PDU 207 Basic Statistics: Variability
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This document provides an overview of variability and different techniques for measuring variability. It discusses how variability describes how spread out scores are in a distribution and serves two purposes: describing the distribution and measuring how well individual scores represent the entire distribution. The document then explains several measures of variability, including the range, interquartile range, standard deviation, and variance. It provides examples of calculating each measure and discusses when different measures would be appropriate depending on the type of variable and measurement scale.
PDU 207 Basic Statistics: Variability
- 1. PDU 207 STATISTIK DASAR SEKSI E SEMESTER GASAL 2016/2017 FAKULTAS PSIKOLOGI / PROGRAM STUDI S1 PSIKOLOGI Variability KULIAH V – 05 SEPTEMBER 2016
- 2. Menguasai teknik-teknik statistika deskriptif dan statistika inferensial, secara khusus terkait dengan: • Tujuan umum dilakukannya perhitungan variabilitas, serta perbedaan kumpulan skor berdasarkan derajat variabilitasnya; • Konsep dan perhitungan berbagai teknik variabilitas. Memiliki kemampuan menyampaikan argumentasi dan penalaran dengan bahasa yang tepat, khususnya berkaitan dengan: • Pemilihan teknik perhitungan variabilitas yang paling tepat sesuai dengan jenis data dan tujuan pengukurannya. One-Day Objectives
- 4. PDU 207 STATISTIK DASAR 2016 © Ardhiati 4 Usia Saat Pertama Kali Jatuh Cinta 15 tahun CENTRAL TENDENCY
- 5. PDU 207 STATISTIK DASAR 2016 © Ardhiati 5 Usia Saat Pertama Kali Jatuh Cinta 15 tahun VARIABILITY 8 tahun 23 tahun
- 6. PDU 207 STATISTIK DASAR 2016 © Ardhiati Variability 6 Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together. THE DEFINITION (Gravetter & Wallnau, 2012: 104) 15 16 171413 Usia Saat Pertama Kali Berpacaran (tahun) 15 19 23118 Usia Saat Pertama Kali Jatuh Cinta (tahun)
- 7. PDU 207 STATISTIK DASAR 2016 © Ardhiati Variability 7 SERVES TWO PURPOSES (Gravetter & Wallnau, 2012: 105) 1 Describes the distribution 2 Measures how well an individual score (or group of scores) represents the entire distribution 158 231713 15 8 23
- 8. PDU 207 STATISTIK DASAR 2016 © Ardhiati Variability 8 THE MEASURES VARIABILITY THE RANGE STANDARD DEVIATION VARIANCE
- 9. PDU 207 STATISTIK DASAR 2016 © Ardhiati Variability 9 THE MEASURES VARIABILITY THE INTERQUARTILE RANGE THE RANGE STANDARD DEVIATION VARIANCE
- 11. PDU 207 STATISTIK DASAR 2016 © Ardhiati The Range 11 The distance covered by the scores in a distribution, from the smallest score to the largest score. (Gravetter & Wallnau, 2012: 106) range = Xmax - Xmin + 1 = URL for Xmax - LRL for Xmin 11 14 13 13 14 14 23 13 15 14 8 15 17 15 14 15 16 16 14 13 Usia Saat Pertama Kali Jatuh Cinta it is completely determined by the two extreme values TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS COUNT vs MEASURE ☐ COUNT ☐ MEASURE MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ ✓ ✓ ✓ ✓ ✓ ✓
- 12. PDU 207 STATISTIK DASAR 2016 © Ardhiati The Interquartile Range 12 The distance covered by the middle 50% of the distribution (Q3 - Q1). 14 15 16 17 18 19 20 21 22 231312111098 1 2 3 4 5 6 Usia Saat Pertama Kali Jatuh Cinta TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS COUNT vs MEASURE ☐ COUNT ☐ MEASURE MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH
- 13. PDU 207 STATISTIK DASAR 2016 © Ardhiati The Interquartile Range 13 The distance covered by the middle 50% of the distribution (Q3 - Q1). 14 15 16 17 18 19 20 21 22 231312111098 1 2 3 4 5 6 Bottom 25% Top 25% Q1 = 13,25 Q3 = 15,25 Interquartile Range = Q3 - Q1 = 2 TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS COUNT vs MEASURE ☐ COUNT ☐ MEASURE MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ ✓ ✓ ✓ ✓ ✓ ✓ Usia Saat Pertama Kali Jatuh Cinta
