1. STATISTIK PENDIDIKAN EDU5950 SEM1 2014-15
STATISTIK INFERENSI: PENGUJIAN HIPOTESIS BAGI ANALISIS KORELASI ATAU HUBUNGAN
(UJIAN – r )
Rohani Ahmad Tarmizi - EDU5950

2. STATISTIK INFERENSI ATAU PENTAKBIRAN (Inferential Statistics)
Bertujuan untuk menerangkan ciri populasi berdasarkan data yang dikumpul daripada sampel.
Tujuan ini berkait rapat dengan objektif kajian serta hipotesis atau soalan kajian.
Membolehkan penyelidik membuat kesimpulan bahawa terdapat “statistik yang signifikan” atau “statistical significance” yang bermaksud boleh diterima pakai dengan meluas, meyakinkan.

3. LANGKAH PENGUJIAN HIPOTESIS
L1. Nyatakan hipotesis hipotesis statistik/sifar (H0) dan hipotesis penyelidikan (HA) – BERARAH ATAU TIDAK BERARAH
L2. Tetapkan aras signifikan, taburan persampelan dan statistik pengujian yang akan digunakan – ARAS ALPHA = 0.01/ 0.05/ 0.10, TABURAN PERSAMPELAN z, t, F, r… STATISTIK PENGUJIAN (z, t, F, r…)
L3. Tentukan nilai kritikal bagi taburan persampelan yang akan digunakan RUJUK JADUAL z, t, F, r…
L4. Kirakan statistik pengujian (tests statistics) bagi taburan persampelan tersebut – RUJUK FORMULA
L5. Buat keputusan, tafsiran, dan kesimpulan.

4. L1. Nyatakan hipotesis Hipotesis penyelidikan –
Terdapat perbezaan yang signifikan antara min tahap kepimpinan pengajaran Pengetua di Sekolah berprestasi tinggi berbanding dengan sekolah Swasta .
Hipotesis nol/sifar –
Tiada terdapat perbezaan yang signifikan antara min tahap kepimpinan pengajaran Pengetua di sekolah berprestasi tinggi berbanding dengan sekolah Swasta.

5. HA : µ1 ≠ µ2 HO : µ1 ≥ µ2 HA : µ1 < µ2 HO : µ1 ≤ µ2 HA : µ1 > µ2
1. Nyata hipotesis nol dan penyelidikan.
HO : µ1 = µ2
HA : µ1 ≠ µ2
HO : µ1 ≥ µ2
HA : µ1 < µ2
HO : µ1 ≤ µ2
HA : µ1 > µ2

6. L1. Nyatakan hipotesis (dua kumpulan)
Hipotesis penyelidikan –
Terdapat perbezaan yang signifikan antara tahap kepimpinan pengajaran Pengetua, GPK2 dan GPK1.
Hipotesis nol/sifar –
Tiada terdapat perbezaan yang signifikan antara tahap kepimpinan pengajaran Pengetua, GPK2 dan GPK1.

7. ANOVA’S Hypothesis H0: 1 = 2 = 3 = ... = c
All population means are equal
No treatment effect (NO variation in means among groups)
H1: not all the k are equal
At least ONE population mean is different
(Others may be the same!)
There is treatment effect
Does NOT mean that all the means are different: 1  2  ...  c

8. UJIAN PERBANDINGAN MIN
Ujian-t bebas (independent sample t-test)
diguna untuk menguji hipotesis bahawa tiada/ada perbezaan min kemahiran IT antara kumpulan lelaki dan perempuan.
Ujian-t bersandar (paired sample t-test)
digunakan untuk menguji hipotesis bahawa tiada/ada perbezaan min tahap kepemimpinan mengarah dengan min tahap kepemimpinan partisipatif.
Ujian analisis varians (analysis of variance, F test)
digunakan untuk menguji hipotesis tiada/ada perbezaan min kepuasan bekerja antara kumpulan yang berbeza taraf pekerjaan.

