INTRODUCTION

In educational research, we are often involved finding out whether there are differences between groups. For example; Is there a difference between males and female? Is there a difference between rural and urban youths? and so forth. The t-test is often used to compare the means between two groups, such as comparing outcomes between control and treatment groups in an experimental study. The t-test is a useful tool for comparing the means of two groups; however, the t-test is not good in situations calling for the comparison of three or more groups. With three or more groups, the t-test is not an effective statistical tool. On a practical level, using the t-test to compare many means (though not impossible) is a cumbersome process in terms of the calculations involved and the high probability of Type I error (which we will discuss later).

SO WHAT DO WE DO?

There are many situations in educational which might require the researcher to compare more than two groups at once. For example, the researcher may be interested in comparing the opinions of low, middle and high income parents or the perceptions of Malays, Chinese, Indians, Kadazandusun and Iban youths on drug addiction. In such situations, the preferred statistical tool is the Analysis Of Variance or ANOVA. Like the t-test, ANOVA can be used to examine differences among the means of several different groups at once. In this section and the next section, the following types of ANOVA will be discussed:

• Oneway Between Groups ANOVA (discussed in this section)
  

• Oneway Repeated Measures ANOVA (discussed in this section)
  

• Two-way Between Groups ANOVA (discussed in the next section)
  

• Two-way repeated Measures ANOVA (discussed in the next section)
  

Learning Outcomes:

After having completed this topic you should be able to:

• explain what is the Oneway ANOVA
  

• provide reasons for using the Oneway ANOVA to test the null hypothesis
  

• state the assumptions for using the Oneway ANOVA
  

• compute Oneway ANOVA using SPSS
  

• interpret the SPSS output for the Oneway ANOVA
  

SELF-CHECK

a) When would you use Oneway ANOVA and not the t-test to compare means?

b) How is the F-ration computed?

c) What are the assumptions that must be met when using ANOVA?

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ANALYSIS OF VARIANCE 

          (ANOVA)

At the heart of ANOVA is the concept of VARIANCE. What is variance? Most of you would say, it the standard deviation squared!. Yes, that is correct. How do use variance used to compute the F-ratio which tells us whether towo or more means are significant. The basic procesure is to derive two different estimates of population variance from the data which is the:

• Between-Group Variance
  

• Within-Group Variance
  

A significant F-value tells us that the population means are probably NOT ALL EQUAL and you reject the null hypothesis if any pairs of means is not equal. Next, you have to locate where the significant lies or which of the means are significantly different. You have to use pos-hoc analysis to determine this.

The F-ratio is obtained by dividing the between-group variance by the within-group variance.

WHAT ABOUT ASSUMPTIONS?

Just like all always, before conducting the Analysis of Variance or ANOVA you must make sure that the necessary assumptions are met. The assumptions for ANOVA are the same as those for the t-test. The TWO most important assumptions are:

• Normality of the Population (Normal distribution): Here you have to make sure that the populations from which you drew the samples are normally distributed. Refer to The Normal Distribution with regards to the graphical and statistical methods in determining population normality.
  

• Homogeneity of Variance: Here you have to determine whether the scores in each group have homogeneous variances. As with the t-test, Levene's Test is used to determine whether variances are equal or unequal.