`install.packages("pwr")`

`library(pwr)`

#### INPUT THE SAMPLE SIZES, MEAN CALVING SUCCESS AND STANDARD ERRORS FROM MANN, ET AL. 2008.

```
# Non-spongers:

n_nonspongers=116
mean_CS_nonspongers=0.132
SE_CS_nonspongers=0.008

# Spongers:

n_spongers=16
mean_CS_spongers=0.156
SE_CS_spongers=0.018

#### CALCULATE DIFFERENCE IN MEASURED CALVING SUCCESS BETWEEN SPONGERS AND NONSPONGERS

percent_increase=(mean_CS_spongers - mean_CS_nonspongers)/mean_CS_nonspongers

print(paste("Percent Increase in Sponger Calving Success: ", 100*round(percent_increase, digits=2), "%"))
```

#### CONVERT STANDARD ERRORS TO STANDARD DEVIATIONS

```
SD_CS_nonspongers=SE_CS_nonspongers*sqrt(n_nonspongers)
SD_CS_spongers=SE_CS_spongers*sqrt(n_spongers)
```

#### CALCULATE TERMS FOR POWER ANALYSIS

```
SS_within=(n_nonspongers-1)*SD_CS_nonspongers^2 + (n_spongers-1)*SD_CS_spongers^2
df_within=n_nonspongers + n_spongers - 2
SD_within=sqrt(SS_within/df_within)
```

#### PERFORM POWER ANALYSIS FOR A TWO-SIDED TEST

```
## RUN POWER ANALYSIS
power_test_results=pwr.t2n.test(n1=n_nonspongers, n2=n_spongers, d=NULL, sig.level = 0.05, power = 0.8,
```