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I am wondering how I should best interpret the results below. This is comparing weekdays with a count of 59 data values each (new shoes produced).

According to documentation, I should reject the null hypothesis (H0: μ1 = μ2 = μ3 = μ4 = μ5) because F is higher than F crit.

Also: the p value (0.04) is slightly lower than the alpha level (0.05) which means I should reject the null hypothesis? Again the difference is only 0.1.

My question about this is, in this case F is only 0.1 higher, so should I still reject the null hypothesis or what conclusion should I draw here? Also, any advice on the next step is appreciated.

Anova: Single Factor            

SUMMARY           
Groups  Count Sum Average Variance    
Monday  59  980 16.61016949 28.82817066   
Tuesday 59  1013  17.16949153 17.45353594   
Wednesday 59  1123  19.03389831 13.44710695   
Thursday  59  1026  17.38983051 21.10403273   
Friday  59  1025  17.37288136 14.13442431   


ANOVA           
Source of Variation SS  df  MS  F P-value F crit
Between Groups  193.579661  4 48.39491525 2.547978632 0.039572509 2.402774956
Within Groups 5508.101695 290 18.99345412     

Total 5701.681356 294       
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    $\begingroup$ 0.05-0.04 is not 0.1 $\endgroup$
    – Glen_b
    Nov 5 '15 at 15:31
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It depends on your rule. If you established ahead of time that $\alpha=0.05$ and that your rule is that you reject $H_0$ when $p<\alpha$, then you should reject when $p<0.05.$ As such, in this case you should reject $H_0$. It doesn't matter how much larger $\alpha$ is, but the rule is merely that you reject $H_0$ when $p<\alpha$ and you fail to reject $H_0$ otherwise.

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  • $\begingroup$ So would such a rule, that α=0.05 and that your rule is that you reject H0 when p<α -- be reasonable? This seems to be "standard practice"? What do I need to be aware of when deciding what the rule should be? $\endgroup$
    – Carlo Otto
    Nov 5 '15 at 15:15
  • $\begingroup$ I would argue that this is "standard practice," yes. I would look into your field's literature - what do other people asking similar questions tend to use? Do they have a fixed $\alpha$ of 0.05? Is it higher/lower? Do they use a different metric? These answers should be online. I also think that a reasonable next step is to explore the TukeyHSD test (or Dwass-Steel-Critchlow-Fligner if your data are not Normal) to see which groups (i.e. Monday, Tuesday) are significantly different from one another. This will give you more information than "at least one group is different from the others." $\endgroup$
    – Matt Brems
    Nov 5 '15 at 15:27
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    $\begingroup$ In fact you should also reject when $p=\alpha$ (as can happen in the case that the statistic has a discrete distribution). $\endgroup$
    – Glen_b
    Nov 5 '15 at 15:33
  • $\begingroup$ Is that standard practice, Glen_b? My understanding is that if $p=\alpha,$ the results are inconclusive. $\endgroup$
    – Matt Brems
    Nov 5 '15 at 15:51

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