Group Comparison

Question

Section 1 data values: 76.6, 87.2, 78.6, 83.5, 68.8, 75.5, 92.9, 84.4, 89.2

Section 2 data values: 65.6, 66.5, 92.1, 71.4, 72.8, 52.4, 76.6, 88.5, 49.8

Section 3 data values: 75.8, 87, 89.5, 82.1, 72.1, 83.5, 82.9, 79, 80.3

Run a one-way ANOVA (fixed effect) with ∝ = 0.05. Round the F-ratio to three decimal places and the p-value to four decimal places. Assume all population and ANOVA requirements are met.

Answer 1

While not impossible to do by hand, since it was not specified I will show a machine method using the R program language. Similar results can be gotten from SAS, SPSS, or JASP.

library(tidyr)

#input data

sec1 = c(76.6, 87.2, 78.6, 83.5, 68.8, 75.5, 92.9, 84.4, 89.2)

sec2 = c(65.6, 66.5, 92.1, 71.4, 72.8, 52.4, 76.6, 88.5, 49.8)

sec3 = c(75.8, 87, 89.5, 82.1, 72.1, 83.5, 82.9, 79, 80.3)

df = data.frame(sec1,sec2,sec3)

# format data for R

df_long <- pivot_longer(df, cols = 1:3, names_to ="section",

# do ANOVA

summary(aov(value~section ,data = df_long))

# Alternate method

model = lm(value~section ,data = df_long)

result = anova(model)

print(result)

Results:

Df Sum Sq Mean Sq F value Pr(>F)

section 2 723.5 361.7 3.740 0.0386 *

Residuals 24 2321.5 96.7

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1