Assignment 3
Choosing the Correct Statistic

The purpose of Assignment 3 is to apply the concepts that you learned this semester.

The assignment consists of three tasks/sections.

Task 1. Provide a paragraph or two description of your proposed dissertation study (it does not have to be your dissertation study, this depends on how far along you are with your dissertation). Because you may not have finished your dissertation proposal, the details may not be completely worked out. The goal of this task is simply to provide me with enough information that I can provide feedback.

Task 2. Write between 3 and 5 quantitative research questions from your proposed dissertation study. These questions should be either comparison questions or relationship questions.

Task 3. Write a paragraph or so description of the statistical analysis that you plan to perform. Because each research question will call for its own analysis (although some research questions may share the same analysis), you will have an analysis description
for each question.

The following template provides you with an example to follow for this assignment. My template will closely mimic the presentation of information in a typical Chapter 3 of a dissertation.

Assignment 3 Example Template
Study Background
The proposed study investigates the influence of an educational intervention designed to improve mathematics problem solving skills. Prior to the start of the fall semester, a sample of students will be assigned to receive the standard curriculum (the comparison or control group) or a new curriculum designed to improve problem-solving skills (the experimental group). For logistical reasons, entire classrooms will be assigned to one of two conditions (i.e., it would not be possible to implement two different teaching methods within a given classroom, so all students in a class will participate in either the experimental or the control condition). The primary dependent variable is scores on a problem-solving test at the end of the spring semester. The problem-solving measure will be administered at the beginning of the fall semester to assess baseline knowledge, then again at the end of the spring semester. Additionally, the following independent variables are of interest: gender, ethnicity (Caucasian, African American, and Hispanic), and previous academic achievement (as measured by standardized test scores from the
previous year).

Research Questions
1. Do males and females differ in their end-of-year problem-solving test scores?
2. Do the three ethnic groups differ in their end-of-year problem-solving test scores?
3. Do the students in the experimental and control groups differ in their end-of-year problem solving skills?
4. Did students in experimental and control groups improve at different rates between the baseline and end of the year?
5. Is there a relationship between previous academic achievement and end-of-year problem-solving test scores?

Proposed Statistical Analyses
1. Research question 1 will be addressed using an independent t test. The independent t test is appropriate for comparison research questions where it is of interest to determine whether two groups of individuals (i.e., the independent variable is categorical such as male and female) have different averages on a dependent variable (e.g., problem-solving scores). The t test yields a probability value that describes the likelihood of the groups differing due to random chance. By convention, probability values less than 5% are deemed statistically significant because the likelihood of chance producing the difference is rather small.

2. Research question 2 will be addressed using a one-factor ANOVA. The one-factor ANOVA is appropriate for comparison research questions where it is of interest to determine whether two or more groups of individuals (i.e., the independent variable is categorical such as Caucasian, African American, and Hispanic) have different averages on a dependent variable (e.g., problem-solving scores). The ANOVA yields a probability value that describes the likelihood of the groups differing due to random chance. By convention, probability values less than 5% are deemed statistically significant because the likelihood of chance producing the difference is rather small.

3. Research question 3 will be addressed using an independent t test. The independent t test is appropriate for comparison research questions where it is of interest to determine whether two groups of individuals (i.e., the independent variable is categorical such as experimental and control) have different averages on a dependent variable (e.g., problem-solving scores). The t test yields a probability value that describes the likelihood of the groups differing due to random chance. By convention, probability values less than 5% are deemed statistically significant because the likelihood of chance producing the difference is rather small.

4. Research question 4 will be addressed using a two-factor ANOVA. The two-factor ANOVA is appropriate for comparison research questions where it is of interest to determine whether two categorical independent variables influence a dependent variable. In this study, the two independent variables are the timing of the test administration (baseline and end-of-year) and experimental condition (control and experimental). In particular, the interaction of these two variables is of interest because it is hypothesized that students in the experimental condition will experience greater improvement than students in the comparison condition (i.e., the two variables exert a synergistic influence on problem solving). The two-factor ANOVA yields a probability value for the two independent variables and the interaction. This probability describes the likelihood of the groups differing due to random chance. By convention, probability values less than 5% are deemed statistically significant because the likelihood of chance producing the difference is rather small.

5. Research question 5 will be addressed using a correlation. The correlation is appropriate for relationship research questions where it is of interest to determine whether a trend exists between two continuous variables (e.g., previous test scores and end-of-year problem-solving scores). The correlation analysis yields a statistic (Pearson's r) that describes the direction of the trend (positive or negative) as well as the strength of the trend. Additionally, the analysis yields a probability value that describes the likelihood of the trend occurring due to random chance. By convention, probability values less than 5% are deemed statistically significant because the likelihood of chance producing the trend is rather small.