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 possible?
Here is the code:
fit5_snow<- lm(Response ~ Stimulus, data=audio_snow)
anova(fit5_snow)
> anova(fit5_snow)
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
Stimulus 5 73.79 14.7578 2.6308 0.02929 *
Residuals 84 471.20 5.6095
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
df<-df.residual(fit5_snow)
MSerror<-deviance(fit5_snow)/df
comparison <- HSD.test(audio_snow$Response, audio_snow$Stimulus, df, MSerror, group=FALSE)
> comparison <- HSD.test(audio_snow$Response, audio_snow$Stimulus, df, MSerror, group=FALSE)
Study:
HSD Test for audio_snow$Response
Mean Square Error: 5.609524
audio_snow$Stimulus, means
audio_snow.Response std.err replication
snow_dry_leaves 4.933333 0.6208034 15
snow_gravel 6.866667 0.5679258 15
snow_metal 6.333333 0.5662463 15
snow_sand 6.733333 0.5114561 15
snow_snow 7.333333 0.5989409 15
snow_wood 5.066667 0.7713110 15
alpha: 0.05 ; Df Error: 84
Critical Value of Studentized Range: 4.124617
Comparison between treatments means
Difference pvalue sig LCL UCL
snow_gravel - snow_dry_leaves 1.9333333 0.232848 -0.5889913 4.455658
snow_metal - snow_dry_leaves 1.4000000 0.588616 -1.1223246 3.922325
snow_sand - snow_dry_leaves 1.8000000 0.307012 -0.7223246 4.322325
snow_snow - snow_dry_leaves 2.4000000 0.071587 . -0.1223246 4.922325
snow_wood - snow_dry_leaves 0.1333333 0.999987 -2.3889913 2.655658
snow_gravel - snow_metal 0.5333333 0.989528 -1.9889913 3.055658
snow_gravel - snow_sand 0.1333333 0.999987 -2.3889913 2.655658
snow_snow - snow_gravel 0.4666667 0.994348 -2.0556579 2.988991
snow_gravel - snow_wood 1.8000000 0.307012 -0.7223246 4.322325
snow_sand - snow_metal 0.4000000 0.997266 -2.1223246 2.922325
snow_snow - snow_metal 1.0000000 0.855987 -1.5223246 3.522325
snow_metal - snow_wood 1.2666667 0.687424 -1.2556579 3.788991
snow_snow - snow_sand 0.6000000 0.982179 -1.9223246 3.122325
snow_sand - snow_wood 1.6666667 0.393171 -0.8556579 4.188991
snow_snow - snow_wood 2.2666667 0.103505 -0.2556579 4.788991
