Math

Part I: One-Way ANOVA

This analysis is looking at the relationship between ethnicity/race and freshman year science scores. Use the tables and graph included below to answer the following questions:

1. What are the null and alternative hypotheses for this analysis?

2. In a few sentences, describe the descriptive data for each ethnicity/race group (include N, mean, standard deviation, minimum, & maximum).

3. Did we violate the assumption of homogeneity in this analysis? Include evidence for your answer (i.e. how do you know?).

4. Were there significant differences in science scores between the different ethnicities?

5. Based on the results of your analysis, should you analyze the post hoc tests?

a. If yes, which groups are significantly different from each other? (List all).

b. Explain what the post hoc tests tell us about the relationship between ethnicity and science scores.

6. Complete Step 4 of hypothesis testing. Include your decision about the null hypothesis, a sentence describing the results (including post hoc tests), and the APA-style string of statistics.

7. In your own words , what is the relationship between ethnicity and science scores?

Post Hoc Tests

8.

Part II: Correlation

· Using the output below (investigating the relationship between different exam scores), describe all 3 different pairs of relationships (reading-writing; reading-math; math-writing). For each, make sure to include the following information:

· Whether the relationship was significant.

· If it was significant, whether it was a positive/negative relationship.

· Describe the relationships (As X increases/decreases, Y increases/decreases).

· APA string of statistics [ r= r value, p=______]

You can do this in bullet format, but make sure to use whole sentences.

Correlations

· Looking at the scatterplot below, describe the relationship between math scores (X) and social studies scores (Y). Make sure to describe the strength and direction of the relationship. You do not need to include an APA string of statistics for this question.

Part III: Regression

The output below is the result of investigating the predictive relationship between freshman year science scores and senior year science scores. Researchers wanted to see if they can predict senior year science scores from each student’s freshman year scores. Answer the following questions using the output below:

· What is the correlation coefficient (r) for the relationship between senior and freshman year scores?

· Does freshman year science scores significantly predict senior year science scores?

· Write out the F statistical string associated with this relationship. [F( dfreg, dfres)= F value, p=________]

· Write out the line of best fit equation for this relationship (Y=bX+a, substituting the b & a with values from the table).

· If someone scored a 70 on their freshman year science test, based on the line of best fit, what would their predicted senior year score be?

Part IV: Chi Square Goodness of Fit Test

For this study, participants were split into 3 groups based on the type of exercise they engage in (martial arts, general exercise, or no exercise). I wanted to see if there were more people who do one type of exercise compared to the others. To do so, I ran a chi square goodness of fit test to determine whether there was a different number of participants in the groups. Answer the following questions using the output below:

· How many people did I sample total?

· Which of the exercise groups had more than the expected N?

· Which of the exercise groups had less than the expected N?

· Was there a significant difference in the number of participants in each group? How do you know?

· Write out the statistical string of information for this test. It should be formatted like this: 2(df, N=##)= Chi-square value, p=###

a. Make sure that you put the actual number in for the df, the chi-square value, and the ## after N and p

· In your own words, what do the results of this test tell you about the distribution of participants in these exercise groups?

Part V: Chi Square Test of Independence

For this study, participants were split into 3 groups based on the type of exercise they engage in (martial arts, general exercise, or no exercise). I wanted to see if there was a difference in the proportion of male and female participants in the different exercise types. To do so, I ran a chi square test of independence to determine whether there was a significant relationship between the variables. Answer the following questions using the output below:

· How many people did I sample total?

· Which of the exercise groups had the same amount of male and female participants?

· Which gender had higher numbers in general exercise?

· Which gender had higher numbers in the no exercise group?

· Which exercise group had the highest number of people total in it?

· Was there a significant relationship between exercise type and gender? How do you know?

· Write out the statistical string of information for this test. It should be formatted like this: 2(df, N=##)= Chi-square value, p=###

a. Make sure that you put the actual number in for the df, the chi-square value, and the ## after N and p

· In your own words, what do the results of this test tell you about these 2 variables?