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PDU 207 Basic Statistics: Correlation
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PDU 207 Basic Statistics: Correlation

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(Lecture slides mostly in Bahasa Indonesia)

(Lecture slides mostly in Bahasa Indonesia)

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  • 1. CORRELATION PDU 207 STATISTIK DASAR SEMESTER GASAL 2014/2015 FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA KULIAH X - 06 November 2014
  • 2. ONE DAY OBJECTIVES Mahasiswa memahami konsep dan melakukan perhitungan korelasi Pearson; Mahasiswa memahami korelasi Spearman dan mampu melakukan perbandingan dengan korelasi Pearson; Mahasiswa memahami penggunaan korelasi Pearson untuk melakukan perhitungan korelasi Point-Biserial ketika salah satu variabel bersifat dikotomi.
  • 3. INTRODUCTION TO CORRELATION PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 4. INTRODUCTION TO CORRELATION Konsumsi Bir/Minggu PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 5. INTRODUCTION TO CORRELATION Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 6. INTRODUCTION TO CORRELATION Konsumsi Bir/Minggu Pemahaman Statistik 100 80 60 40 20 0 0 2 4 6 8 10 Konsumsi Bir/Minggu (Liter) Pemahaman Statistik (Nilai Tugas) PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 7. INTRODUCTION TO CORRELATION Correlation is a statistical technique that is used to measure and describe the relationship between two variables. Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 8. INTRODUCTION TO CORRELATION Correlation is a statistical technique that is used to measure and describe the relationship between two variables. • Usually the two variables are simply observed as they exist naturally in the environment— there is no attempt to control or manipulate the variables. Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 9. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 10. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The direction of the relationship The strength or consistency of the relationship The form of the relationship PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 11. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The direction of the relationship PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 12. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The direction of the relationship 0 2 4 6 8 10 Konsumsi Bir/Minggu (Liter) Pemahaman Statistik 100 80 60 40 20 0 0 2 4 6 8 10 Konsumsi Bir/Minggu (Liter) Kecepatan Berkendara (km/jam) 150 125 100 75 50 25 0 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 13. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The direction of the relationship 0 2 4 6 8 10 Konsumsi Bir/Minggu (Liter) Pemahaman Statistik 100 80 60 40 20 0 0 2 4 6 8 10 Konsumsi Bir/Minggu (Liter) Kecepatan Berkendara (km/jam) 150 125 100 75 50 25 0 (a) Positive Correlation (b) Negative Correlation PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 14. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The strength or consistency of the relationship PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 15. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The strength or consistency of the relationship PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 16. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The strength or consistency of the relationship r = +1 r = -0,5048 r = +0,0043 r = -0,8251 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 17. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The form of the relationship PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 18. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The form of the relationship 0 2 4 6 8 10 Konsumsi Weight Gain/Minggu (Liter) Berat Badan (kg) 70 60 50 40 30 20 10 0 0 2 4 6 8 10 Konsumsi Bir/Minggu (Liter) Pemahaman Statistik 100 80 60 40 20 0 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 19. INTRODUCTION TO CORRELATION THE CHARACTERISTICS OF A RELATIONSHIP The form of the relationship 0 2 4 6 8 10 Konsumsi Weight Gain/Minggu (Liter) Berat Badan (kg) 70 60 50 40 30 20 10 0 0 2 4 6 8 10 Konsumsi Bir/Minggu (Liter) Pemahaman Statistik 100 80 60 40 20 0 (a) Linear Correlation (b) Non-linear Correlation PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 20. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 21. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 22. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 23. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables Konsumsi Bir/Minggu Pemahaman Statistik VARIASI variabel X VARIASI variabel Y VARIASI dalam hubungan variabel X dan Y PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 24. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables Konsumsi Bir/Minggu Pemahaman Statistik VARIASI variabel X VARIASI variabel Y VARIASI dalam hubungan variabel X dan Y variability X covariability X & Y variability Y PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 25. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables VARIASI dalam hubungan : ( VARIASI VARIASI ) variabel X dan Y variabel X variabel Y covariability X & Y variability X variability Y PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 26. