ANOVA

What is ANOVA?

- ANOVA is apply for more than 2 groups or category independent variable.

- If only 1 classifying the variable, then we have one-way ANOVA but if 2 classifying variables are present, then we will have two-ways ANOVA

One-way ANOVA is conducted to access whether population means significantly different among groups. If overall ANOVA test is significant then pairwise comparison test should be conducted to investigate which 2 populations means significantly different.

For example:

We have result of the treatment for three different races which is Malay1, Chinese2 and Indian3 and we interested in testing whether these population means different.

Step 1: Generate the hypothesis

Ho: m1=m2=m3

Ha: At least two of the treatment groups are different.

Step 2: Set the significance level

α = 0.05

Step 3: Checking the assumptions

Assumptions for ANOVA

- Random sample from statement

              - The observations are independent:

                 Each observation refer to different group

* If the distribution is normal

 Select Analyze=>Descriptive Statistics=> Explore

               •Insert treatment in the Dependent List box.

               •Insert group in the Factor List box.

•               * In the Explore: Plot, click on the Normality Plots with Test and Histogram.  

From statistical technique,

*p value Shapiro-Wilk for Malay1= 0.441 (>0.05), not significant (Normal)

*p value Shapiro-Wilk for Chinese2= 0.611 (>0.05), not significant (Normal)

*p value Shapiro-Wilk for Indian3= 0.222 (>0.05), not significant (Normal)

From graphically, all graphs show normal distribution

So, assumption is met. Distribution is normal

Step 4 :Test statistics using SPSS:

        »Analyze => Compare mean  = > One-way ANOVA.

        »Insert Treatment in Dependent List box.

        »Insert Group in Factor box.

        »Select Post Hoc and click Bonferroni and continue.

        »Select Option and click Descriptive and Homogeneity of variance test and continue.

        »Select Ok.

Step 5: Interpretation

        •p value is 0.001, reject Ho.

        •At least two groups of treatment is significance difference

        •Use Post Hoc test: Bonferroni

      •To check which groups has significance difference

    

Step 6: Conclusion

  At 5% level of significance, at least two groups of treatment is statistically significance difference (p value=0.001).

  By using Post Hoc Test, there is statistically significance difference between races (p value = 0.001).

By: Nur Fariza

References :

- http://www.statisticssolutions.com/manova-analysis-anova/

- http://support.minitab.com/en-us/minitab/17/topic-library/modeling-statistics/anova/basics/what-is-anova/

- http://www.statisticssolutions.com/Conduct-and-Interpret-One-Way-ANOVA/