ONE WAY ANOVA USING SPSS

Hello everyone, In this post, we will be discussing that how to run the One Way ANOVA using SPSS. One-way analysis of variance is a statistical technique used for comparing means of more than two groups. This technique can be used in a situation where the data is measured either on interval or ratio scale. In one-way ANOVA, group means are compared by comparing the variability between groups with that of variability within the groups. This is done by computing an F-statistic. There are varieties of situations in which one-way analysis of variance can be used to compare the means of more than two groups.

Lets illustrate this with an example using SPSS. Imagine that a researcher is interested to see that if annual income level (in US$) is same or different across the four regions of a particular city e.g. New York. The regions in his study are east, west, north, and south. To check this, you need to follow the procedure of developing hypothesis, collection of data, running the One way ANOVA, and then based on the test results accepting or rejecting the hypothesis, and finally arriving on conclusion.

Suppose that researcher developed the following hypothesis

Null Hypothesis= H0= Annual income level of residents in the four regions of city are same.

Alternative Hypothesis= H1= Annual income level of residents in the four regions of city are statistically different.

To test this hypothesis, the researcher collects random annual income data from twenty people belonging to four regions. Let say the data collected is as under in US$ per annum.

East= 22000, 15000, 30000, 22000, 26000

West= 35000, 37000, 42000, 39000, 29000

North=45000, 39000, 35000, 45000, 29000

South=19000, 25000, 22000, 24000, 30000

To run the One Way ANOVA in SPSS, you need to first input the variables and data. For this study, you need to put two variables namely Annual Income in US$ and Region (For details on how to input the variables and data in to SPSS, please see our previous posts)

Once you have input the variables and data in to SPSS, now you are in position to run the one way ANOVA test by applying the following command.

Analyze---Compare Means---- One Way ANOVA

A dialogue box will appear which will show both variables Now take the ‘AnnualIncomeUS$’ to the ‘dependent list’, and ‘Region’ variable in to ‘Factor’ box. Then click on ‘Post Hoc’ option and check the ‘Scheffe’, click on continue. Then click on ‘Options’ and check the ‘Descriptive’ and ‘Means plot’ and click on continue, and then on ‘OK’.

 The results will appear in the ‘output window’ which can be interpreted as follow. 

The first table with the heading ‘Descriptive’ is only giving basic information including sample size for each group, mean, standard deviation, minimum, and maximum values. 

The second table with the heading ‘ANOVA’ will show the basic statistics such as F statistics, sig value and so on. In this example, the value of F is 11.229 with the Sig value of 0.000 which shows that there are significant mean differences between groups. In another words, the mean annual income in this example is statistically different among four groups namely east, west, north, and south. The F Statistics has some limitation as it only tells us that whether there are differences in means between different groups or not. Further, post hoc tests such as test Scheffe is used to identify the differences between means of individual groups.

The next table with the heading ‘Multiple Comparisons’ is based on the test Schefffe to discover that which groups have significant differences between them. Starting with the first row, you will find that here the reference point is east and further its comparison with west, north, and south is given. Here, the important point is the individual Sig value which shows that whether east has significant differences with other groups. So in this example, the value of Sig which is .012 in the first row shows that there are significant differences between annual income in US$ between east and west citizens. Similarly, in second row, the sig value of 0.003 shows that the average difference between east and north is also statistically significant. In the third row, the sig value of .993 shows that the mean annual income difference between the citizens of east and south are not statistically different; or in another words they are very similar (you can also check this by simply going through data visually)

Similarly, the comparison is also based on west, north, and south with other groups is given which can be interpreted accordingly.

(Note: if in Post hoc test, the sig value appears less than 0.05 then the interpretation will be that there are significant differences exist between those two groups; however, if sig value appears greater than 0.05, then the interpretation will be that there are insignificant differences exist between those two groups.)

The graph with heading ‘Mean Plot’ is used to visually see the differences between four groups. Its interpretation is also relatively simple, as you can see the average income on one axis and four groups on the other.

Finally, based on the value of F statistics and its Sig value given in the first table, we can accept the alternative hypothesis and reject the null hypothesis. Thus, the conclusion is that the average income in US$ in this city are statistically different among four regions.

(Note: If F statistics appears smaller and Sig value greater than 0.05, then we will reject the alternative hypothesis and accept the null hypothesis. Similarly, if F statistics appears greater than 4 and sig value appears less than 0.05, then we will accept the alternative hypothesis and reject the null hypothesis.)

Sample SPSS File is as under.
One Way ANOVA SPSS Practice file

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