One Way Anova

1. To examine mean differences between two or more groups.

2. It is a bivariate test with one IV and one DV. 3. The IV must be categorical and the DV must

be continuous.4. Post hoc comparisons. 5. Check for whether the homogeneity of

variance has been met.

Assumptions:

The assumptions are:1. Each sample is an independent random sample2. The distribution of the response variable

follows a normal distribution3. The population variances are equal across

responses for the group levels. This can be evaluated by using the following rule of thumb: if the largest sample standard deviation divided by the smallest sample standard deviation is not greater than two, then assume that the population variances are equal.

Example: One-way ANOVA with post-hoc analysis

• Analyze• Compare Means

and One-Way ANOVA

• Select variable, click button into Dependent List box

• Select independent variable and click the button to move into the Factor box

Example: One-way ANOVA with post-hoc analysis

• Select variable, click button into Dependent List box

• Select independent variable and click the button to move into the Factor box

• Click Option• Click Descriptive

and Homogeneity of variance test

• Click Continue

Example: One-way ANOVA with post-hoc analysis

• Select variable, click button into Dependent List box

• Select independent variable and click the button to move into the Factor box

• Click Option• Click Descriptive and

Homogeneity of variance test

• Click Continue

Example: One-way ANOVA with post-hoc analysis

• Click on the Post Hoc

• You can see One Way ANOVA

• Click on the check box Tukey for Tukey’s HSD multiple comparison

• Click Continue and OK

Example: One-way ANOVA with post-hoc analysis

Levene’s test for homogeneity of variances is not significant (p>.05), so we could say that the population variances for each group are approximately equal

Significant can be determined by looking at the F-probabilityvalue. Given that p < 0.05, we can reject the null hypothesisand accept the alternative hypothesis that states expenditureon electricity and gas is different across capital cities

Example: One-way ANOVA with post-hoc analysis

We can go further and determine which cities is there a significant difference in energy cost? Tukey’s HSD test shows that Adelaide and Perth have significantly different mean energy costs.

Example: One-way ANOVA with post-hoc analysis

Descriptivesmikro1

N Mean Std. Deviation Std. Error

95% Confidence Interval for Mean

Minimum MaximumLower Bound Upper Bound

matrik 12 61.92 7.561 2.183 57.11 66.72 45 70

stpm 11 73.73 8.615 2.598 67.94 79.51 58 84

diploma 12 70.33 9.528 2.751 64.28 76.39 56 85

Total 35 68.51 9.748 1.648 65.17 71.86 45 85

ANOVA

mikro1

Sum of Squares df Mean Square F Sig.

Between Groups 860.978 2 430.489 5.813 .007

Within Groups 2369.765 32 74.055

Total 3230.743 34

Example: One-way ANOVA with post-hoc analysis

Multiple Comparisons

mikro1Tukey HSD

(I) saluran (J) saluranMean Difference

(I-J) Std. Error Sig.

95% Confidence Interval

Lower Bound

Upper Bound

matrik stpm -11.811* 3.592 .007 -20.64 -2.98

diploma -8.417 3.513 .057 -17.05 .22

stpm matrik 11.811* 3.592 .007 2.98 20.64

diploma 3.394 3.592 .616 -5.43 12.22

diploma matrik 8.417 3.513 .057 -.22 17.05

stpm -3.394 3.592 .616 -12.22 5.43

*. The mean difference is significant at the 0.05 level.