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## BTM8107-8 Week 6

by: kimwood Notetaker

170

1

15

# BTM8107-8 Week 6

Marketplace > BTM8107 8 Week 6
kimwood Notetaker
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## About this Document

Activity #6 consists of two parts. In the first part, you will utilize an existing dataset to analyze the dataset from repeated-measures experimental design. All SPSS output should be pasted into y...
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Date Created: 11/05/15
Activity #6 consists of two parts. In the first part, you will utilize an existing dataset to analyze the dataset from repeated-measures experimental design. All SPSS output should be pasted into your Word document. In the second part, you will be asked to create a dataset for a hypothetical repeated-measures experimental design. Finally, you will answer questions about your hypothetical dataset. Part A. SPSS Activity The “Activity 6.sav” file contains a dataset of a high school teacher interested in determining whether his students’ test scores increase over the course of a 12 week period. In the dataset, you will find the following variables: Participant: unique identifier Gender: Male (M) or Female (F) Score_0 – score on the initial course pre-test (first day of class) Score_2 – score at the end of week 2 Score_4 – score at the end of week 4 Score_6 – score at the end of week 6 Score_8 – score at the end of week 8 Score_10 – score at the end of week 10 Score_12 – score at the end of the course (week 12) Activity #6 1. Exploratory Data Analysis. a. Perform exploratory data analysis on the relevant variables in the dataset. When possible, include appropriate graphs to help illustrate the dataset. Descriptive Statistics N Minimum Maximum Mean Std. Deviation Pre­test score 12 16 59 29.58 12.221 Week 2 score 12 22 60 33.08 10.113 Week 4 score 12 27 63 35.42 9.885 Week 6 score 12 20 60 35.67 10.671 Week 8 score 12 28 65 39.92 9.718 Week 10 score 12 33 67 45.67 8.690 Week 12 score 12 34 73 50.00 10.189 Valid N (listwise) 12 Gender Female Male Mean Mean Pre­test score 28 32 Week 2 score 30 40 Week 4 score 34 39 Week 6 score 36 35 Week 8 score 39 41 Week 10 score 45 47 Week 12 score 48 53 Oveall Mean Score 60.00 50.00 40.00 30.00 20.00 Mean Score 10.00 .00 Mean Score for Males 60 50 40 30 20 Mean Score 10 0 Mean Score for Females 60 50 40 30 20 Mean Score 10 0 b. Give a one to two paragraph write up of the data once you have done this c. Create an APA style table that presents descriptive statistics for the sample. From the above analysis and graphs we can easily see that the mean score of the participants are increasing with the increase over the course duration. So mean score is going high as the weeks are increasing from 0 to 12. The same thing is represented by the line graphs. First table is a descriptive statistics table with taking all participants together; second table is a divided with the gender of the participants. Similarly we have graphs shown above with taking all the participants as well as the participants with males and females. All are showing the increasing trend in the mean score. It clearly indicates that the mean score is increasing overall as well as within each category. 2. Repeated-Measures ANOVA. Perform a repeated-measures ANOVA using the “Activity 6.sav” data set. You will use Score_0 through Score_12 as your repeated measure (7 levels), and gender as a fixed factor. Within­Subjects Factors Measure:MEASURE_1 SCORE Dependent Variable 1 Score_0 2 Score_2 3 Score_4 di4ensio Score_6 n1 5 Score_8 6 Score_10 7 Score_12 Between­Subjects Factors Value Label N Gender F Female 8 M Male 4 Descriptive Statistics Gender Mean Std. Deviation N Pre­test score Female 28.25 8.172 8 Male 32.25 19.432 4 Total 29.58 12.221 12 Week 2 score Female 29.75 6.319 8 Male 39.75 