9. UJIAN PERBANDINGAN MIN-MIN
Terdapat perbezaan min antara dua kumpulan yang dikaji
(hipotesis penyelidikan)
Tiada terdapat perbezaan min antara kumpulan yang dikaji
(hipotesis sifar atau statistik).
Disini yang dibanding adalah min ia itu skor pembolehubah bersandar daripada dua atau lebih daripada dua kumpulan yang dikaji.

10. Uji diri anda!!!-Apakah pengujian statistik yang diperlukan, JIKA ANDA HENDAK?
1: Mengkaji sama ada terdapat perkaitan min kecekapan menjalankan penyelidikan dengan min pengetahuan statistik di kalangan pelajar Masters.
2: Menentukan sama ada terdapat hubungan antara tahap penglihatan “left field” dengan “right field” di kalangan pelajar.
3: Menguji terdapat hubungan antara kemahiran berkomunikasi dengan tahap keyakinan-diri dikalangan pelajar FPP.
4: Menguji terdapat hubungan kemahiran IT antara abang dan adik.
5. Mengenal pasti hubungan kecerdasan intelek dengan kecerdasan emosi

11. BAGI TUJUAN SEDEMIKIAN!!
ANDA PERLUKAN ANALISIS
KORELASI ATAU HUBUNGAN

12. ANALISIS KORELASI (Correlation Analysis)
Analisis ini membolehkan penyelidik menguji hipotesis bahawa terdapat
hubungan (relationship),
korelasi (correlation) atau
perkaitan (association)
antara dua atau lebih pembolehubah
Analisis ini bertujuan untuk menentukan hubungan/korelasi antara pembolehubah- pembolehubah yang dikaji yang diperoleh/diukur daripada responden kajian iaitu kumpulan sampel ataupun populasi.

13. Adakah terdapat hubungan antara dua pembolehubah tersebut?
Analisis ini digunakan untuk menjawab persoalan kajian seperti berikut:
Adakah terdapat hubungan antara dua pembolehubah tersebut?
“Is there relationship between the two variables?”
Sejauh manakah hubungan tersebut?
“How strong is the relationship?”
Apakah arah hubungan tersebut?
“What is the direction of the relationship?”

14. ANALISIS KORELASI
Analisis korelasi juga boleh dilanjutkan menjadi beberapa pembolehubah – MULTICORELATIONAL ANALYSIS
Ia mengukur sejauh manakah dua atau lebih pembolehubah berubah (covary) secara serentak ataupun bersama-sama.
It is a measure of how variables covary together, hence the word CORRELATION

15. ANALISIS KORELASI
Analisis juga membabitkan dua kategori pembolehubah iaitu pembolehubah prediktif dan pembolehubah kriterion.
P/U prediktif adalah yang memberi kesan atau mempengaruhi P/U yang kedua.
P/U kriterion adalah yang menerima kesan atau pengaruh daripada P/U pertama.
X (prediktif) Y (kriterion)
X1, X2, X3,.. Y (kriterion)
Walau bagaimanapun, analisis ini hanya memeri gambaran hubungan dan tidak memberi rumusan “cause-and-effect relationship”.

16. Sebagai contoh, penyelidik hendak menentukan hubungan antara:
minat terhadap bidang dengan prestasi,
pendapatan dan kepuasan bekerja
kadar baja dan pertumbuhan pokok
frekuensi merokok dengan frekuensi mendapat serangan jantung
Umur dengan kadar ingatan
jam mentelaah, amalan pemakanan, IQ dengan prestasi.

17. Other Examples of Correlation Analysis
A researcher interested in the relationship between measures of depression and violence among fathers.
Relationship between age in years and performance in motor skills.
Relationship between hours of leisure and performance in course.

18. Specific Example
Temperature (F)
Water Consumption (ounces) 75 16 83 20
85  25 85 27 92 32 97 48 99
For seven random summer days, a person recorded the temperature and their water consumption, during a three-hour period spent outside.  
(The data is shown in the table with the temperature placed in increasing order.)

19. How would you describe the graph?
This graph helps us visualize what appears to be a somewhat linear relationship between temperature and the amount of water one drinks.

