Differences Between Groups: t-Test and ANOVA/ANCOVA

You will take part in several data analysis assignments in which you will develop a report using tables and figures from the IBM SPSS® output file of your results. Using the resources and readings provided, you will interpret these results and test the hypotheses and writeup these interpretations. As doctoral students, your assignments are expected to follow the principles of high-quality scientific standards and promote knowledge and understanding in the field of public administration.

You should apply a rigorous and critical assessment of a body of theory and empirical research, articulating what is known about the phenomenon and ways to advance research about the topic under review.

Research syntheses should identify significant variables, a systematic and reproducible search strategy, and a clear framework for studies included in the larger analysis.

Copy and paste all tables and figures into a Word document and format the results in APA current edition.

Interpret your results.

Final report should be formatted using APA current edition, and in a Word document.

15-20 double-spaced pages of content in length (not counting the title page or references).

Manuscripts should not be written in first person (“I”).

All material should be 12-point, Times New Roman type, double-spaced with margins of one inch.

All manuscripts should be clearly and concisely written, with technical material set off. Do not use jargon, slang, idioms, colloquialisms, or bureaucratese. Use acronyms sparingly and spell them out the first time you use them. Do not construct acronyms from phrases you repeat frequently in the text.

This assignment has three parts and uses the Florida County Government. sav dataset. Load the data set into SPSS.

Address the following research question using an independent samples t-test:

RQ 3: Is there a significant difference in the percent of total spending that is environmental spending between coastal counties and non-coastal counties?

H03: There is no statistically significant difference in the percent of total spending that is environmental spending between coastal counties and non-coastal counties.

Ha3: There is a statistically significant difference in the percent of total spending that is environmental spending between coastal counties and non-coastal counties.

Open the data file Florida County Government. sav.

Perform an error bar plot first.

Click on Graphs/Legacy Dialogs/Error Bar.

Click on Simple button and then radio button “summaries for groups of cases” then click on Define.

Move to Variable box on the right the dependent variable Average % Envir. Spending in Total spending (AverageEnvirTotal).

Move Coastal Area or Not to Category Axis box. This is the independent groups variable. There are two groups: coastal county=1 and not coastal county=0.

Click OK.

Edit the error bar plot by adding data labels and title.

Follow directions in Cronk and in the resources provided. What do you think from that plot you would expect to find in an independent samples t-test?

Now, perform an independent t samples t-test with:

coastal (1)/non-coastal county (0) as your independent variable groups and

Average % Envir. Spending in Total spending (AverageEnvirTotal) as your dependent variable.

Use Cronk and resources provided to interpret the results of the Levene’s test of assumed equal variances and then interpret the t-test results and report based on the testing of your hypotheses.

Address the following research question using a One-Way ANOVA test:

RQ 4: Is there a significant difference in the intergovernmental revenue growth rate (IGR) based on county type (metro/suburban/rural)?

H04: There is no statistically significant difference in the intergovernmental revenue growth rate (IGR) based on county type (metro/suburban/rural).

Ha4: There is a statistically significant difference in the intergovernmental revenue growth rate (IGR) based on county type (metro/suburban/rural).

Open the data file Florida County Government. sav.

Perform an error bar plot first.

Move to Variable box on the right the dependent variable intergovernmental revenue growth rate (IGR).

Move county type (metro/suburban/rural) to Category Axis box. This is the independent groups variable. There are three groups.

Click OK.

Edit the error bar plot by adding data labels and title. Follow directions in Cronk and in the resources provided. What do you think from that plot you would expect to find in a One-Way ANOVA test?

Now, perform a One-Way ANOVA test with:

County type as your independent variable groups and

Intergovernmental revenue growth rate (IGR Growth rate) as your dependent variable.

Run post-hoc tests as well.

Use Cronk and the Learn items provided to interpret the results of the Levene’s test of assumed equal variances, interpret the One-Way ANOVA results, interpret the results of post-hoc tests, and produce a report based on the testing of your hypotheses.

Add a covariate to your One-Way ANOVA and rerun as an ANCOVA. The new research question is:

RQ 5: Controlling for political orientation (political), is there a significant difference in the intergovernmental revenue growth rate (IGR) based on county type (metro/suburban/rural)?

H05: Controlling for political orientation (political), there is no statistically significant difference in the intergovernmental revenue growth rate (IGR) based on county type (metro/ suburban/rural).

Ha5: Controlling for political orientation (political), there is a statistically significant difference in the intergovernmental revenue growth rate (IGR) based on county type (metro/suburban/rural).

Perform an error bar plot first. What do you think from that plot you would expect to find in an ANCOVA test?

Then, perform an ANCOVA test with:

County type as your independent variable groups, political as your covariate, and

Intergovernmental revenue growth rate (IGR Growth rate) as your dependent variable.