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables VARIASI dalam hubungan : ( VARIASI VARIASI ) variabel X dan Y variabel X variabel Y covariability X & Y variability X variability Y PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 27. THE PEARSON CORRELATION UNDERSTANDING measures the degree and the direction of the linear relationship between two variables SCORES DEVIATIONS SQUARED DEVIATIONS PRODUCTS X Y X-MX Y-MY (X-MX)2 (Y-MY)2 (X-MX) (Y-MY) 0 2 -6 -2 36 4 +12 10 6 +4 +2 16 4 +8 4 2 -2 -2 4 4 +4 8 4 +2 0 4 0 0 8 6 +2 +2 4 4 +4 SSX = 64 SSY = 16 SP = +28 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 28. THE PEARSON CORRELATION HYPOTHESIS TESTING PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 29. THE PEARSON CORRELATION HYPOTHESIS TESTING Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 30. THE PEARSON CORRELATION HYPOTHESIS TESTING TWO-TAILED HYPOTHESIS Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 31. THE PEARSON CORRELATION HYPOTHESIS TESTING TWO-TAILED HYPOTHESIS • H0: tidak ada hubungan antara konsumsi bir/minggu dan pemahaman statistik H0: ρ = 0 • H1: ada hubungan antara konsumsi bir/minggu dan pemahaman statistik Konsumsi Bir/Minggu H1: ρ ≠ 0 Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 32. THE PEARSON CORRELATION HYPOTHESIS TESTING TWO-TAILED HYPOTHESIS • H0: tidak ada hubungan antara konsumsi bir/minggu dan pemahaman statistik H0: ρ = 0 • H1: ada hubungan antara konsumsi bir/minggu dan pemahaman statistik H1: ρ ≠ 0 ONE-TAILED HYPOTHESIS Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 33. THE PEARSON CORRELATION HYPOTHESIS TESTING TWO-TAILED HYPOTHESIS • H0: tidak ada hubungan antara konsumsi bir/minggu dan pemahaman statistik H0: ρ = 0 • H1: ada hubungan antara konsumsi bir/minggu dan pemahaman statistik H1: ρ ≠ 0 ONE-TAILED HYPOTHESIS • H0: tidak ada hubungan yang positif antara konsumsi bir/ minggu dan pemahaman statistik H0: ρ ≤ 0 • H1: ada hubungan yang positif antara konsumsi bir/minggu dan pemahaman statistik H1: ρ > 0 Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 34. THE PEARSON CORRELATION USING & INTERPRETING PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 35. THE PEARSON CORRELATION USING & INTERPRETING PREDICTION if two variables are known to be related in a systematic way, then it is possible to use one of the variables to make accurate predictions about the other THEORY VERIFICATION the prediction of the theory could be tested by determining the correlation between the two variables VALIDITY measure the correlation between the new test and each of these other measures of the same construct to demonstrate that the new test is valid RELIABILITY a measurement procedure is considered reliable to the extent that it produces stable, consistent measurements; produces the same (or nearly the same) scores when the same individuals are measured twice under the same conditions PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 36. THE PEARSON CORRELATION FOUR ADDITIONAL CONSIDERATIONS SIMPLY DESCRIBES A RELATIONSHIP BETWEEN TWO VARIABLES it does not explain why the two variables are related; should not and cannot be interpreted as proof of a cause-and-effect relationship between the two variables. RESTRICTED RANGE the value of a correlation can be affected greatly by the range of scores represented in the data. OUTLIERS one or two extreme data points, often called outliers, can have a dramatic effect on the value of a correlation. CORRELATION AND THE STRENGTH OF THE RELATIONSHIP when judging how “good” a relationship is, it is tempting to focus on the numerical value of the correlation; a correlation should not be interpreted as a proportion. PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 37. PARTIAL CORRELATION Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 38. PARTIAL CORRELATION Konsumsi Bir/Minggu Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 39. PARTIAL CORRELATION Konsumsi Bir/Minggu Daya Tahan Tubuh Pemahaman Statistik PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 40. PARTIAL CORRELATION Konsumsi Bir/Minggu Daya Tahan Tubuh Pemahaman Statistik measures the relationship between two variables while controlling the influence of a third variable by holding it constant PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 41. PARTIAL CORRELATION Konsumsi Bir/Minggu Daya Tahan Tubuh Pemahaman Statistik measures the relationship between two variables while controlling the influence of a third variable by holding it constant PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 42. PARTIAL CORRELATION Konsumsi Bir/ Minggu Pemahaman Statistik Daya Tahan Tubuh 1 4 1 2 3 1 3 1 1 4 2 1 5 5 1 7 8 2 8 11 2 9 9 2 10 7 2 11 10 2 13 15 3 14 14 3 15 16 3 16 17 3 17 13 3 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 43. PARTIAL CORRELATION • rXY = 0,923 rXZ = 0,961 rYZ = 0,961 Konsumsi Bir/ Minggu Pemahaman Statistik Daya Tahan Tubuh 1 4 1 2 3 1 3 1 1 4 2 1 5 5 1 7 8 2 8 11 2 9 9 2 10 7 2 11 10 2 13 15 3 14 14 3 15 16 3 16 17 3 17 13 3 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 44. PARTIAL CORRELATION • rXY = 0,923 rXZ = 0,961 rYZ = 0,961 • rXY-Z = 0 Konsumsi Bir/ Minggu Pemahaman Statistik Daya Tahan Tubuh 1 4 1 2 3 1 3 1 1 4 2 1 5 5 1 7 8 2 8 11 2 9 9 2 10 7 2 11 10 2 13 15 3 14 14 3 15 16 3 16 17 3 17 13 3 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 45. ALTERNATIVES TO THE PEARSON CORRELATION PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 46. ALTERNATIVES TO THE PEARSON CORRELATION PEARSON CORRELATION when both variables are measured on interval and/or ratio scales SPEARMAN CORRELATION when both variables are measured on ordinal scales POINT-BISERIAL CORRELATION when one of the variable is measured on interval or ratio scale and the other on nominal scale BISERIAL CORRELATION when one of the variable is measured on continuous and the other on dichotomous variable PHI-COEFFICIENT when both variables are measured on dichotomous variable PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 47. ANALYSIS THE CORRELATION COEFFICIENT PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 48. ANALYSIS THE CORRELATION COEFFICIENT distribution of correlation coefficient in z-scores μ = 0 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 49. ANALYSIS THE CORRELATION COEFFICIENT distribution of correlation coefficient in z-scores α = 0,05 α = 0,05 TWO-TAILED ONE-TAILED PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 50. ANALYSIS THE CORRELATION COEFFICIENT distribution of correlation coefficient in z-scores α = 0,05 α = 0,05 TWO-TAILED ONE-TAILED z = -1,96 z = +1,96 z = +1,65 PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 51. ANALYSIS THE CORRELATION COEFFICIENT distribution of correlation coefficient in z-scores α = 0,05 α = 0,05 TWO-TAILED ONE-TAILED z = -1,96 z = +1,96 z = +1,65 rcritical PDU 207 STATISTIK DASAR FAKULTAS PSIKOLOGI UNIVERSITAS KATOLIK INDONESIA ATMA JAYA ardhiati © 2014
  • 52. Want to Know More? Gravetter, F.J. & Wallnau, L.B. (2012). Statistics for the behavioral sciences (9th ed.). Australia: WADSWORTH CENGAGE Learning.