20. Other Direction of Correlation
Direction of the Association: The association can be either positive or negative. Positive Correlation: as the x variable increases so does the y variable. Example: In the summer, as the temperature increases, so does thirst. Negative Correlation: as the x variable increases, the y variable decreases. Example: As the price of an item increases, the number of items sold decreases.

21. Correlation x y Response Explanatory (Dependent) (Independent)
A relationship between two variables.
Explanatory
(Independent)
Variable
Response
(Dependent)
Variable x y
Hours of Training
Number of Accidents
Shoe Size
Height
Cigarettes smoked per day
Lung Capacity
Score on MUET
Grade Point Average
Height IQ
What type of relationship exists between the two variables and is the correlation significant?

22. Dua Cara Menentukan Korelasi
Secara bergambar iaitu dinamakan gambarajah sebaran (scatter diagram) yang menunjukkan pola kedudukan pasangan titik-titik.
Daripada gambarajah sebaran kita dapat merumus keteguhan (magnitud) korelasi tersebut serta arah korelasinya.

23. Dua Cara Menentukan Korelasi
Secara berangka iaitu dengan menentukan pekali, koefisi atau indeks.
Daripada pekali tersebut kita dapat mengetahui keteguhan (magnitud) korelasi tersebut serta arahnya sama positif atau negatif.

24. MEMBINA GAMBAR RAJAH SEBARAN
Lakarkan dua paksi mengufuk dan mencancang
Letakkan p/u X (IV or predictive) pada paksi mengufuk dan tandakan paksi tersebut
Letakkan p/u Y (DV or criterion) pada paksi mencancang.
Plotkan titik-kedudukan bagi setiap pasangan skor di lakaran tersebut ia itu titik persilangan titik bagi X dan titik bagi Y bagi setiap pasangan skor.

25. Pola Kedudukan Titik Serta Garis Lurus Yang Terbentuk Menggambarkan Korelasi Atau Hubungan Iaitu:
titik-titik yang terletak di atas garis lurus yang mendongak menunjukkan korelasi sempurna dan positif.
titik-titik yang terletak di atas garis lurus yang menunduk menunjukkan korelasi sempurna dan negatif.
titik-titik yang bersepah tanpa pola garis lurus menunjukkan tiada korelasi.

26. Pola Kedudukan Titik Serta Garis Lurus Yang Terbentuk Menggambarkan Korelasi Atau Hubungan Iaitu:
titik-titik yang menghampir dengan garis lurus yang mendongak menunjukkan korelasi teguh dan positif.
titik-titik yang berjauhan daripada garis lurus serta juga mendongak menunjukkan korelasi lemah dan positif.

27. Pola Kedudukan Titik Serta Garis Lurus Yang Terbentuk Menggambarkan Korelasi Atau Hubungan Iaitu:
titik-titik yang menghampiri dengan garis lurus yang menunduk menunjukkan korelasi teguh dan negatif.
titik-titik yang berjauhan daripada garis lurus yang juga menunduk menunjukkan korelasi lemah dan negatif.

28. Scatter Plots and Types of Correlation
x = SAT score
y = GPA
GPA
Positive Correlation
as x increases y increases

29. Scatter Plots and Types of Correlation
Accidents
x = hours of training
y = number of accidents
Negative Correlation
as x increases, y decreases

30. x y 8 78 2 92 5 90 12 58 15 43 9 74 6 81 x Absences Grade Absences x 2 4 6 8 10 12 14 16 40 45 50 55 60 65 70 75 80 85 90 95 x
Final
Grade
Ask students to identify the type of linear correlation described by the scatter plot.
Absences

31. Scatter Plots and Types of Correlation
x = height
y = IQ IQ
No linear correlation

32. Displays of scores in a Scatterplot
Hours of
Internet
use
per week
Depression
scores
from 15-45
Depression scores
Y=D.V. 50 40 30 20 10 M + -
Hours of Internet Use
X=I.V. 5 15 +

33. Association Between Two Scores Linear and non-linear patterns
A. Positive Linear (r=+.75)
B. Negative Linear (r=-.68)
C. No Correlation (r=.00)

