PY 375 - Psychological Statistics Homework and Computer Assignments - Spring 2008

note: page numbers refer to Robert Pagano's 8th Edition of Understanding Statistics

ASP - A Statistical Package computer program

HW - Homework assignment     C - ASP Computer assignment

Note: If you have a question e-mail: your statistics professor

assigned 1/18/08 due 1/23/08

HW #1 - Use data from Chapter 3 problem 10 (p.63) then use the following parts a - e for the problem.

a. use 8 interval classes to construct a grouped frequency distribution including all six frequency data expressions: frequency, relative frequency, percent  frequency, cumulative  frequency, cumulative relative frequency, cumulative percent frequency

b. construct a histogram or frequency polygon based on the grouped frequency distribution

c. construct a stem and leaf diagram of the data with the last digit being a leaf and the first digit a stem. Repeat stem values two or five times.

d. find P₇₅ and P₂₅

e. find percentile rank of the scores 40 and 20

assigned 2/8/08  due 2/11/08

HW #2 - Chapter 7 - do problem 12 (p. 157) -  answer a, b, c, d, e, &  f : Show all work

C #1 - Use ASP to analyze the data from problem 12 producing the desired results for parts a, c, & d. Please provide a printed listing of the data, output of the scatter plot, regression analysis, and correlation. Use Statistics and Graphs menus. Be careful which variable is selected for the plot axes:  Vertical Axis = Variable 1 (Y), Horizontal Axis = Variable 2 (X).

NOTE: Be sure to do this assignment and bring it to class on Monday, February 11, 2008

assigned 2/20/08  due 2/22/08

HW #3 - Chapter 8 - do problems  13, 15, 16, 26 (p.196 - 197)

show all work on your paper

NOTE: Be sure to do this assignment and bring it to class on Friday, February 22, 2008

There will be an in-class assignment on February 22.

assigned 2/29/08  due 3/3/08

HW #4 - Chapter 9 - do problems 4, 6*, 12, 17  (p. 213 - 214)

*for problem #6 show the binomial expansion for possible outcomes

There will be an in-class assignment on March 3

assigned 3/10/08  due 3/12/08

HW #5 - Chapter 10  - do problems  9, 11 (p. 241 - 243)

assigned 3/19/08  due 3/31/08 (after spring break)

HW #6 - Chapter 13 - do problems  19, 20 (p. 318)  and state null and alternative hypotheses for these problems. Do 95 and 99 confidence internals for problem 20.

C#2 - Chapter 13 do problem 20 using ASP, and do 95 and 99 percent confidence intervals, too.

assigned 3/31/08  due 4/2/08

HW #7 - Chapter 14 - do problem  18 (p. 352)

On these problems be sure to state the null and alternative hypotheses. In the conclusion be sure to include the descriptive statistics.

C #3 - Chapter 14 do problems 18, remember to list the data for this problem.  Remember to select "Matched" for correlated groups.

assigned 4/2/08  due 4/4/08

HW #8 - Chapter 14 - do problems  24 (p. 354)

On these problems be sure to state the null and alternative hypotheses. In the conclusion be sure to include the descriptive statistics.

C #4 - Chapter 14 do problems 24, remember to list the data for this problem. Remember to select "Independent"  for independent groups analyses.

assigned 4/11/08  due 4/14/08

HW #9 - Chapter 15 - do problem 24 (p. 394)

On this problem:

1) state statistical hypotheses in notation and words;

2) identify the independent/classification variable and the dependent variable;

3) perform the analysis of variance.

4) If appropriate do post hoc analyses using Tukey's HSD and Newman-Keuls.

5) Assess the degree of relationship between the variables in the study. What is the size of the effect (use both indices)? 

6) What conclusions can be drawn from the study?  In the conclusion be sure to include the descriptive statistics.

C #5 - Chapter 15 do problem 24

Note: To use ASP for one way analysis of variance there will be a special coding procedure to use. There will be an independent/classification variable and dependent variable. When the data matrix is created, it uses two variables. The first variable will be coded by which group or level of the independent/classification variable the participant is in. The second variable will be the dependent variable. The data matrix created will have two columns. The layout of the data will look different than the data presented for the problem in the textbook.

assigned 4/23/08  due 4/25/08

HW #10 -  Chapter 16 - problem 13 (p. 425)

Additional instructions: 

1. state the alternative hypotheses for part a, in words and notation

2. Present a graph of the appropriate cell means of this study. What could be said about the possible outcome of this study based on the descriptive information provided by the graph?

