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# PDU 207 Basic Statistics: Variability

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Variability as a part of descriptive statistic …

Variability as a part of descriptive statistic
(Lecture slides mostly in Bahasa Indonesia)

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• 1. VARIABILITY PDU 207 STATISTIK DASAR SEMESTER GASAL 2014/2015 FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA KULIAH V - 11 September 2014
• 2. ONE DAY OBJECTIVES Mahasiswa memahami tujuan umum dilakukannya perhitungan variability, serta mampu mengenali perbedaan kumpulan skor berdasarkan derajat variabilitasnya; Mahasiswa mampu memahami konsep dan melakukan perhitungan berbagai teknik variability; Mahasiswa mampu melakukan perbandingan terhadap berbagai teknik variability, sehingga dapat memilih teknik yang paling tepat sesuai tujuan pengukurannya.
• 3. BERAPA KALI BERPACARAN? PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 4. BERAPA KALI BERPACARAN? 20 kali PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 5. BERAPA KALI BERPACARAN? 1 kali 20 kali 43 kali PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 6. BERAPA KALI BERPACARAN? 1 kali 20 kali 43 kali VARIABILITY PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 7. OVERVIEW OF VARIABILITY PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 8. OVERVIEW OF VARIABILITY 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. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 9. OVERVIEW OF VARIABILITY 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. Usia Pertama Kali Jatuh Cinta (tahun) Usia Pertama Kali Berpacaran (tahun) PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 10. OVERVIEW OF VARIABILITY 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. 8 11 12 14 16 8 11 15 19 23 Usia Pertama Kali Jatuh Cinta (tahun) Usia Pertama Kali Berpacaran (tahun) PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 11. OVERVIEW OF VARIABILITY 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. describes the distribution PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 12. OVERVIEW OF VARIABILITY 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. describes the distribution 1 20 43 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 13. OVERVIEW OF VARIABILITY 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. describes the distribution 1 20 43 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 14. OVERVIEW OF VARIABILITY 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. describes the distribution measures how well an individual (or group of) score represents the entire distribution 1 20 43 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 15. OVERVIEW OF VARIABILITY 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. describes the distribution measures how well an individual (or group of) score represents the entire distribution 43 1 20 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 16. OVERVIEW OF VARIABILITY 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. describes the distribution measures how well an individual (or group of) score represents the entire distribution 43 1 20 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 17. OVERVIEW OF VARIABILITY 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. RANGE STANDARD DEVIATION VARIANCE SEMI-INTERQUARTILE RANGE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 18. THE RANGE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 19. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 20. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 21. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 22. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin 5 4 3 3 4 4 8 3 5 4 2 5 7 5 4 5 6 6 4 3 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 23. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin 5 4 3 3 4 4 8 3 5 4 2 5 7 5 4 5 6 6 4 3 it is completely determined by the two extreme values PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 24. THE RANGE the distance covered by the scores in a distribution, from the smallest score to the largest score. MEASUREMENT ✓ ✓ ✓ SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ ✓ ✓ range = Xmax - Xmin + 1 = URL Xmax - LRL Xmin 5 4 3 3 4 4 8 3 5 4 2 5 7 5 4 5 6 6 4 3 it is completely determined by the two extreme values PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 25. THE INTERQUARTILE RANGE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 26. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 27. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 28. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 29. THE INTERQUARTILE RANGE the distance covered by the middle 50% of the distribution (Q3 - Q1). MEASUREMENT ✓ ✓ ✓ SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ✓ ☐ DISCRETE ✓ ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 30. STANDARD DEVIATION & VARIANCE PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 31. STANDARD DEVIATION & VARIANCE FOR POPULATION PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 32. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 33. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. 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 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 34. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation VARIANCE take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 35. STANDARD DEVIATION & VARIANCE FOR POPULATION the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation VARIANCE STANDARD DEVIATION take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 36. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 37. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 38. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION SAMPLES 4 8 3 3 2 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 39. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION SAMPLES 4 8 3 3 2 less variability PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 40. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 5 4 3 3 4 2 5 7 5 4 4 8 3 5 4 5 6 6 4 3 POPULATION SAMPLES 4 8 3 3 2 sample population variability variability less variability biased estimate PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 41. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. 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 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 42. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. find the deviation (distance from the mean) for each score square each deviation VARIANCE STANDARD DEVIATION take the square root of the variance PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 43. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. n = 3 M = 5 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 44. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. n = 3 M = 5 2 9 ? PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 45. STANDARD DEVIATION & VARIANCE FOR SAMPLES the average distance from the mean. n = 3 M = 5 2 9 ? no restrictions restricted DEGREES OF FREEDOM PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 46. STANDARD DEVIATION & VARIANCE the average distance from the mean. MEASUREMENT SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 47. STANDARD DEVIATION & VARIANCE the average distance from the mean. MEASUREMENT ✓ ✓ SCALE ☐ NOMINAL ☐ ORDINAL ☐ INTERVAL ☐ RATIO TYPES OF VARIABLES ☐ DISCRETE ✓ ☐ CONTINUOUS ACCURACY ☐ LOW ☐ MODERATE ☐ HIGH ✓ PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 48. COMPARING MEASURES OF VARIABILITY PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 49. COMPARING MEASURES OF VARIABILITY RANGE SEMI-INTERQUARTILE RANGE STANDARD DEVIATION VARIANCE EXTREME SCORES SAMPLE SIZE STABILITY UNDER SAMPLING OPEN-ENDED DISTRIBUTION ✗ ✗ ✗ ✗ ✓ ✓ ✓ ✓ ✗ ✓ ✓ ✗ ✗ ✓ ✓ ✗ PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
• 50. Want to Know More? Gravetter, F.J. & Wallnau, L.B. (2009). Statistics for the behavioral sciences (8th ed.). Australia: WADSWORTH CENGAGE Learning. Gravetter, F.J. & Wallnau, L.B. (2012). Statistics for the behavioral sciences (9th ed.). Australia: WADSWORTH CENGAGE Learning.