One-way ANOVA (Analysis of variance) is used to determine if the difference between means of two or more unrelated groups is statistically significant. People don’t usually perform one-way ANOVA when there are just two groups because student t test is already available for such condition. When there are more than two groups, one-way ANOVA tells whether at least two group differ in their means but doesn’t specify which are those groups. If we really want to know in specific which are those groups that differ, we have to run a post-hoc test. If there is a third intervening variable, we have to statistically control that variable using “ANCOVA” which is known as Analysis of Co-variance
Criteria for using one-way ANOVA
b. The dependent variable should be numeric
c. The members in one group should not be part of another group (i.e. groups should be unrelated)
d. For more accurate results, the outliers from the observation should be removed as far as possible.
e. The dependent variable should be normally distributed (as far as possible)
f. There should be homogeneity of variance between the groups. The homogeneity of variance can be tested using “Levene’s test of homogeneity”
g. In case of non-homogenous variance, the alternative to one-way ANOVA is Welch ANOVA and alternative to post-hoc is Games-Howell test
Steps of calculating One-way ANOVA using SPSS:
Step 1. First identify the independent variable that defines two or more groups. For example, "Educational status" with 5 different categories.
Step 2. Select the dependent variable which is numeric. For example, income (expressed in numbers). We compare the mean of that dependent dependent variable across those five different groups as stated in step 1.
Step 3: Go to analyze, compare means and select One way ANOVA.
Step 4: A dialog box appears in which you have to drag the dependent variable (e.g. household income) to the dependent List and drag the independent variable (e.g. level of education) to Factor.
Step 5: If you want to show means plot and descriptive statistics too in addition, then go to options and select descriptive and means plot and click continue then click ok.
Step 6. Then you see the following output with two tables and a figure.
Interpretation of output:
- The first table shows the descriptive statistics of dependent variable i.e. income for each category of independent variable.
- The second table is about the one way ANOVA statistics in which P value is shown as 0.000 (which is less than 0.05 and even 0.01) so we can conclude that the mean income difference across different levels of education is statistically significant.
- The third picture is an illustration of the mean income plotted in graph among different levels of education.
- However, if we want to know the comparison between each level of education against another, we have to run post-hoc tests which we shall cover in later tutorials!
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