The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state.

Following is the multiple regression output with Y= % Passing as the dependent variable, X 1 = Salaries and X 2 = Spending:

Regression Statistics

Multiple R	0.4276
R Square	0.1828
Adjusted R Square	0.1457
Standard Error	5.7351
Observations	47

 

ANOVA

	d¦	SS	MS	F	Significance F
Regression	2	323.8284	161.9142	4.9227	0.0118
Residual	44	1447.2094	32.8911
Total	46	1771.0378

 

	Coefficients	Standard Error	t Start	P-value	Lower 95%	Upper 95%
Intercept	-72.9916	45.9106	-1.5899	0.1190	-165.5184	19.5352
Salary	2.7939	0.8974	3.1133	0.0032	0.9853	4.6025
Spending	0.3742	0.9782	0.3825	0.7039	-1.5972	2.3455

 

Referring to Scenario 13-15, estimate the mean percentage of students passing the proficiency test for all the schools that have a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

When you choose to analyse your data using a ANOVA, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a one-way ANOVA. You need to do this because it is only appropriate to use a one-way ANOVA if your data "passes" six assumptions that are required for a one-way ANOVA to give you a valid result. In practice, checking for these six assumptions just adds a little bit more time to your analysis, requiring you to click a few more buttons in SPSS Statistics when performing your analysis, as well as think a little bit more about your data, but it is not a difficult task.

Assumptions :

Assumption #1: Your dependent variable should be measured at the interval or ratio level (i.e., they are continuous). Examples of variables that meet this criterion include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth.

Assumption #2: Your independent variable should consist of two or more categorical, independent groups. Typically, a one-way ANOVA is used when you have three or more categorical, independent groups, but it can be used for just two groups (but an independent-samples t-test is more commonly used for two groups). Example independent variables that meet this criterion include ethnicity (e.g., 3 groups: Caucasian, African American and Hispanic), physical activity level (e.g., 4 groups: sedentary, low, moderate and high), profession (e.g., 5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.

Assumption #3: You should have independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you can test for, but it is an important assumption of the one-way ANOVA. If your study fails this assumption, you will need to use another statistical test instead of the one-way ANOVA (e.g., a repeated measures design).

Assumption #4: There should be no significant outliers. Outliers are simply single data points within your data that do not follow the usual pattern (e.g., in a study of 100 students' IQ scores, where the mean score was 108 with only a small variation between students, one student had a score of 156, which is very unusual, and may even put her in the top 1% of IQ scores globally). The problem with outliers is that they can have a negative effect on the one-way ANOVA, reducing the validity of your results. Fortunately, when using SPSS Statistics to run a one-way ANOVA on your data, you can easily detect possible outliers. In our enhanced one-way ANOVA guide, we: (a) show you how to detect outliers using SPSS Statistics; and (b) discuss some of the options you have in order to deal with outliers.

Assumption #5: Your dependent variable should be approximately normally distributed for each category of the independent variable. We talk about the one-way ANOVA only requiring approximately normal data because it is quite "robust" to violations of normality, meaning that assumption can be a little violated and still provide valid results. You can test for normality using the Shapiro-Wilk test of normality, which is easily tested for using SPSS Statistics.

Assumption #6: There needs to be homogeneity of variances. You can test this assumption in SPSS Statistics using Levene's test for homogeneity of variances. If your data fails this assumption, you will need to not only carry out a Welch ANOVA instead of a one-way ANOVA, which you can do using SPSS Statistics, but also use a different post hoc test. In our enhanced one-way ANOVA guide, we (a) show you how to perform Levene's test for homogeneity of variances in SPSS Statistics, (b) explain some of the things you will need to consider when interpreting your data, and (c) present possible ways to continue with your analysis if your data fails to meet this assumption, including running a Welch ANOVA in SPSS Statistics instead of a one-way ANOVA, and a Games-Howell test instead of a Tukey post hoc test.

Steps to perform the AVOVA:

1. Click Analyze > Compare Means > One-Way ANOVA
2. You will be presented with the One-Way ANOVA dialogue box.
3. Transfer the dependent variable, Time, into the Dependent List: box and the independent variable, Course, into the Factor: box using the appropriate Right arrow buttons (or drag-and-drop the variables into the boxes).
4. Click on the Post hoc button. Tick the Tukey checkbox
5. Click on the Continue button.
6. Click on the Options button. Tick the Descriptive checkbox in the -Statistics- area
7. Click on the Continue button.
8. Click on the OK button.