34. Linear and non-linear patterns
D. Curvilinear
E. Curvilinear
F. Curvilinear

35. Analisis Korelasi Menunjukkan 3 perkara penting, iaitu:
Arah/Direction (positive or negative)
Bentuk/Form (linear or non-linear)
Kekuatan/Magnitude (size of coefficient)

36. PEKALI ATAU KOEFISI KORELASI
TERDAPAT BEBERAPA JENIS PEKALI KORELASI IAITU:
Pearson product-moment correlation
Digunakan apabila p/u x dan y adalah pada skala sela atau nisbah atau gabungan kedua-duanya.
Spearman rho correlation
Digunakan apabila p/u x dan y adalah pada skala ordinal atau gabungan ordinal dengan sela/nisbah.
Point-biserial correlation
Digunakan apabila p/u x adalah dikotomus dan p/u y adalah pada skala sela atau nisbah.

37. Pekali Pearson [ n  x2 - ( x) 2 ] [ n  y2 - ( y) 2 ]
r = n [  x y ] - [  x  y ]
[ n  x2 - ( x) 2 ] [ n  y2 - ( y) 2 ]
n = bilangan pasangan skor
 x y = jumlah skor x didarab dengan skor y
 x = jumlah skor x
 y = jumlah skor y

38. Pekali Spearman n [ n2 - 1 ] r = 1 - [ 6  B 2 ]
n = bilangan pasangan skor
 B = jumlah beza pasangan setiap skor

39. Pekali Point-biserial
r = y1 – y [ n1 n2 ]
sy n [ n - 1 ]

40. Interpreting Value of the Correlation Coefficient
The coefficient vary from zero to one.
Zero means there is simply no correlation between the two variables.
One means a perfect correlation.
Values approaching one is considered highly correlated.
Values approaching zero is least correlated.
A middle score indicates moderate or average correlation.

41. Interpreting Positive Correlation
A correlation can either be positively or negatively correlated.
Positive correlation is indicated by a positive value is obtained.
This means that the two variables are varying from each other: as X increases Y will also increase.
Y being the criterion variables (dependent variables) and X the predictive variables (independent variables)

42. Non-linear associations statistics
Spearman rho (rs) - correlation coefficient for nonlinear ordinal data
Point-biserial - used to correlate continuous interval data with a dichotomous variable
Phi-coefficient - used to determine the degree of association when both variable measures are dichotomous

43. Association Between Two Scores Degree and strength of association
.20–.35:
When correlations range from .20 to .35, there is only a slight relationship
.35–.65:
When correlations are above .35, they are useful for limited prediction.
.66–.85:
When correlations fall into this range, good prediction can result from one variable to the other. Coefficients in this range would be considered very good.
.86 and above:
Correlations in this range are typically achieved for studies of construct validity or test-retest reliability.

44. Interpreting Value of the Correlation Coefficient
The coefficient vary from zero to one.
Zero means there is simply no correlation between the two variables.
One means a perfect correlation.
Values approaching one is considered highly correlated.
Values approaching zero is least correlated.
A middle score indicates moderate or average correlation.

45. Guildford Rule of Thumb
r Strength of Relationship
< Negligible Relationship
0.2 – 0.4 Low Relationship
0.4 – 0.7 Moderate Relationship
0.7 – High Relationship
> Very high Relationship

46. Other Strengths of Association- By Johnson and Nelson (1986)
r-value
Interpretation
0.00
No relationship
Low relationship
Slightly Moderate relationship
Moderate relationship
Strong relationship
1.00
Perfect relationship
*  No other values of r have precise definitions of strength. See the chart below.
Note:  All of the values in the second table are positive. Thus the associations are positive. The same strength interpretations hold for negative values of r, only the direction interpretations of the association would change.

47. TYPES OF CORRELATION Pearson correlation coefficient.
Spearman’s rank correlation coefficient.
Point-biserial correlation coefficient.