- 14. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 14 The average distance from the mean. (Gravetter & Wallnau, 2012: 106-114) FOR POPULATION X X - μ (X - μ)2 8 -6,35 40,32 11 -3,35 11,22 13 -1,35 1,82 13 -1,35 1,82 13 -1,35 1,82 13 -1,35 1,82 14 -0,35 0,12 14 -0,35 0,12 14 -0,35 0,12 14 -0,35 0,12 14 -0,35 0,12 14 -0,35 0,12 15 0,65 0,42 15 0,65 0,42 15 0,65 0,42 15 0,65 0,42 16 1,65 2,72 16 1,65 2,72 17 2,65 7,02 23 8,65 74,82 find the deviation (distance from the mean) for each score square each deviation find the average of the squared deviations take the square root of the variance STANDARD DEVIATION VARIANCE 7,43 2,73 μ = 14,35 SS = 148,55μ = 0,00
- 15. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 15 The average distance from the mean. (Gravetter & Wallnau, 2012: 113) FOR POPULATION find the deviation (distance from the mean) for each score square each deviation find the average of the squared deviations take the square root of the variance STANDARD DEVIATION VARIANCE
- 16. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 16 The average distance from the mean. (Gravetter & Wallnau, 2012: 114) FOR SAMPLES 11 14 13 13 14 14 23 13 15 14 8 15 17 15 14 15 16 16 14 13 11 16 13 15 16 POPULATION SAMPLES
- 17. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 17 The average distance from the mean. (Gravetter & Wallnau, 2012: 114) FOR SAMPLES X X - M (X - M)2 11 -3,20 10,24 13 -1,20 1,44 15 0,80 0,64 16 1,80 3,24 16 1,80 3,24 find the deviation (distance from the mean) for each score square each deviation find the average of the squared deviations take the square root of the variance 3,76 1,96 M = 14,20 SS = 18,80M = 0,00
- 18. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 18 The average distance from the mean. (Gravetter & Wallnau, 2012: 114) FOR SAMPLES 11 14 13 13 14 14 23 13 15 14 8 15 17 15 14 15 16 16 14 13 11 16 13 15 16 POPULATION SAMPLES lessvariability POPULATION VARIABILITY SAMPLES VARIABILITY biasedestimate
- 19. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 19 The average distance from the mean. (Gravetter & Wallnau, 2012: 117-118) FOR SAMPLES μ = 14,35 ? M ≈ 14,35 n = 5 11 16 13 15 No restrictions Restricted DEGREES OF FREEDOM
- 20. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 20 The average distance from the mean. (Gravetter & Wallnau, 2012: 114) FOR SAMPLES X X - M (X - M)2 11 -3,20 10,24 13 -1,20 1,44 15 0,80 0,64 16 1,80 3,24 16 1,80 3,24 find the deviation (distance from the mean) for each score square each deviation find the average of the squared deviations take the square root of the variance STANDARD DEVIATION VARIANCE 4,70 2,17 M = 14,20 SS = 18,80M = 0,00
- 21. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 21 The average distance from the mean. (Gravetter & Wallnau, 2012: 117-118) find the deviation (distance from the mean) for each score square each deviation find the average of the squared deviations take the square root of the variance STANDARD DEVIATION VARIANCE FOR SAMPLES
- 22. PDU 207 STATISTIK DASAR 2016 © Ardhiati Standard Deviation & Variance 22 The average distance from the mean. TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS COUNT vs MEASURE ☐ COUNT ☐ MEASURE MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ ✓ ✓ ✓ ✓
- 24. PDU 207 STATISTIK DASAR 2016 © Ardhiati Selecting a Measure 24 OF CENTRAL TENDENCY & VARIABILITY TYPE OF VARIABLES MEASUREMENT SCALE CENTRAL TENDENCY THE MODE THE MEDIAN THE MEAN VARIABILITY COUNT OF VARIATIONS THE RANGE THE INTERQUARTILE RANGE STANDARD DEVIATION VARIANCE DISCRETE CONTINUOUS NOMINAL ORDINAL INTERVAL RATIO
- 25. PDU 207 STATISTIK DASAR 2016 © Ardhiati 25 WANT TO KNOW MORE? Gravetter, F.J. & Wallnau, L.B. (2012). Statistics for the behavioral sciences (9th ed.). Australia: WADSWORTH CENGAGE Learning.