1STATISTICS Table of Contents Introduction:-...................................................................................................................................3 Question and Answers:-...................................................................................................................3 Answer 1......................................................................................................................................3 Part I.........................................................................................................................................3 Part II.......................................................................................................................................3 Part III......................................................................................................................................3 Answer 2......................................................................................................................................4 Part I.........................................................................................................................................4 Part II.......................................................................................................................................4 Part III......................................................................................................................................4 Answer 3......................................................................................................................................4 Part I.........................................................................................................................................4 Part II.......................................................................................................................................5 Part III......................................................................................................................................5 Answer 4......................................................................................................................................5
2STATISTICS
3STATISTICS Introduction:- The survey data is based on a Graduate Diploma in Educational Psychology students of Melbourne, Australia and surrounding diatrict. The study was designed to explore the factors that influence on respondents’ psychological adjustment and wellbeing. In this study, there is a variety of validated scales measuring constructs. The scale included the measurement of self- esteem, optimism, perceptions of control, perceived stress, good and bad effect and satisfaction in lifespan. A “Likert” scale was also involved that measured tendency of people to present themselves in a favourable or socially desirable manner. Question and Answers:- Answer 1 Case Processing Summarya Cases ValidMissingTotal NPercentNPercentNPercent 42697.0%133.0%439100.0% a. Squared Euclidean Distance used Agglomeration Schedule StageCluster CombinedCoefficientsStage Cluster First AppearsNext Stage Cluster 1Cluster 2Cluster 1Cluster 2 1105133.00300161 2154160.00800278 3341402.01500110 4298312.0210041 5247373.02700190 6145197.03500283
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34STATISTICS ANOVA Sum of SquaresdfMean SquareFSig. Total Optimism Between Groups2219.52721109.76375.561.000 Within Groups6212.57642314.687 Total8432.103425 Total positive affect Between Groups4177.21022088.60549.427.000 Within Groups17874.27642342.256 Total22051.486425 Total negative affect Between Groups10522.06025261.030204.051.000 Within Groups10906.18442325.783 Total21428.244425 Total life satisfaction Between Groups4763.54222381.77167.450.000 Within Groups14936.78742335.312 Total19700.329425 Total perceived stress Between Groups7224.30523612.153204.774.000 Within Groups7461.60142317.640 Total14685.906425 Total Self esteem Between Groups7034.25323517.127286.143.000 Within Groups5199.30842312.292 Total12233.561425 Total social desirability Between Groups155.207277.60420.487.000 Within Groups1602.2794233.788 Total1757.486425 Part I 1.a) According to the hierarchical clustering, in dissimilarity matrix, we calculated the one- to-one distances between the 426 samples among 439 samples.
35STATISTICS The number of cases in Cluster 1 is 128 (29.2%), Cluster 2 is 263 (59.9%) and Cluster 3 is 35 (8.0%). Part II 1.b) We have considered three clusters and calculated the Ward linkage. Here also the total number of cases is 426. The Ward linkage dendogram is also executed in the analysis. The cases in each cluster have been provided in a new table. Part III 1.c)TheWardlinkageissinglehierarchicallinkage.Thiskindofagglomerative hierarchical clustering created the dendogram diagram. Most of the samples are located in cluster 2. There are statistically significant differences between the variables used to study outdoor lifestyle and the cluster means at 0.05 level of significance (p-value < 0.000). Answer 2 Initial Cluster Centers Cluster 123 Total Optimism26919 Total Self esteem402331 Total positive affect492015 Total negative affect363914 Total life satisfaction33533 Total perceived stress314619 Total social desirability328 Iteration Historya IterationChange in Cluster Centers
36STATISTICS 123 121.70122.73820.581 22.347.7253.255 3.011.009.025 45.030E-005.000.000 52.329E-0071.181E-0061.552E-006 61.078E-0091.389E-0081.213E-008 75.000E-0121.634E-0109.475E-011 82.436E-0141.921E-0127.363E-013 9.0002.119E-0141.020E-014 10.000.000.000 a. Convergence achieved due to no or small change in cluster centers. The maximum absolute coordinate change for any center is .000. The current iteration is 10. The minimum distance between initial centers is 44.034. Final Cluster Centers Cluster 123 Total Optimism241921 Total Self esteem362834 Total positive affect392830 Total negative affect172816 Total life satisfaction271620 Total perceived stress243426 Total social desirability556
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49STATISTICS Total Optimism1142.863214.53042378.653.000 Total Self esteem2544.653216.889423150.665.000 Total positive affect5603.862225.635423218.599.000 Total negative affect4770.436228.103423169.751.000 Total life satisfaction3954.891227.874423141.886.000 Total perceived stress3267.305219.270423169.552.000 Total social desirability26.17824.0314236.494.002 The F tests should be used only for descriptive purposes because the clusters have been chosen to maximize the differences among cases in different clusters. The observed significance levels are not corrected for this and thus cannot be interpreted as tests of the hypothesis that the cluster means are equal. Number of Cases in each Cluster Cluster 1196.000 298.000 3132.000 Valid426.000 Missing13.000 Part I 2.a) The k-means clustering for three different clusters indicate that most of the samples are located in cluster 1 (196) whereas the least number of samples are located in cluster 2 (98). The number of samples is 426 for k-mean clustering. Part II 2.b) There are three clusters calculated for seven variables over 426 samples. Part III 2.c) The Distances between cluster 1 and cluster 2 is maximum (23.722) and the distances between cluster 1 and cluster 3 is minimum (12.005).
50STATISTICS The mean-square error is higher in case of positive effect and negative effect. The life satisfaction is higher than total optimism, total life satisfaction and total perceived stress in this case. The significant p-values all are less than 0.05 when F-test in handled. The F-test is used for descriptive purposes as the clusters have been chosen to optimize the differences among cases in different clusters. The hypothesis of equal cluster means is rejected at 95% confidence level. Answer 3
51STATISTICS Part I 3.a) In two-step cluster analysis, samples in cluster 2 (187, 43.9%) is highest followed by samples in cluster 1 (164, 38.5%). The Lowest number of samples in cluster 3 is 75 and 17.6% in percentage. Part II 3.b) The sharing percentages of seven variables of 426 samples are clustered in the output table. Part III 3.c) Both total perceived stress and total negative effect is highest in cluster 3 and lowest in cluster 1. Conversely, the total self-esteem, total optimism, total positive effect, total social desirability and total life satisfaction is highest in cluster 1 and lowest in cluster 3. Answer 4 4. For k-means and two-step clustering, most of the samples lie in cluster 2. However, in hierarchical clustering, most of the samples lie in cluster 1. In all the clusters, the minimum numbers of samples lie in cluster 3. The clusters took into account the 426 samples in each case. All the clustering methods were incorporated with the division of three clusters.
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