48. L1. Nyatakan hipotesis Hipotesis penyelidikan –
Terdapat hubungan yang signifikan antara tahap kepimpinan pengajaran Pengetua dengan prestasi akademik sekolah di Sabah
Hipotesis nol/sifar –
Tiada terdapat hubungan yang signifikan antara tahap kepimpinan pengajaran Pengetua dengan prestasi akademik sekolah di Sabah

49. L2. TETAPKAN ARAS ALPHA = 0. 01/ 0. 05/ 0
L2. TETAPKAN ARAS ALPHA = 0.01/ 0.05/ 0.10, TABURAN PERSAMPELAN, STATISTIK PENGUJIAN
Nilai alpha ditetapkan oleh penyelidik.
Ia merupakan nilai penetapan bahawa penyelidik akan menerima sebarang ralat semasa membuat keputusan pengujian hipotesis tersebut.
Ralat yang sekecil-kecilnya ialah 0.01 (1%), 0.05 (5%) atau 0.10(10%).
Nilai ini juga dipanggil nilai signifikan, aras signifikan, atau aras alpha.

50. L2. Taburan Persampelan
Taburan yang bersesuaian dengan analisis yang dijalankan. Ia merupakan model taburan korelasi yang mana nilai korelasi itu bertabur secara normal.
Di kawasan kritikal terletak nilai korelasi yang “luar biasa” -> Ha adalah benar
Dikawasan tak kritikal terletak nilai korelasi yang “biasa” -> Ho adalah benar

51. L3. Nilai Kritikal
Nilai kritikal adalah nilai yang menjadi sempadan bagi kawasan Ho benar dan Hp benar.
Nilai ini merupakan nilai dimana penyelidik meletakkan penetapan sama ada cukup bukti untuk menolak Ho (maka boleh menerima Hp) ataupun tidak cukup bukti menolak Ho (menerima Ho).
Nilai ini bergantung kepada nilai alpha dan arah pengujian hipotesis yang dilakukan.

52. L4. Nilai Statistik Pengujian
Ini adalah nilai yang dikira dan dijadikan bukti sama ada hipotesis sifar benar atau salah.
Jika nilai statistik pengujian masuk dalam kawasan kritikal maka Ho adalah salah, ditolak dan Hp diterima
Jika nilai statistik pengujian masuk dalam kawasan tak kritikal maka Ho adalah benar, maka terima Ho.

53. L4. Nilai Statistik Pengujian
r uji =
r uji =

54. L5. Membuat Keputusan, Tafsiran, dan Kesimpulan
Jika nilai statistik pengujian masuk dalam kawasan tak kritikal maka Ho adalah benar, maka terima Ho.

55. L5. Membuat Keputusan, Kesimpulan dan Tafsiran
Jika nilai statistik pengujian masuk dalam kawasan kritikal maka Ho adalah tak benar, maka Ho ditolak dan seterusnya, Hp diterima (bermakna ada bukti Hp adalah benar)

56. If r is close to 0 there is no linear correlation
Correlation Coefficient - A measure of the strength and direction of a linear relationship between two variables
The range of r is from -1 to 1. -1 1
Give several examples r = -0.97, r = 0.02 and ask for the strength of the correlation. For values like 0.63 a hypothesis test is necessary to determine whether it is strong or not.
If r is close to -1 there is a strong negative correlation
If r is close to 0 there is no linear correlation
If r is close to 1 there is a strong positive correlation

57. Descriptive : Magnitude and Direction of Correlation, r
Purpose – Determine relationship between two metric variables
Requirement : DV - Interval / Ratio scale and IV- Interval / ratio scale
Descriptive : Magnitude and Direction of Correlation, r
Hypotheses:
HO: ρp= 0
HA: ρp≠ 0
ρp> 0
ρp< 0
Inferential: Hypothesis testing

58. Objektif kajian
Mengkaji sama ada terdapat perkaitan bilangan ponteng kelas dengan prestasi dalam ujian.
Soalan kajian
Apakah perkaitan antara bilangan ponteng kelas dengan prestasi dalam ujian
Hipotesis kajian
Ho : Tiada terdapat hubungan antara bilangan ponteng kelas dengan prestasi dalam ujian
HA : Terdapat hubungan antara bilangan ponteng kelas dengan prestasi dalam ujian

59. Application 1 x y 8 78 2 92 5 90 12 58 15 43 9 74 6 81 Absences Grade
Ask students to identify the type of linear correlation described by the scatter plot.

