# Project #52263 - Statistics in the Behavioral Sciences

Imagine you are a researcher who just finished collecting data on a sample of public school students. In this study, you were interested in the following variables: math scores, science scores, parents’ education (highest of the two parents), and achievement self-concept as measured at the beginning of the school year and at the end of the school year. (This data set appears at the end of the prompt). Ask yourself the following questions:

1. How many students scored between 50 and 60 on their math test? How many scored between 70 and 80? Between 80 and 90? Between 90 and 100? What are the relative frequencies of these categories?
2. Does a significant correlation exist between math and science scores? If so, what is the relationship?
3. Does a significant correlation exist between math scores and parent education? If so, what is the relationship?
4. Does a significant correlation exist between science scores and parent education? If so, what is the relationship?
5. Did student achievement self-concept scores improve from the beginning of the year to the end of the year?
6. Do students who have a parent who graduated from high school have better achievement self-concept scores (beginning of the year) than students who do not have a parent who graduated from high school? (This will require you to group parents into two groups: less than 12 years of education and 12 years of education or higher. Consider creating a column next to the parent education column and identifying them as a “1” or a “2,” and then test for differences in student achievement self-concept between these two groups. It may be helpful to sort your data.)
7. Do math scores differ across the three grades? If so, where are the differences?
8. Do science scores differ across the three grades? If so, where are the differences?
9. Do achievement self-concept scores (beginning of the year) differ across the three grades? If so, what are the differences?

For this assignment, decide which chart or graph you will need to produce or which statistical analysis you will need to conduct to answer each of these questions. Hint: You will run at least one of each of the following (you may have to run one more than once): correlation, t-test (either independent or dependent samples), or an F-test (ANOVA).

For each statistical analysis you run, state the null and alternative hypotheses, the degrees of freedom (if applicable), the critical values, and other appropriate values (e.g., between group variance, within group variance), the test statistic itself, and your conclusion. For an F-test (ANOVA), be sure to run a Sheffé test (if applicable) to determine where the differences (if any) exist. Conduct tests at the .05, two-tailed level.

You may use statistical software to calculate values for this assignment. However, you must include all printouts and explain what the values in these printouts mean. In other words, you cannot just turn in the printouts. The instructor needs to know you understand what these values are and what these printouts mean. Students may earn extra credit if they calculate all statistics by hand and show their work.

After you complete all analyses and draw your conclusions, summarize your findings in a page-long report. What conclusions can you draw about this population of students? Be specific, especially where significant correlations or significant differences exist. This report should be the first page of a longer document that includes explanations, printouts, or handwritten work for all individual analyses (i.e., all 9 questions posed).

 Subject ID Grade in School Math Score (0–100) English Score (0–100) Parent's Years of Education (highest) Achievement Self-Concept Score (beginning of school year, 0–20) Achievement Self-Concept Score (end of school year, 0–20) 1 5th 80 90 12 10 14 2 5th 89 70 12 10 15 3 5th 87 70 13 8 10 4 6th 90 83 15 13 20 5 6th 93 69 8 15 17 6 5th 70 80 9 16 19 7 5th 79 97 18 9 16 8 5th 82 89 18 7 12 9 6th 70 89 9 6 14 10 7th 90 67 7 12 18 11 7th 99 82 12 15 16 12 7th 69 89 12 13 19 13 7th 68 84 12 8 14 14 5th 70 92 12 9 13 15 6th 80 99 13 5 10 16 6th 80 98 16 10 14 17 7th 90 65 14 10 17 18 7th 99 81 14 10 13 19 7th 67 86 16 3 9 20 7th 60 90 16 15 17 21 7th 69 95 18 16 19 22 5th 90 80 16 19 18 23 5th 87 74 18 6 8 24 6th 76 83 16 10 15 25 6th 89 88 16 11 13

 Subject Mathematics Due By (Pacific Time) 12/16/2014 01:00 pm
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