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

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.

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.

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.

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

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.

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

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.

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.

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

BAGI TUJUAN SEDEMIKIAN!! ANDA PERLUKAN ANALISIS KORELASI ATAU HUBUNGAN

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.

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?”

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

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”.

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.

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.

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.)

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.

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.

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?

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.

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.

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.

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.

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.

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.

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

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

x y 8 78 2 92 5 90 12 58 15 43 9 74 6 81 x Absences Grade Absences x 8 78 2 92 5 90 12 58 15 43 9 74 6 81 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

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

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 +

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

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

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

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.

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

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

Pekali Point-biserial r = y1 – y2 [ n1 n2 ] sy n [ n - 1 ]

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.

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)

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

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.

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.

Guildford Rule of Thumb r Strength of Relationship < 0.2 Negligible Relationship 0.2 – 0.4 Low Relationship 0.4 – 0.7 Moderate Relationship 0.7 – 0.9 High Relationship > 0.9 Very high Relationship

Other Strengths of Association- By Johnson and Nelson (1986) r-value Interpretation 0.00 No relationship 0.01-0.19 Low relationship 0.20-0.49 Slightly Moderate relationship 0.50-0.69 Moderate relationship 0.70-0.99 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.

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

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

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.

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

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.

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.

L4. Nilai Statistik Pengujian r uji = r uji =

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

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)

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

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

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

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

x y 8 78 2 92 5 90 12 58 15 43 9 74 6 81 Absences Grade Absences x 8 78 2 92 5 90 12 58 15 43 9 74 6 81 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

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

Computation of r xy x2 y2 x y 1 8 78 2 2 92 3 5 90 4 12 58 5 15 43 1 8 78 2 2 92 3 5 90 4 12 58 5 15 43 6 9 74 7 6 81 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. = - 0.975

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

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 8.5 88 6 66 9 94 10 98 8 87 7 72 5 45 6 63 7.5 85 5 77

Pearson Correlation [ 10 (544.5) - (72) 2 ] [ 10 (62441)- (775) 2 ] r p = 10 [ 5795.5 ] - [ 72 x775 ] [ 10 (544.5) - (72) 2 ] [ 10 (62441)- (775) 2 ] r = 0.8649

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:

Calculate the test statistic X 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

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

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.

Calculate the test statistic X 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

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 = -0.451 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) = - .45 , 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.

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

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

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

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

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

r = 1 - [ 6  D 2 ] n [ n2 - 1 ] r = 1 - [ 6(105 )] 630 10 [ 100 - 1 ] 990 r = 1 – 0.642 r = 0.36 2. There is a positive and weak relationship between dominance and popularity.

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.

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 1 6 15 2 5 34 3 8 11 4 4 9 5 9 17 6 6 12 7 7 13 8 5 23 9 4 11 10 7 12 11 6 14 12 7 16

r = 1 - [ 6 (242.5)] 1455 12 [ 144 - 1 ] 1716 r = 0.1521 r2 = COEFFICIENT OF DETERMINATION – TELL YOU HOW MUCH VARIATION OF Y IS EXPLAINED BY X

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

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. 587 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.

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

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

Pangkat Agresif Pangkat Agresif Subjek 8 10 4 1 5 6 3 9 7 2 14 12 9 4 11 10 1 Subjek 1 2 3 4 5 6 7 8 9 10

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