13.889 4 Total 33.08 10.113 12 Week 4 score Female 33.63 5.181 8 Male 39.00 16.432 4 Total 35.42 9.885 12 Week 6 score Female 35.88 6.556 8 Male 35.25 17.802 4 Total 35.67 10.671 12 Week 8 score Female 39.38 5.370 8 Male 41.00 16.633 4 Total 39.92 9.718 12 Week 10 score Female 44.88 5.743 8 Male 47.25 13.961 4 Total 45.67 8.690 12 Week 12 score Female 48.38 8.518 8 Male 53.25 13.793 4 Total 50.00 10.189 12 b Multivariate Tests Effect Value F Hypothesis df Error df Sig. a SCORE Pillai's Trace .961 20.439 6.000 5.000 .002 a Wilks' Lambda .039 20.439 6.000 5.000 .002 Hotelling's Trace 24.526 20.439 a 6.000 5.000 .002 Roy's Largest Root 24.526 20.439 a 6.000 5.000 .002 a SCORE * Gender Pillai's Trace .491 .804 6.000 5.000 .607 a Wilks' Lambda .509 .804 6.000 5.000 .607 Hotelling's Trace .965 .804a 6.000 5.000 .607 Roy's Largest Root .965 .804a 6.000 5.000 .607 a. Exact statistic b. Design: Intercept + Gender   Within Subjects Design: SCORE Mauchly's Test of Sphericity b Measure:MEASURE_1 Within Subjects  Epsilona Effect Approx. Chi­ Greenhouse­ Huynh­ Lower­ Mauchly's W Square df Sig. Geisser Feldt bound dimension1 .001 56.876 20 .000 .441 .674 .167 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are  displayed in the Tests of Within­Subjects Effects table. b. Design: Intercept + Gender   Within Subjects Design: SCORE Tests of Within­Subjects Effects Measure:MEASURE_1 Source Type III Sum of Squares df Mean Square F Sig. SCORE Sphericity Assumed 3246.536 6 541.089 20.609 .000 Greenhouse­Geisser 3246.536 2.646 1227.164 20.609 .000 Huynh­Feldt 3246.536 4.045 802.659 20.609 .000 Lower­bound 3246.536 1.000 3246.536 20.609 .001 SCORE * Gender Sphericity Assumed 182.155 6 30.359 1.156 .342 Greenhouse­Geisser 182.155 2.646 68.853 1.156 .341 Huynh­Feldt 182.155 4.045 45.035 1.156 .344 Lower­bound 182.155 1.000 182.155 1.156 .307 Error(SCORE) Sphericity Assumed 1575.321 60 26.255 Greenhouse­Geisser 1575.321 26.456 59.546 Huynh­Feldt 1575.321 40.447 38.948 Lower­bound 1575.321 10.000 157.532 Tests of Within­Subjects Contrasts Measure:MEASURE_1 Source SCORE Type III Sum of Squares df Mean Square F Sig. SCORE Linear 2962.680 1 2962.680 46.905 .000 Quadratic 143.040 1 143.040 4.305 .065 Cubic 51.361 1 51.361 2.242 .165 Order 4 73.724 1 73.724 2.765 .127 Order 5 3.584 1 3.584 .405 .539 Order 6 12.147 1 12.147 4.444 .061 SCORE * Gender Linear 25.537 1 25.537 .404 .539 Quadratic 21.254 1 21.254 .640 .442 Cubic 66.694 1 66.694 2.911 .119 Order 4 55.767 1 55.767 2.092 .179 Order 5 5.060 1 5.060 .572 .467 Order 6 7.841 1 7.841 2.869 .121 Error(SCORE) Linear 631.638 10 63.164 Quadratic 332.272 10 33.227 Cubic 229.083 10 22.908 Order 4 266.594 10 26.659 Order 5 88.403 10 8.840 Order 6 27.330 10 2.733 Tests of Between­Subjects Effects Measure:MEASURE_1 Transformed Variable:Average Source Type III Sum of Squares df Mean Square F Sig. Intercept 114349.339 1 114349.339 188.733 .000 Gender 290.720 1 290.720 .480 .504 Error 6058.804 10 605.880 a. Is the assumption of sphericity violated? How can you tell? What does this mean in the context of interpreting the results? Mauchly's Test of Sphericity b Measure:MEASURE_1 a Within Subjects Epsilon Effect Mauchly's Approx. Chi- Greenhouse- Huynh- Lower- W Square df Sig. Geisser Feldt bound dimension1 SCORE .001 56.876 20.000 .441 .674 .167 Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix. a. 