Question

Scenario: You conducted research on annual salary for randomly-selected college graduates five years after their graduation dates. There were three groups of graduates:

• Nursing College Degree (1)
• Math College Degree (2)
• Biology College Degree (3)

The following hypothesis guided your research:

1. There is no statistically significant difference in the annual salaries of the three degree types

type   salary (in thousands)
1.00   22.00
1.00   15.00
1.00   28.00
1.00   64.00
1.00   35.00
1.00   31.00
1.00   20.00
1.00   46.00
1.00   21.00
1.00   13.00
1.00   11.00
1.00   12.00
1.00   30.00
1.00   27.00
1.00   29.00
1.00   23.00
1.00   21.00
1.00   20.00
1.00   25.00
1.00   23.00
2.00   29.00
2.00   60.00
2.00   50.00
2.00   75.00
2.00   84.00
2.00   31.00
2.00   32.00
2.00   40.00
2.00   45.00
2.00   23.00
2.00   61.00
2.00   55.00
2.00   26.00
2.00   28.00
2.00   39.00
2.00   44.00
2.00   42.00
2.00   51.00
2.00   41.00
2.00   58.00
3.00   50.00
3.00   52.00
3.00   31.00
3.00   90.00
3.00   99.00
3.00   82.00
3.00   71.00
3.00   40.00
3.00   31.00
3.00   28.00
3.00   46.00
3.00   49.00
3.00   52.00
3.00   19.00
3.00   45.00
3.00   54.00
3.00   38.00
3.00   38.00
3.00   59.00
3.00   27.00

1. Were the results of the omnibus ANOVA test statistically significant? Explain why or why not.

2. If the results of the ANOVA were statistically significant, run the appropriate post-hoc comparisons the answer the research hypothesis

Be sure to include SPSS outputs when needed

Answer 1

Omnibus tests are a kind of statistical test. They test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall.

ANOVA (Analysis of Variance)

ANOVA is a statistical technique that assesses potential differences in a scale-level dependent variable by a nominal-level variable having 2 or more categories. For example, an ANOVA can examine potential differences in IQ scores by Country (US vs. Canada vs. Italy vs. Spain). Developed by Ronald Fisher in 1918, this test extends the t and the z test which have the problem of only allowing the nominal level variable to have two categories. This test is also called the Fisher analysis of variance.

The use of ANOVA depends on the research design. Commonly, ANOVAs are used in three ways: one-way ANOVA, two-way ANOVA, and N-way ANOVA.

One-Way ANOVA

A one-way ANOVA has just one independent variable. For example, difference in IQ can be assessed by Country, and County can have 2, 20, or more different categories to compare.

Two-Way ANOVA

A two-way ANOVA (are also called factorial ANOVA) refers to an ANOVA using two independent variables. Expanding the example above, a 2-way ANOVA can examine differences in IQ scores (the dependent variable) by Country (independent variable 1) and Gender (independent variable 2). Two-way ANOVA can be used to examine the interaction between the two independent variables. Interactions indicate that differences are not uniform across all categories of the independent variables. For example, females may have higher IQ scores overall compared to males, but this difference could be greater (or less) in European countries compared to North American countries.

N-Way ANOVA

A researcher can also use more than two independent variables, and this is an n-way ANOVA (with n being the number of independent variables you have). For example, potential differences in IQ scores can be examined by Country, Gender, Age group, Ethnicity, etc, simultaneously.

Post hoc tests are an integral part of ANOVA. When you use ANOVA to test the equality of at least three group means, statistically significant results indicate that not all of the group means are equal. However, ANOVA results do not identify which particular differences between pairs of means are significant. Use post hoc tests to explore differences between multiple group means while controlling the experiment-wise error rate.

A post hoc test is used only after we find a statistically significant result and need to determine where our differences truly came from. The term “post hoc” comes from the Latin for “after the event”. There are many different post hoc tests that have been developed, and most of them will give us similar answers. We will only focus here on the most commonly used ones. We will also only discuss the concepts behind each and will not worry about calculations.

SPSS Statistics generates quite a few tables in its one-way ANOVA analysis. In this section, we show you only the main tables required to understand your results from the one-way ANOVA and Tukey post hoc test. For a complete explanation of the output you have to interpret when checking your data for the six assumptions required to carry out a one-way ANOVA.

This includes relevant boxplots, and output from the Shapiro-Wilk test for normality and test for homogeneity of variances. Also, if your data failed the assumption of homogeneity of variances, we take you through the results for Welch ANOVA, which you will have to interpret rather than the standard one-way ANOVA in this guide.