8.4 Analysis

Here we want to investigate the effects of species and temperature on pulses of individual crickets. Our null hypotheses are that there is no difference in Pulse between Species and no change in Pulse with increasing temperature. We conduct the test at the default \(\alpha\) = 0.05.

We use the lm() function to fit the model, and the formula looks identical to the main-effects ANOVA and linear regression models from Chapter 4. Isn’t that handy?

# Fit the model
cricket_mod <- lm(Pulse ~ Species + Temp, data=crickets)

Install the car package. We need a function from this package for model summary because now we have a mix of categorical and continuous explanatory variables. This means we want to calculate the sums of squared errors a little differently than we did before.

# Load the package after it's installed
library(car)

Now we create the ANVOA table for our ANCOVA model

car::Anova(cricket_mod, type='III')

## Anova Table (Type III tests)
## 
## Response: Pulse
##             Sum Sq Df   F value    Pr(>F)    
## (Intercept)   25.5  1    7.9906  0.008582 ** 
## Species      598.0  1  187.3994 6.272e-14 ***
## Temp        4376.1  1 1371.3541 < 2.2e-16 ***
## Residuals     89.3 28                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

And we can look at the summary:

summary(cricket_mod)

## 
## Call:
## lm(formula = Pulse ~ Species + Temp, data = crickets)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.0128 -1.1296 -0.3912  0.9650  3.7800 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -7.21091    2.55094  -2.827  0.00858 ** 
## Speciesniv  -10.06529    0.73526 -13.689 6.27e-14 ***
## Temp          3.60275    0.09729  37.032  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.786 on 28 degrees of freedom
## Multiple R-squared:  0.9896, Adjusted R-squared:  0.9888 
## F-statistic:  1331 on 2 and 28 DF,  p-value: < 2.2e-16

We see that there are significant effects of species and temperature on the pulse of individual crickets. Everything else proceeds as in the analyses Chapter 4! We can build in complexity as needed, and we can make predictions as we did before.