60. x y 8 78 2 92 5 90 12 58 15 43 9 74 6 81 Absences Grade Absences x 2 4 6 8 10 12 14 16 40 45 50 55 60 65 70 75 80 85 90 95 x
Final
Grade
Ask students to identify the type of linear correlation described by the scatter plot.
Absences

61. Pearson Correlation [ n  x2 - ( x) 2 ] [ n  y2 - ( y) 2 ]
r p = n [  x y ] - [  x  y ]
[ n  x2 - ( x) 2 ] [ n  y2 - ( y) 2 ]
n = no of pairs
 x y = summation of x multiply by y
 x = summation of x
 y = summation of y

62. Computation of r xy x2 y2 x y 1 8 78 2 2 92 3 5 90 4 12 58 5 15 43
6084
8464
8100
3364
1849
5476
6561
624
184
450
696
645
666
486 64 4 25
144
225 81 36 57
516
3751
579
39898
Have students interpret this result. Since r is close to -1, there is a strong negative correlation. As the number of absences increase, grades tend to decrease. =

63. Inferential Analysis – Hypothesis Testing
Steps in Hypothesis Testing
1. State the null and alternative hypothesis
HO: ρp= 0
HA: ρp≠ 0 or ρp> 0 or ρp< 0
2. Determine critical value
df = n – 2 One-tailed or Two-tailed
3. Calculate the test statistic
4. Make your decision
5. Make conclusion
Reject HO: Significant relationship between the two variables
Fail to Reject Ho: No significant relationship between the two variables

64. 1. Calculated an appropriate correlation coefficient.
Example 1 :
Data were collected from a randomly selected sample to determine relationship between average assignment scores and test scores in statistics. Distribution for the data is presented in the table below. Assuming the data are normally distributed.
1. Calculated an appropriate correlation
coefficient.
2. Describe the nature of relationship
between the two variable.
3. Test the hypothesis on the relationship
at 0.01 level of significance.
Data set:
Assign Test
6 66
9 94
8 87
7 72
5 45
6 63
5 77

65. Pearson Correlation [ 10 (544.5) - (72) 2 ] [ 10 (62441)- (775) 2 ]
r p = [ ] - [ 72 x775 ]
[ 10 (544.5) - (72) 2 ] [ 10 (62441)- (775) 2 ]
r =

66. Inferential Analysis – Hypothesis Testing
Steps in Hypothesis Testing
1. State the null and alternative hypothesis
HO: ρ p = 0,
HA: ρ p ≠ 0
2. Calculate the test statistic:
3. Determine critical value: df = n – 2, Two-tailed .
4. Make your decision:
Make conclusion:

67. Calculate the test statisticX Y XY X2 Y2
8.5 88
748
72.25
7744 6 66
396 36
4356 9 94
846 81
8836 10 98
980
100
9604 8 87
696 64
7569 7 72
504 49
5184 5 45
225 25
2025 63
378
3969
7.5 85
637.5
56.25
7225 77
385
5929

68. Steps in Hypothesis Testing
1. State the null and alternative hypothesis
HO: ρ p = 0, HA: ρ p ≠ 0
2. Calculate the test statistics: r = .865
3. Determine critical value: df = n – 2, Two-tailed.
r critical= 0.765
Make your decision: r cal > r critical so reject null hypothesis, accept alternative hypothesis
Make conclusion: There is significant relationship between assignment scores and test scores r (8) = 0.87, p<0.01

69. Example 2 :
A clinical psychologist hypothesizes a correlation between a personality dimension (Extroversion/introversion) and depression. Two questionnaires are administered. One measures the personality trait, with bigger scores indicating more extroversion and lower scores tending toward introversion. The other measures depression, with bigger scores reflecting greater depression. Lower scores on the depression inventory are not indicative of depression.
1. Calculated and describe the appropriate correlation
coefficient.
3. Test the hypothesis on the relationship at 0.05 level of significance.

