First, let’s plot the data
bwplot(Pair~Percentage, data=fish)
densityplot(~Percentage, groups = Pair, auto.key = TRUE, data=fish)
We might be wondering whether the length matters, or whether there is a lot of variation between the different male pairs. Let’s plot the data:
plot(fish$Length, fish$Percentage)
It certainly doesn’t look like there is a linear trend there.
Let’s go back to the boxplot
bwplot(Pair~Percentage, data=fish)
Do the variances look equal here? It looks like there is an outlier.
Let’s look at some diagnostic plots
fit <- lm(Percentage~Pair, data=fish)
plot(fit, 1)
plot(fit, 2)
There are definitely outliers there – maybe it’s love!
summary(lm(Percentage~Pair, data=fish))
##
## Call:
## lm(formula = Percentage ~ Pair, data = fish)
##
## Residuals:
## Min 1Q Median 3Q Max
## -52.429 -8.414 0.247 10.859 28.871
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 56.406 3.864 14.597 <2e-16 ***
## PairPair2 4.479 5.657 0.792 0.4308
## PairPair3 6.023 5.384 1.119 0.2667
## PairPair4 10.594 5.657 1.873 0.0649 .
## PairPair5 7.805 6.441 1.212 0.2292
## PairPair6 6.929 5.657 1.225 0.2243
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.46 on 78 degrees of freedom
## Multiple R-squared: 0.04796, Adjusted R-squared: -0.01307
## F-statistic: 0.7858 on 5 and 78 DF, p-value: 0.563
The F-test doesn’t say that the pairs are different.
Let’s check for normality one last time, and run the test
hist(fish$Percentage)
t.test(mean(Percentage ~ Pair, mu=50, data = fish))
##
## One Sample t-test
##
## data: mean(Percentage ~ Pair, mu = 50, data = fish)
## t = 42.864, df = 5, p-value = 1.304e-07
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 58.63722 66.11885
## sample estimates:
## mean of x
## 62.37803