**ANOVA, Chi-Square Tests, and Regression**

Complete the following problems within this Word document. Do not submit other files. Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. You may want to highlight your answer or use a different type color to set it apart.

## ANOVA

#### Problem Set 4.1: Critical Value

**Criterion:** Explain the relationship between *k* and power based on calculated *k* values.

**Instructions:** Read the following and answer the questions.

Work through the following and write down what you see in the *F-*table. This will help familiarize you with the table.

The *F-*table: The degrees of freedom for the numerator (*k* − 1) are across the columns; the degrees of freedom for the denominator (*N* − *k*) are across the rows in the table. A separate table is included for a .05 and .01 level of significance.

##### Increasing the levels of the independent variable (*k*):

Suppose we have a sample size of 24 participants (*N* = 24). Record the critical values given the following values for *k*:

.05

.01

*k* = 2

*k* = 4

*k* = 6

*k* = 8

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As *k* increases (from 1 to 8), does the critical value increase or decrease? Based on your answer, explain how *k* is related to power.

#### Problem Set 4.2: One-way ANOVA in SPSS

**Criterion:** Calculate an ANOVA in SPSS.

**Data: **The following is the amount of fat (in grams) consumed in a buffet-style lunch among professional bodybuilders under conditions of high, moderate, and low stress:

Stress Levels

**High **

**Moderate**

**Low**

10

9

9

7

4

4

8

7

6

12

6

5

6

8

7

**Instructions:** Complete the following steps:

a. Open SPSS and open a **New DataSet**.

b. Click the **Variable View** tab at the bottom and enter **Stress** and enter **Fat **as the variables. Click the **Values** box for the **Stress **row and define 1 as high, 2 as medium, and 3 as low.

c. Enter the data. For example, type 1 in row 1 under **Stress **and type 10 in row 1 under **Fat**. Continue typing in all the data. Please remember to change to 2 in column 1 when the stress is moderate and change to 3 in column 1 when the stress is low

d. In the **Toolbar**, click **Analyze**, select **Compare Means**, and then select **One-Way ANOVA.**

e. Select **Fat** and then click **Arrow** to send it over to the **Dependent List** box.

f. Select **Stress** and then click **Arrow** to send it over to the **Factor** box.

g. Click **OK** and copy and paste the output below.

#### Problem Set 4.3: One-way ANOVA in Excel

**Criterion:** Calculate an ANOVA in Excel.

**Instructions:** Use the data from Problem Set 4.3 to complete the following steps:

a. Open **Excel** to an empty sheet.

b. Enter the data from **Problem Set 4.3.**

c. In **Row 1**, enter High in cell A1, Moderate in cell B1, and Low in cell B1.

d. In the toolbar, click **Data Analysis**, select **Anova: Single Factor,** and click **OK.**

e. In **Input Range**: $A$1:$C$6, put a check next to **Labels in First Row**, click **OK.**

f. Results will appear in a new sheet to the left; copy and paste the input below.

#### Problem Set 4.4: One-way ANOVA Results in APA Style

**Criterion:** Report ANOVA results in APA format.

**Data:** Use the results from Problem Set 4.4.

**Instructions:** Complete the following:

a. State the null hypothesis. ___________________________________

b. Report your results in APA format (as you might see them reported in a journal article). ___________________________________

#### Problem Set 4.5: Interpret ANOVA Results

**Criterion:** Interpret the results of an ANOVA.

**Instructions:** Read the following and answer the question.

**Data:** __Life satisfaction among sport coaches.__ Drakou, Kambitsis, Charachousou, and Tzetzis (2006) tested differences in life satisfaction among sport coaches. They tested differences by sex, age, marital status, and education. The results of each test in the following table are similar to the way in which the data were given in their article.