70. Calculate the test statisticX Y XY X2 Y2 8
6.5 52 64
42.25 6 4 24 36 16 9
3.5
31.5 81
12.25 10 35
100 2 12
7.5 30
56.25 5
4.5
22.5 25
20.25 7
2.5
17.5 49
6.25 3 15 60 45
251.5
420
230.5
Calculate the test statistic

71. Steps in Hypothesis Testing
1. State the null and alternative hypothesis
HO: ρ p = 0, HA: ρ p ≠ 0
2. Calculate the test statistic:
r =
3. Determine critical value: df = n – 2, Two-tailed. r critical = 0.67
Make your decision: r cal < r critical so reject null hypothesis accept alternative hypothesis.
Make conclusion: There is no significant relationship between extroversion and depression measurement, r (8) = , p>0.05. Therefore we cannot conclude that those people who are extroverts are more likely to be depressed, whilst those people who are introverts are more likely not depressed.

72. Spearman’s rank correlation coefficient
Non parametric method:
Less power but more robust.
Does not assume normal distribution.
The correlation coefficient also varies between -1 and 1

73. Correlation Coefficient, r
Purpose – Determine relationship between two rank scores
Requirement : variables measured at ordinal scale and ordinal scale, ordinal scale and interval scale, ordinal scale and ratio scale
Descriptive
Direction
Correlation Coefficient, r
Strength / Magnitude
Hypotheses:
HO: ρs = 0
HA: ρs ≠ 0
ρs > 0
ρs < 0
Inferential

74. Spearman rho Correlation
r = [ 6  D 2 ]
n [ n2 - 1 ]
n = no of pairs
 D = summation of the differences between pairs of scores

75. As a measure of popularity, the classroom teacher is asked to rank
all of the children from the most to least popular. To measure dominance, the children are given the opportunity to play a new video game, but they must come to an agreement about which of them will go first, which will go second, and so on. The order which the children
play the game is taken as the dominance hierarchy. A rank of 1 on Dominance is assigned to the most dominant child and A rank of 1is assigned to the most on popular child.
1. Calculate the appropriate correlation coefficient
2. Describe the nature of relationship between the two variables
3. Test the hypothesis on the relationship at 0.05 level of significance

76. Example for Spearman rho
Dominance X
Popularity Y D D2 1 7 8 -1 6 9 -3 5 3 4 10 16 2 -8 64

77. r = [ 6  D 2 ]
n [ n2 - 1 ]
r = [ 6(105 )]
10 [ ]
r = 1 – 0.642
r = 0.36
2. There is a positive and weak relationship between dominance and popularity.

78. 3. Test the hypothesis on the relationship between the two variable at 0.05 level of significance.
a. State the null and alternative hypotheses
HO : ρs = 0
HA : ρs ≠ 0
b. rs = 0.36
c. Determine critical value
Critical rs = 0.648
d. Decision: Since calculated rs (0.36) is smaller than critical
rs (0.648.), fail to reject the null hypothesis, accept null
hypothesis.
e. Conclusion
Conclude there is no significant relationship between dominance and popularity at 0.05 level of significance, rs =0.36, p> .05. Results showed that the more popular the child does not mean he or she is more likely to assume a dominant position in the class.

79. Example2:
Data solicited from a randomly selected sample were used to measure relationship
between working environment and work commitment. EDA revealed the work commitment data did not meet the assumption of normality.
1. Calculate and describe the appropriate correlation coefficient
3. Test the hypothesis on the relationship at 0.05 level of significance
ID X Y

80. r = [ 6 (242.5)]
12 [ ]
r =
r2 = COEFFICIENT OF DETERMINATION – TELL YOU HOW MUCH VARIATION OF Y IS EXPLAINED BY X

81. X –WORK ENV
Y-WORK COMM
Pangkat untuk X
Pangkat untuk Y D D2 6 15 8 -2 4 5 34
3.5 12
-8.5
72.25 11
2.5
8.5 9
1.5 1
0.5
0.25 17 10 2
4.5
2.25 7 13 3 23
-7.5
56.25
-1.0
20.25 14 16
242.5

