is related to the student’s major. To get more insight into that relationship, we can look at the confidence intervals above (marked in red). The top confidence interval is the set of plausible values forμ, the mean frustration level of business students. The confidence interval below it is the set of plausible values forμ, the mean frustration level of English students, etc.

What we see is that the business confidence interval is way below the other three (it doesn’t overlap with any of them). The math confidence interval overlaps with both the English and the psychology confidence intervals; however, there is no overlap between the English and psychology confidence intervals.

This gives us the impression that the mean frustration level of business students is lower than the mean in the other three majors. Within the other three majors, we get the impression that the mean frustration of math students may not differ much from the mean of both English and psychology students, however the mean frustration of English students may be lower than the mean of psychology students.

Note that this is only an exploratory/visual way of getting an impression of why Hwas rejected, not a formal one. There is a formal way of doing it that is called “multiple comparisons,” which is beyond the scope of this course. An extension to this course will include this topic in the future.

LO 5.1: For a data analysis situation involving two variables,determine the appropriate alternative (non-parametric) method when assumptions of our standard methods are not met.

We will look at one non-parametric test in the k > 2 independent sample setting. We will cover more details later ( Details for Non-Parametric Alternatives ).

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Klay Thompson
Dan Crawford

I love the view from his house, but aye look at Klay living his best life #KlayThompson

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(@teamklay.ig) on

Here’s your weekly summer Klay Thompson update. It looks like he made back to the states after dominating China for the second year in a row just in time to celebrate our country’s birthday yesterday. Just a little backyard BBQ at some Hollywood Hills house featuring somewhere between 25-50 women (I won’t call them IG models, but we can assume) all chilling around the hot tub and pool while Klay practices his chipping stroke. China Klay is officially America Klay once again.

China Klay Thompson Dominates School Beauty Pageant

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When people say “living your best life” this is what they mean. You’re still on the celebration tour of another championship, you just did your thing in China for a few weeks, now it’s time to do it up in back home American style. Food, drinks, sun, pool, and lots of ladies. I can’t imagine many people are living harder than Klay right now.

IN OTHER NEWS: Serena Williams Wins Her First Wimbledon Match as a Mom
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I would say Warriors fans held their breath here, but if we’re being honest Klay could fall off the face of the Earth today and Golden State would still be the betting favorite in Vegas.

I can’t stop watching this… Klay living his best life on the Fourth of July. #KlayFor3 #klaythompson #chinaklay @gsw.all.day

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