**Independent Variables**

**Life Satisfaction**

*M*

*SD*

*F*

*p*

**Sex**

0.68

.409

Men

3.99

0.51

Women

3.94

0.49

**Age**

3.04

.029

20s

3.85

0.42

30s

4.03

0.52

40s

3.97

0.57

50s

4.02

0.50

**Marital status**

12.46

.000

Single

3.85

0.48

Married

4.10

0.50

Divorced

4.00

0.35

**Education**

0.82

.536

High school

3.92

0.48

Postsecondary

3.85

0.54

University degree

4.00

0.51

Masters

4.00

0.59

1. Which factors were significant at a .05 level of significance? _____________________

State the number of levels for each factor. ____________________________________

#### Problem Set 4.6: Tukey HSD Test in SPSS

**Criterion:** Calculate post hoc analyses in SPSS.

**Data:** Use SPSS data from Problem Set 4.3.

**Instructions:** Complete the following steps:

a. In the **Toolbar**, click **Analyze**, select **Compare Means**, and then select **One-Way ANOVA**.

b. Select **Fat** then click **Arrow** to send it over to the **Dependent List** box.

c. Select **Stress**, then click **Arrow** to send it over to the **Factor** box.

d. Click **Post Hoc** and then check the box **Tukey**. Click **Continue**.

e. Click **OK** and copy and paste the output to the Word document.

#### Problem Set 4.7: Tukey HSD Interpretation

**Criterion:** Interpret Tukey HSD results from SPSS output.

**Data:** Use your output from Problem Set 4.6.

**Instructions:** Identify where significant differences exist at the .05 level between the stress levels.

## Chi-Square Tests

#### Problem Set 4.8: Critical Values

**Criterion:** Explain changes in critical value based on calculations.

**Instructions:** Read the following and answer the questions.

__The chi-square table__. The degrees of freedom for a given test are listed in the column to the far left; the level of significance is listed in the top row to the right. These are the only two values you need to find the critical values for a chi-square test.

Work through the following exercise and write down what you see in the chi-square table. This will help familiarize you with the table.

##### Increasing *k* and a in the chi-square table:

1. Record the critical values for a chi-square test, given the following values for *k* at each level of significance:

.10

.05

.01

*k* = 10

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*k* = 16

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*k* = 22

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*k* = 30

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Note: Because there is only one *k* given, assume this is a goodness-of-fit test and compute the degrees of freedom as (*k* − 1).

2. As the level of significance increases (from .01 to .10), does the critical value increase or decrease? Explain. ___________________________________

3. As *k* increases (from 10 to 30), does the critical value increase or decrease? Explain your answer as it relates to the test statistic. ___________________________________

#### Problem Set 4.9: Parametric Tests

**Criterion:** Identify parametric tests.

**Instructions:** Based on the scale of measurement for the data, identify if a test is parametric or nonparametric.

- A researcher measures the proportion of schizophrenic patients born in each season. ___________________________________
- A researcher measures the average age that schizophrenia is diagnosed among male and female patients. ___________________________________
- A researcher tests whether frequency of Internet use and social interaction are independent. ___________________________________
- A researcher measures the amount of time (in seconds) that a group of teenagers uses the Internet for school-related and non-school-related purposes. ___________________________________

#### Problem Set 4.10: Chi-Square Analysis in SPSS

**Criterion:** Use SPSS for a chi-square analysis.

**Data: **Tandy’s Ice Cream shop serves chocolate, vanilla, and strawberry ice cream. Tandy wants to plan for the future years. She knows that on average she expects to purchase 100 cases of chocolate, 75 cases of vanilla, and 25 cases of strawberry (4:3:1). This year, the ice cream sales increased, and she purchased 133 cases of chocolate, 82 cases of vanilla, and 33 cases of strawberry.