82. 3. Test the hypothesis on the relationship between the two variable at 0.05 level of significance.
a. State the null and alternative hypotheses
HO : ρs = 0
HA : ρs ≠ 0
b. rs =
c. Determine critical value
Critical rs = 0.887
d. Decision: Since calculated rs (0.887 is larger than critical
rs (0.587.), we reject the null hypothesis, accept alternative
hypothesis.
e. Conclusion
Conclude there ino significant relationship between perception towards work environment with level of work commitment at 0.05 level of significance, rs =0.36, p< .05. Results showed that the positive and high perception on work environment has positive impact on work commitment of employees.

83. Uji diri anda!!!-Apakah pengujian statistik yang diperlukan dan seterusnya jalankan analisis yang diperlukan

84. Parents Marital Satisfaction
EXAMPLE DATA
Parents Marital Satisfaction 1 3 7 9 8 4 5
Children Marital Satisfaction 3 2 6 7 8
Performance 70 80 40 35 50 30
Subject 1 2 3 4 5 6 7

85. Pangkat Agresif Pangkat Agresif Subjek 8 10 4 1 5 6 3 9 7 2 14 12 9 411 10 1
Subjek 1 2 3 4 5 6 7 8 9 10

86. Persepsi Prestasi oleh Guru
CONTOH DATA 3
Persepsi Prestasi oleh Guru 20 30 40 85 70 80 25 75
Tahap Kepemimpinan 18 20 24 11 15 16 12 19 17 22
Stail Kepimpinan
Autokratik
Demokratik
Jantina 1 2

87. Point-biserial Correlation
Purpose – Determine relationship between A DICHOTOMOUS VARIABLE (2 categories) and a continuous variable (interval/ratio data)
Requirement : normally distributed continuous variables and independent variable with only two categories (ex: male/female, high/low, yes/no, part-time/full-time)
r = y1 – y [ n1 n2 ]
sy n [ n - 1 ]
Mean of group 1
Mean of group 2
Std dev of continuous variable
No of subjects in group 1
No of subjects in group 2
Total no of subjects

88. Example1:
A psychologist hypothesizes an association between marital status and need for achievement. A questionnaire measuring need for achievement is administered
to married and single people.
Calculate the appropriate
correlation coefficient
Describe the nature of
relationship between the two variables.
Test the hypothesis on the
relationship at 0.05 level of significance
Marital status Need for Achievement

89. Point-biserial Correlation
r = y1 – y [ n1 n2 ]
sy n [ n - 1 ]
Mean of married subject = 8.5 (group 2)
Mean of single subjects = (group 1)
Std dev of need of achievement scores = 5.89
No of married subjects = 6
No of single subjects = 8
Total no of subjects = 14

90. Calculate the test statisticy y2 3 9 7 49 12
144 16
S =  y (y) 2/ n 24
n - 1 11
121 15
S = / 14 10 18
S = 22
484 81 19
361 17
289
194
3140

91. Point-biserial Correlation
r = – [ 8 x 6 ]
[ ]
r pb = (1.595) (0.514)
r pb = 0.82
The mean need for achievement for single individual is 17.9 and for married individuals is 8.5. There is a strong relationship between marital status and need for achievement with correlation coefficient of Need of achievement for single individual is higher than married individual.

92. 3. Test the hypothesis on the relationship between the two variable at 0.05
level of significance.
a. State the null and alternative hypotheses
HO : ρ pb = 0
HA : ρ pb ≠ 0
b. r pb = 0.82
c. Determine critical value
Critical r pb = 0.532
d. Decision
Since calculated r pb (0.82) is greater than critical r pb (0.532),
reject the null hypothesis thus accept alternative hypothesis.
e. Conclusion
Conclude there is significant relationship between
marital status and need for achievement, r pb (12)=.82, p<0.05
Findings indicated that single individuals showed a higher
need for achievement compared to married individuals.