146 views

Reject $H_0: \mu_1 = \mu_2 = \mu_3$ but not $H_0: \mu_1 = \mu_2, H_0: \mu_3 = \mu_2,$ or $H_0: \mu_1 = \mu_3$? [duplicate]

Is it possible to reject $$H_0\!: \mu_1 = \mu_2 = \mu_3,$$ for example, with an F test in the context of an ANOVA table, but not reject any of the following: \begin{align} H_0\!: \mu_1 &= \mu_2 ...
• 2,186
100 views

Is it possible to get non-significant post hoc test in a significant ANOVA test while the unpair t-tests are significant? [duplicate]

I conducted One-Way ANOVA to compare means in 4 groups. The ANOVA was significant, but the post hoc tests were non-significant. Then, I applied unpair t-tests to compare each group to the lowest group....
25k views

Do we need a global test before post hoc tests?

I often hear that post hoc tests after an ANOVA can only be used if the ANOVA itself was significant. However, post hoc tests adjust $p$-values to keep the global type I error rate at 5%, don't they?...
• 2,197
3k views

Datasets constructed for a purpose similar to that of Anscombe's quartet

I've just come across Anscombe's quartet (four datasets that have almost indistinguishable descriptive statistics but look very different when plotted) and I am curious if there are other more or less ...
58k views

How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure?

I performed with R an ANOVA and I got significant differences. However when checking which pairs were significantly different using the Tukey's procedure I did not get any of them. How can this be ...
• 1,473
22k views

Collinearity between categorical variables

There's a lot about collinearity with respect to continuous predictors but not so much that I can find on categorical predictors. I have data of this type illustrated below. The first factor is a ...
• 3,231
64k views

How can a regression be significant yet all predictors be non-significant? [duplicate]

My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant. All the regression assumptions are met. No multicollinearity ...
• 811
8k views

Significant ANOVA interaction but non-significant pairwise comparisons [duplicate]

I ran a two-way ANOVA and got a significant interaction. I ran a Tukey.HSD() post-hoc test in R and no pairwise comparisons were significant. Is this an error on my ...
• 480
1k views

How much smaller can $p$ values from ANOVA's $F$-test be vs. those from multiple $t$-tests on the same data?

Intro: Having noted the attention received today by this question, "Can ANOVA be significant when none of the pairwise t-tests is?," I thought I might be able to reframe it in an interesting way that ...
• 11.6k
1 vote
2k views

How can I interpret a significant one-way repeated measures ANOVA with non-significant pairwise, bonferroni adjusted, comparisons?

I have a dataset with one factor consisting of four levels. I've run a one-way repeated measures ANOVA on the data, which came out significant. However, for the follow-up pairwise, bonferroni adjusted,...
• 668
491 views

Transitivity of statistical significance

Say I have three sets of observations, $A$, $B$, and $C$ (say, the heights of Australians, Americans and Brits). I assume that they are all normally distributed, independent etc. I perform two-sided ...
534 views

Multiple tests plus correction versus ANOVA - is one always better?

A colleague was using three pair-wise t-tests plus Bonferroni correction to detect any differences in the means of three groups. My first response was to tell him to use an ANOVA instead, since my ...
• 2,212
280 views

Wald test and Type III test don't agree?

I am having trouble understanding the output here. In the green table, it seems like SAS is saying "Gender F" and "Gender M" are not significant. However, in the blue table, seems like it's saying ...
• 1,396
1 vote
271 views

T- test for A, B, C, D

As you know, Student´s t-test is only valid for a pair of variable/experiment. for instance, we can do t-test(A, B). Now, I need to test whether variables A, B, C, D are close to each other or not. ...
• 211