3. test null hypotheses at α = .01 level as well α = .05 level in part b

4. present the results of the ANOVA in a summary table

5. What can be concluded in this study at this point in the analyses?

Computer #6 - use ASP to verify the analyses

Coding hints for ASP:

With the new data matrix specify 3 variables. Var1 will the dependent variable, Var2 will be the Factor A, and Var3 will be Factor B. Be sure to given the variables appropriate names.  Coding as follows: Var1 - time to sleep  Var2 - previous use  Var3 - concentration. The coding is for the first and last cases in a cell.  Please note there are additional cases (the case ranges) and values for the DV (indicated by the ##) that need to be entered into the ASP data matrix. This table illustrates the coding scheme to do a factorial ANOVA in ASP (N Way Analysis of Variance). There will be a total of 32 cases and numerical entries for each cell.

sample problem presented in class with coding scheme in ASP for two-way ANOVA (download ASP file)

assigned 4/25/08  due 4/28/08

HW #11 -  Chapter 16 - problem 13 (p. 425)

This is a continuation of the HW #10, problem 13 (p. 425)

6) If appropriate conduct a simple main effects analysis.

7) What conclusions can be drawn in relation to the research hypothesis in problem 13, especially with the results of the SME?

Computer #7 - verify SME analyses using ASP

Note: It is possible to produce codes in ASP to determine SS to perform simple main effects analysis. A handout was provided to demonstrate the coding. Use one-way ANOVAs with this coding to determine the specific simple main effects sums of squares (SS - A at B1, etc.).

Note: This is the last homework/computer assignment for PY375 in the Spring 2008 semester. Please complete this assignment by class time on April 28, 2008.

Note: April 30, 2008 (Wednesday) at 1 p.m. is the last day to turn in this homework or computer exercise for credit (HW#11/C#7).

Interpretative strategy for two-way ANOVA  

1. Identify the research problem and design. The 2 X 2 factorial is the simplest form.

2. Identify the independent or classification variables in the design. Note that independent variables are directly manipulated in an experiment. What are the levels of each of the factors (variables) used in the study? Know the variables and use their names in presenting and discussing the results of the analyses.  

3. Identify the dependent variable. You will use this variable throughout the analyses, presentation of results, and discussion. Use the variable name not just “dependent variable.”  

4. Clearly state the null hypotheses and alternate hypotheses. The independent or classification variables used for the main effects (A and B) should be clear. State the interaction effect. Be clear in the written hypotheses and use appropriate notations.

5. Determine the means for each cell. This represents the combination of the levels of the independent or classification variables. You will plot these means in a graph. The graph will have as the vertical axis the dependent variable. On the graph be clear what you label and the scale used for the dependent variable. Both the A factor and B factor with levels should be clearly labeled. The descriptive interpretation of these means is important if you have main effects and an interaction effect.

 6. Determine the means for each level of the main effects factors. Report these means in the discussion of the results of the ANOVA for the main effects. The means comparison will show the descriptive difference and the ANOVA will provide the inference of the difference. Also report the F ratios for testing all null hypotheses with degrees of freedom (df) and the p level.

 7. In computing the ANOVA determine the totals (sum of the scores) for the cells and levels of each factors. This will be useful in the computation of the simple main effects.

 8. If the null hypothesis for the interaction effect is rejected, this decision justifies performing a simple main effects (SME) analysis. When the simple main effects analysis is perform, this will be a series of one-way ANOVAs. Be sure to state the hypotheses for each simple main effect. For example, for analyzing the levels of the A factor at level 1 of factor B, use the name of the A factor and the level of the B factor on which the analysis is performed. The null hypothesis states that there is no difference or no effect. Be sure to use the adjusted alpha level for testing the F ratio you obtain for each simple main effect. Be sure to check the sums of the SS of simple main effects against the sum of the SS for main effect and SS interaction effect.

    In the special case of a 2 X 2 factorial design, the SS (sums of squares) calculated for each simple main effect also equals the MS (s²  variance estimate), because there is only 1 degree of freedom (df). For other factorial designs this might not be the case.  

9. To interpret the simple main effects analysis use the cell means to support the inference of the SME analysis. The purpose of the SME analysis is to determine the nature of the interaction in the study based on the data. The SME analysis is functionally a series of one-way ANOVAs, which analyzes one of the main effect factors (e.g. A) at separate levels of the other main effect factor (e.g., first B1, then B2). This should provide for a clearer interpretation of the analyzed results.  

10. The conclusion from the ANOVA can be stated in terms of the research question. What support for the research question was found from the data? What statement of interpretation and generalization of findings can be offered?