statistic

practice_565.docx

Home >Mathematics homework help >Statistics homework help >statistic

Educational Psychology 565 Practice Quiz

(use α = .05 unless otherwise stated).

1. A small school district wants to know what type of teaching/learning is most effective at helping students learn to read. Three methods are proposed (top-down, bottom-up, and interactive). It is believed that the gender of the teacher may also be important in student learning, so the study also aims to determine if gender of the teacher is important. There are 12 schools in the district, and each school has 1 second grade class (each class has 10 students). Two female teachers and two male teachers’ classrooms are randomly assigned to each of the three methods (all 12 teachers have just been hired in the district). At the end of the year, the students all took a 100 item standardized multiple-choice reading test called the “EZreading” test (note: the analysis was performed at the student level).

Coding:

teachgender = gender of teacher: 1= men, 2 = women

Teachmeth = teaching method (1=top-down, 2=bottom-up, 3=interactive)

EZread = scores on the Ezread reading test

Use SPSS output “SPSS printout for question 1”to help answer the parts below.

a. What is/are the independent variable(s) in this experiment (Be specific)? What level of measurement is/are the IV(s)? Explain why?

b. What is/are the dependent variable(s) in this experiment (Be specific)? What level of measurement is/are the DV(s)? Explain why?

c. State the null hypotheses and alternative hypotheses for the factors and the interaction in symbols and words.

d. Do you think the assumption of homogeneity of variance has been met? Support your answer.

e. Do you think the assumption of independence has been met? Support your answer.

f. Calculate Cohen’s d for the difference between the top-down and interactive methods. Explain what Cohen’s d means for this comparison.

g. Is the interaction of the two factors statistically significant? Explain your answer.

h. Report the results of the study along with an interpretation for the results. You do not need to write up the results like a results section; you can just report the findings with statements about each factor and the interaction of the two factors. Be sure to cite evidence from your analysis.

i. Based on the results of the study what would you recommend about teaching method and gender of teachers?

2. Answer the following questions.

Source	SS	df	MS	F
Between	100		20
Within		2	50
Total	200	7

a. Complete the ANOVA source table (fill in all blank spaces)

b. How many people are in this study. (hint: use degrees of freedom)

c. What is the critical F at α = .01? Would you reject the null hypothesis? Explain your answer.

d. What are the critical F at α = .05? Would you reject the null hypothesis? Explain your answer.

e. Why do the conclusions from items c and d differ? Explain your answer in terms of Type I and II errors.

3. A researcher wants to know whether there are differences between two teaching techniques and baseline in improving math skills. Due to economic considerations he could not use a between-subjects design. Therefore, he measured participants’ math skills at baseline, gave them teaching method A for two weeks and measured their math skills, and then gave them teaching method B for two weeks and measured their math skills. On the measure low scores indicated low math skills. Using the provided SPPS output to answer the following questions:

a. Was the assumption of sphericity met? Explain your answer.

b. According to the omnibus test was there a difference between baseline and/or the methods. Explain your answer.

c. Using the output from the pairwise comparisons. Explain which levels of the within-subjects factor differ.

d. What is the primary weakness of this design?

SPSS printout for question 1.

1. Teachmeth

2. Teachgender

3. Teachmeth * Teachgender

SPSS printout for question 3.

Estimates

Dependent Variable: Ezread

74.025

1.612

70.831

77.219

70.225

1.612

67.031

73.419

64.750

1.612

61.556

67.944

Teachmeth

Mean

Std. Error

Lower Bound

Upper Bound

95% Confidence Interval

Pairwise Comparisons

Dependent Variable: Ezread

3.800

2.280

.098

-.717

8.317

9.275

2.280

.000

4.758

13.792

-3.800

2.280

.098

-8.317

.717

5.475

2.280

.018

.958

9.992

-9.275

2.280

.000

-13.792

-4.758

-5.475

2.280

.018

-9.992

-.958

(J) Teachmeth

(I) Teachmeth

Mean

Difference

(I-J)

Std. Error

Sig.

Lower Bound

Upper Bound

95% Confidence Interval for

Difference

Based on estimated marginal means

The mean difference is significant at the .05 level.

Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).

