Visualization – Histogram

Analysis Variable: Age
Class Mean Std Dev Min Max N Variance Skewness {-1 to 1} Kurtosis {-2 to 2}
Freshman 19.22 1.08 17.00 21.00 37 1.17 -0.041 -0.467
Junior 20.84 1.19 19.00 23.00 31 1.41 -0.052 -0.879
Senior 22.09 1.23 20.00 25.00 32 1.51 0.704 0.519
Sophomore 20.33 1.34 18.00 23.00 34 1.80 0.082 -1.082

Dependent variable: Interval or Ratio?

Independent variable: Has two or more categories?

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Observations: Are they independent?

Dependent variable: Normally distributed each group?

HoV: Is Levene’s Test significant (Pr>F is less than α)?

If no, fail to reject the null hypothesis, you have HoV.

If significant then you do not have HoV and must use another test, Welch’s ANOVA for example.

ANOVA results: Are they significant (Pr>F less than α)?

If no, fail to reject the null hypothesis

If yes, reject the null hypothesis and accept the alternative hypothesis, the group means are different at a statistically significant level. (Remember α = 0.05)

However, which group is different?

Visually, looking at the boxplot, they all look different from each other, but statistically, SAS gives us a method to examine the difference between each group.

Source DF Sum of Squares Mean Square F Value Pr > F
Model 3 146.40 48.80 33.28 <.0001
Error 130 190.62 1.47
Corrected Total 133 337.02

ANOVA Results

Levene’s Test for Homogeneity of Age Variance
ANOVA of Squared Deviations from Group Means
Source DF Sum of Squares Mean Square F Value Pr > F
Class 3 6.67 2.22 0.76 0.516
Error 130 378.30 2.91

Group Comparison (Tukey-Kramer): Example

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