### Analysis of one-way ANOVA in SPSS Statistics

The One-Way ANOVA model is SPSSThis model (the one-way ANOVA) is used to determine if there is a significant difference between the means of two or more independent groups given a continuous dependent variable. The independent variable in a one-way ANOVA is called a factor and the categories of the variable are called factor levels. You will rarely see a comparison being made between two categories but it is a common practice especially in coursework activities to see three or more groups. For example, one might be interested in testing how the students perform in an exam based on their anxiety level (low, medium and high-stressed). Remember that you can differentiate which group is different from which group when you use a one-way ANOVA. Thus, it is an

Omnibustest.Before conducting an analysis using a one-way ANOVA, it is important to assess whether your data meets the following assumptions.

Assumption 1: The dependent variable should be measured on a continuous scale, i.e the variable should either interval or ratio. The assumption can be met by ensuring that appropriate data measurements are used when collecting the data.

Assumption 2: You should have

. Generally, people will always use the independent two-sample t-test when they have two groups.at least two categories for the independent variableAssumption 3: Your observations must be

The observations for each group must be independent.independent.Assumption 4:

Outliers can reduce the validity of your results. The outliers can be detected by use of a Boxplot, a boxplot of each of the categories and the dependent.No significant outliers.Assumption 5: The distribution of the dependent variable for each of the category of the independent variable should be

. The Shapiro-Wilk normality test can be used to test the assumption in SPSS.approximately normalAssumption 6: The

homogeneity of variancesassumptions. This assumption can be tested in SPSS using the Levene's test of homogeneity of variances.Remember that the first three assumptions are related to the data collection procedures.

Case:

The following procedures relate to an analysis which was conducted to determine the

timethat the students took to complete a set of problems based on thecourse level.Therefore, there are three-course levels: beginner, intermediate and advanced course level. Follow the following procedures to run the data analysis in SPSS.

Step by Step Analysis of one-way ANOVA data in SPSSStep 1: Click Analyze > Compare Means > One-Way ANOVA, The screenshot is shown below

Step 2: In the

box transfer your dependent variable to theone-way ANOVA dialoguedependent listand the independent variable to thefactorbox as shown below.Step 3: Click the

Post Hocbutton and check theTukeybox and clickcontinue.Step 4: Click the options button to check the

descriptivecheckbox as shown below.Step 5: Click

Continueand clickOKto get the one-way ANOVA output in SPSS.The following output will be generated for our analysis.

Descriptive statistics

The descriptive statistics table displays the means and the standard deviations by category. The statistics for the combined sample are also displayed.

The ANOVA table

Read the significance of the effect from the ANOVA table depending on your alpha level. For this case, the test statistic is significant at an alpha of 0.05. F(2,27) = 4.467, P = 0.021.

With these results, we do not know which groups are different from which groups, thus it is necessary to conduct multiple comparisons of groups.

Multiple comparison results.

The multiple comparison results using the Tukey test are displayed below, this can be used to check which groups have significantly different means from each other.

We can see from the table below that there is a statistically significant difference in time to complete the problem between the group that took the beginner course and the intermediate course (p = 0.046), as well as between the beginner course and advanced course (p = 0.034). However, there were no differences between the groups that took the intermediate and advanced course (p = 0.989).

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