Estimates

Dependent Variable: Ezread

70.083

1.316

67.475

72.691

69.250

1.316

66.642

71.858

Teachgender

Mean

Std. Error

Lower Bound

Upper Bound

95% Confidence Interval

Pairwise Comparisons

Dependent Variable: Ezread

.833

1.862

.655

-2.855

4.522

-.833

1.862

.655

-4.522

2.855

(J) Teachgender

(I) Teachgender

Mean

Difference

(I-J)

Std. Error

Sig.

Lower Bound

Upper Bound

95% Confidence Interval for

Difference

Based on estimated marginal means

Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).

Estimates

Dependent Variable: Ezread

74.150

2.280

69.633

78.667

73.900

2.280

69.383

78.417

70.600

2.280

66.083

75.117

69.850

2.280

65.333

74.367

65.500

2.280

60.983

70.017

64.000

2.280

59.483

68.517

Teachgender

Teachmeth

Mean

Std. Error

Lower Bound

Upper Bound

95% Confidence Interval

Pairwise Comparisons

Dependent Variable: Ezread

.250

3.225

.938

-6.138

6.638

-.250

3.225

.938

-6.638

6.138

.750

3.225

.817

-5.638

7.138

-.750

3.225

.817

-7.138

5.638

1.500

3.225

.643

-4.888

7.888

-1.500

3.225

.643

-7.888

4.888

(J) Teachgender

(I) Teachgender

Teachmeth

Mean

Difference

(I-J)

Std. Error

Sig.

Lower Bound

Upper Bound

95% Confidence Interval for

Difference

Based on estimated marginal means

Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).

Teachgender

FemaleMale

Estimated Marginal Means

72.5

67.5

Teachmeth

Estimated Marginal Means of Ezread

Mauchly's Test of Sphericity

Measure: MEASURE_1

.980

.062

.970

.980

1.000

.500

Within Subjects Effect

factor1

Mauchly's W

Approx.

Chi-Square

Sig.

Greenhous

e-Geisser

Huynh-Feldt

Lower-bound

Epsilon

Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is

proportional to an identity matrix.

May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in

the Tests of Within-Subjects Effects table.

Design: Intercept

Within Subjects Design: factor1

Tests of Within-Subjects Effects

Measure: MEASURE_1

11.200

5.600

5.508

.031

11.200

1.960

5.714

5.508

.032

11.200

2.000

5.600

5.508

.031

11.200

1.000

11.200

5.508

.079

8.133

1.017

8.133

7.840

1.037

8.133

8.000

1.017

8.133

4.000

2.033

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Source

factor1

Error(factor1)

Type III Sum

of Squares

Mean Square

Sig.

Estimates

Measure: MEASURE_1

4.400

.600

2.734

6.066

4.000

.548

2.479

5.521

6.000

.316

5.122

6.878

factor1

Baseline

Method A

Method B

Mean

Std. Error

Lower Bound

Upper Bound

95% Confidence Interval

Pairwise Comparisons

Measure: MEASURE_1

.400

.600

.541

-1.266

2.066

-1.600

.678

.078

-3.483

.283

-.400

.600

.541

-2.066

1.266

-2.000

.632

.034

-3.756

-.244

1.600

.678

.078

-.283

3.483

2.000

.632

.034

.244

3.756

(J) factor1

(I) factor1

Mean

Difference

(I-J)

Std. Error

Sig.

Lower Bound

Upper Bound

95% Confidence Interval for

Difference

Based on estimated marginal means

The mean difference is significant at the .05 level.

Adjustment for multiple comparisons: Least Significant Difference (equivalent to no

adjustments).

Between-Subjects Factors

Teachmeth

Teachgender

Tests of Between-Subjects Effects

Dependent Variable: Ezread

1767.967

353.593

3.400

.007

582413.333

5600.742

.000

1739.217

869.608

8.363

.000

20.833

.200

.655

7.917

3.958

.038

.963

11854.700

114

103.989

596036.000

120

13622.667

119

Source

Corrected Model

Intercept

Teachmeth

Teachgender

Teachmeth *

Teachgender

Error

Total

Corrected Total

Type III Sum

of Squares

Mean Square

Sig.

R Squared = .130 (Adjusted R Squared = .092)

Levene's Test of Equality of Error Variances

Dependent Variable: Ezread

.010

114

1.000

df1

df2

Sig.

Tests the null hypothesis that the error variance of

the dependent variable is equal across groups.

Design:

Intercept+Teachmeth+Teachgender+

Teachmeth * Teachgender