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. b. Design: Intercept + Gender Within Subjects Design: SCORE This table shows the results of Mauchly's Test of Sphericity which tests for one of the assumptions of the ANOVA with repeated measures, namely sphericity (homogeneity of covariance). It is important to look at this table as this assumption is commonly violated. Since here P-value is less than .05, we conclude that there are significant differences between the variance of difference; the condition of sphericity has been not met. b. Is there a main effect of gender? If so, explain the effect. Use post hoc tests when necessary or explain why they are not required in this specific case. There is no main effect of gender because gender has a P-value .504 which depicts that this is not significant at 5% level. Here the effect is not significant so there is no need of post hoc test. If the effect is significant then we also not able to perform the post hoc test because here we have only two categories. Post hoc can be run if we have more than two categories. c. Is there a main effect time (i.e., an increase in scores from Week 0 to Week 12)? If so, explain the effect. Use post hoc tests when necessary or explain why they are not required in this specific case. Examine the output carefully and give as much detail as possible in your findings. d. Write up the results in APA style and interpret them. Be sure that you discuss both main effects and the presence/absence of an interaction between the two. Tests of Within-Subjects Effects Measure:MEASURE_1 Source Type III Sum of Squares df Mean Square F Sig. SCORE Sphericity Assumed 3246.536 6 541.089 20.609 .000 Greenhouse-Geisser3246.536 2.646 1227.164 20.609 .000 Huynh-Feldt 3246.536 4.045 802.659 20.609 .000 Lower-bound 3246.536 1.000 3246.536 20.609 .001 SCORE * Gender Sphericity Assumed 182.155 6 30.359 1.156 .342 Greenhouse-Geisser182.155 2.646 68.853 1.156 .341 Huynh-Feldt 182.155 4.045 45.035 1.156 .344 Lower-bound 182.155 1.000 182.155 1.156 .307 Error(SCORE) Sphericity Assumed 1575.321 60 26.255 Greenhouse-Geisser1575.321 26.456 59.546 Huynh-Feldt 1575.321 40.447 38.948 Lower-bound 1575.321 10.000 157.532 Pairwise Comparisons Measure:MEASURE_1 (I) SCORE (J) SCORE 95% Confidence Interval for a Difference Mean Difference (I-J)Std. Error Sig. Lower Bound Upper Bound 1 2 -4.500 3.383 .213 -12.039 3.039 3 -6.062* 2.412 .031 -11.437 -.688 dim * 4 -5.312 2.117 .031 -10.029 -.596 ensi on2 5 -9.937* 2.693 .004 -15.938 -3.937 * 6 -15.813 2.683 .000 -21.791 -9.834 7 -20.563* 3.524 .000 -28.415 -12.710 2 1 4.500 3.383 .213 -3.039 12.039 3 -1.562 1.542 .335 -4.998 1.873 dim 4 -.812 2.324 .734 -5.990 4.365 ensi on2 5 -5.437* 1.914 .018 -9.701 -1.174 6 -11.313* 2.063 .000 -15.909 -6.716 * 7 -16.063 3.154 .000 -23.089 -9.036 3 1 6.062* 2.412 .031 .688 11.437 2 1.562 1.542 .335 -1.873 4.998 dim 4 .750 1.097 .510 -1.693 3.193 ensi * on2 5 -3.875 1.058 .004 -6.233 -1.517 6 -9.750* 1.336 .000 -12.726 -6.774 * 7 -14.500 2.739 .000 -20.603 -8.397 4 1 5.312* 2.117 .031 .596 10.029 2 .812 2.324 .734 -4.365 5.990 dim dim 3 -.750 1.097 .510 -3.193 1.693 ensi ensi * on1 on2 5 -4.625 1.019 .001 -6.895 -2.355 6 -10.500* 1.202 .000 -13.177 -7.823 The main effect score is significant at 5% level of significance. From this table we are able to discover the F value for the " score " factor, its associated significance level and effect size (Partial Eta Squared). As our data violated the assumption of sphericity we look at the values in the Greenhouse-Geisser row. Had sphericity not been violated we would have looked under the Sphericity Assumed row. We can report that when using an ANOVA with repeated measures with a Greenhouse-Geisser correction, the mean scores for weeks were statistically significantly different (F(2.646, 60) = 20.609, P < 0.0005). Looking at the table above for pair wise compression we need to remember the labels associated with the score in our experiment from the Within-Subject Factors table. This table gives us the significance level for differences between the individual time points. We can see that there was a significant difference in scores between training from pre to week 12. The P- values shaded with yellow color shows the significant differences between groups.

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