**Instructions:** Complete the following steps:

a. Open SPSS and create a **New DataSet**.

b. Go to the **Variable View** tab and type **Flavor** in the first row and **Frequency** in the second row. Adjust the decimal value to 0. Go to **Values** in the **Flavor **row and enter **1** for chocolate, **2** for vanilla, and **3** for strawberry and click **OK**.

c. Go to the **Data View** tab and under the **Flavor** column, enter **1** in row 1, **2** in row 2, and **3** in row 3. Under the frequency column, enter **133** in row 1, **82 **in row 2, and **33** in row 3.

d. In the **Toolbar**, click **Data**, then select **Weight Cases.**

e. Select **Weight Cases By**, select **Frequency**, and then click **Arrow** to send it over to the **Frequency Variable** box. Click **OK**.

f. In the **Toolbar**, click **Analyze**, then **Nonparametric Tests**, then **Legacy Dialogs**, and then **Chi-Square**.

g. Select** Flavor** and then click **Arrow** to send to the **Test Variable List**.

h. Under **Expected Values**, select **Values** and then enter the following three values in the order: 100, 75, and 25.

i. Click **OK** and copy and paste the output to the Word document.

j. Answer this: Was Tandy’s distribution of proportions the same as expected?

## Regression

#### Problem Set 4.11: Analysis of Regression in SPSS

**Criterion:** Use SPSS to complete an analysis of regression.

**Data: **

*X* (Age in Years)

*Y* (Life Satisfaction)

18

6

18

8

26

7

28

5

32

9

19

8

21

5

20

6

25

7

42

9

**Instructions:** Complete the following steps.

a. Open SPSS and create a **New DataSet**.

b. Go to the **Variable View** tab and type X in the name column, then enter Y in the column below it.

c. Go to **Data View** and enter the data from the table above.

d. Go to the **tool bar**, click **Analyze,** select **Regression, **then select** Linear.**

e. Select **Y **and then click the **Arrow** to send to **Dependent.**

f. Select **X **and the click the **Arrow **to send it to **Independent(s).**

g. Select **Ok**. Copy and paste the output to this Word document.

#### Problem Set 4.12: Analysis of Regression in Excel

**Criterion:** Use Excel to complete an analysis of regression.

**Data:** Use the data from Problem Set 4.11.

**Instructions:** Complete the following steps.

a. Open Excel and work in a new sheet.

b. Enter the data from the table in Problem Set 4.11. Cell A1 will be X. Cell B1 will be Y. Then, enter the data below.

c. Go to the **tool bar**, click **Data Analysi**s, and select **Regression.**

d. Put a check next to **Labels **and **Confidence Level.**

e. In **Input Y Range**: $B$1:$B$11, In **Input X Range**: $A$1:$A$11

f. Select **Ok**. Your data will appear in a new Sheet to the left.

g. Copy and paste the output to this document.

#### Problem Set 4.13: Identify Tests for Ordinal Data

**Criterion:** Identify tests for ordinal data.

**Instructions:** Read the following and answer the questions.

Identify the appropriate nonparametric test for each of the following examples and explain why a nonparametric test is appropriate.

1. A researcher measures fear as the time it takes to walk across a presumably scary portion of campus. The times (in seconds) that it took a sample of 12 participants were 8, 12, 15, 13, 12, 10, 6, 10, 9, 15, 50, and 52. ___________________________________

2. Two groups of participants were given 5 minutes to complete a puzzle. The participants were told that the puzzle would be easy. In truth, in one group, the puzzle had a solution (Group Solution), and in the second group, the puzzle had no solution (Group No Solution). The researchers measured stress levels and found that frustration levels were low for all participants in Group Solution and for all but a few participants who showed strikingly high levels of stress in Group No Solution. ___________________________________

3. A researcher measured student scores on an identical assignment to see how well students perform for different types of professors. In Group Adviser, their professor was also their adviser; in Group Major, their professor taught in their major field of study; in Group Nonmajor, their professor did not teach in their major field of study. Student scores were ranked in each class, and the differences in ranks were compared. ___________________________________

4. A researcher has the same participants rank two types of advertisements for the same product. Differences in ranks for each advertisement were compared. ___________________________________

A professor measures student motivation before, during, and after a statistics course in a given semester. Student motivation was ranked at each time in the semester, and the differences in ranks were co