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Analyze Statistic by Using SPSS 3 rd Day 1Fadwa Flemban.

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1 Analyze Statistic by Using SPSS 3 rd Day 1Fadwa Flemban

2 الاعجاز الرقمي في القرآن الكريم الرقم 7 له مدلول كبير في القرآن والكون والحياة ، فعدد أحرف الأبجدية العربية ( لغة القرآن ) هو 28 حرفاً ( أي 7 × 4) ، والحديث الصحيح ( أُنزل القرآن على سبعة أحرف ) يؤكد أن الرقم 7 له علاقة بالقرآن ، وقد خلق اللّه تعالى سبع سماوات وسبع أراضين وجعل الجمعة سبعة أيام. أما عبادة الحج فتعتمد على الرقم 7 ( سبعة أشواط في الطواف والسعي ) وسبع جمرات. والذي لا يؤمن بكل هذا فجزاؤه نار جهنم التي خلق لها اللّه تعالى سبعة أبواب لكل بابٍ ملاحظة : كلمة جهنم تكررت في القرآن 77 مرة أي 7 × 11. ولا ننسى أن أعظم سورة في القرآن هي الفاتحة التي سمَّاها اللّه [ السبع المثاني ] ، عدد آياتها 7. كما أن عبارة السماوات السبع ( وسبع سماوات ) تكررت في القرآن 7 مرات بالضبط. كلمة [ سبعة ] تكررت في القرآن 4 مرات في الآيات التالية : 1 ـ { فَصِيَامُ ثَلَاثَةِ أَيَّامٍ فِي الْحَجِّ وَسَبْعَةٍ إِذَا رَجَعْتُمْ } [ البقرة : 196 [ 2 ـ { لَهَا سَبْعَةُ أَبْوَابٍ لِكُلِّ بَابٍ مِنْهُمْ جُزْءٌ مَقْسُومٌ } [ الحجر : 44 [ 3 ـ { وَيَقُولُونَ سَبْعَةٌ وَثَامِنُهُمْ كَلْبُهُمْ } [ الكهف : 22 [ 4 ـ { مِنْ بَعْدِهِ سَبْعَةُ أَبْحُرٍ مَا نَفِدَتْ كَلِمَاتُ اللَّهِ ] { لقمان : 27 [ كلمة [ سبعة ] تكررت في القرآن 4 مرات لقمان الكهف الحج البقرة اسم السورة رقم الآية = 7 × = 7 × 7 × إذاً : العدد الذي يمثل الآيات الأربعة ( التي وردت فيها كلمة [ سبعة ]) يقبل القسمة على 7 مرتين متتاليتين ، فمن الذي نظَّم مواضع هذه الكلمة بهذا التناسب المذهل مع الرقم 7 ؟ أليس هو اللّه ؟ 2Fadwa Flemban

3 Chi-Squared Tests اختبارات مربع كاي (1) Goodness of fit tests(2) Independent tests(3) Homogeneity tests 3Fadwa Flemban

4 لمقارنة توزيع البيانات مع عدة توزيعات احتمالية وهي : 1- التوزيع الطبيعي Normal Dist. 2 - توزيع بواسون Poisson Dist. 3- التوزيع الأسي Exponential Dist. 4- التوزيع المنتظم Uniform Dist. Fadwa Flemban4 (1) Goodness of fit tests اختبار جودة التوفيق

5 Hypotheses of Test : Hₒ: The data are consistent with a S distribution. : Hₒ البيانات تتبع التوزيع س. H1: The data are not consistent with S distribution. H1: البيانات لا تتبع التوزيع س. Fadwa Flemban5 (1) Goodness of fit tests اختبار جودة التوفيق

6 Goodness of fit tests Example This data are representing the number of persons who ate the dinner in a small restaurant on 50 days: Is a variable of the persons' number who ate the dinner in the restaurant following the normal distribution at the level of significance (0.05)? Fadwa Flemban

7 Solution Hₒ: The data are consistent with the normal distribution. H1: The data are not consistent with the normal distribution. Fadwa Flemban7

8 Normality Test two way: By Fadwa Flemban8 (1) Analyze  Descriptive Statistics  Explore Plots  check in Normality plots with test

9 Normality Test for (male) Fadwa Flemban9

10 10 Normality Test for (female)

11 Output بما أن : جميع النقاط تقع على وحول الخط المستقيم إذن : العينة تتبع التوزيع الطبيعي Fadwa Flemban11

12 Fadwa Flemban12 Normality Test two way: By (2) Analyze  Nonparametric test  1-sample kolmogorov-smirnov test

13 Analyze  Nonparametric test  1-sample kolmogorov-smirnov test Fadwa Flemban13

14 Fadwa Flemban14

15 Output : Fadwa Flemban15 P-value (0.898)>α(0.05) We don't reject Hₒ the persons' number who ate the dinner in the restaurant following the normal distribution at degree of confidence 95%. P-value (0.898)>α(0.05) We don't reject Hₒ the persons' number who ate the dinner in the restaurant following the normal distribution at degree of confidence 95%.

16 Make the same steps but : Choose Poison test distribution Fadwa Flemban16

17 Fadwa Flemban17 Output : P-value (0.047)<α(0.05) We reject Hₒ the persons' number who ate the dinner in the restaurant don’t following the Poisson distribution at degree of confidence 95%. P-value (0.047)<α(0.05) We reject Hₒ the persons' number who ate the dinner in the restaurant don’t following the Poisson distribution at degree of confidence 95%.

18 Fadwa Flemban18 Hypotheses of Test : H 0 : The variables are independent. H 1 : The variables are not independen. : Hₒ المتغيران مستقــلان. H1: المتغيران غيرمستقــلان, أي توجد علاقة بينهما. (2) Independent tests اختبارات الاستقلال

19 Independent tests Example In a study of the relationship between the grade of student in the university and his gender: There is a relationship between the student’s grade & his gender? Fadwa Flemban19 FFFFBADAB Female CBBCDDDFA DFDDDFBBC CCABACCC FCCCFBFBBA Male BCFFFFFDA DAAFFDDAC ACCDFFCCB

20 Solution Hₒ: The student’s grade & his gender are independent. H1: There is a relationship between the student’s grade & his gender. Fadwa Flemban20

21 Analyze  Descriptive Statistics  Crosstabs Fadwa Flemban21

22 Crosstabs Window: Fadwa Flemban22 Press Statistics button Press Statistics button

23 Chi-square to Independent Test Fadwa Flemban23

24 Fadwa Flemban24 P-value = P-value > 0.05 We don’t reject H The two variables are independent P-value = P-value > 0.05 We don’t reject H The two variables are independent

25 للإجابة عن السؤال : هل تكرارات المشاهدات موزعة بشكل متجانس ( متماثل ) بين فئات المجتمع. Fadwa Flemban25 Hypotheses of Test : H 0 : P i1 = P i2 =…………= P is OR σ²1=σ²2=……= σ²i H 1 : at least one of the null hypothesis statements is false. (3) Homogeneity tests اختبارات التجانس

26 Homogeneity tests Example for Clarification In a study of the television viewing habits of children, a developmental psychologist selects a random sample of 300 first graders boys and 200 girls. Do the boys' preferences for these TV programs differ significantly from the girls' preferences? Use a 0.05 level of significance. Fadwa Flemban26 Rows total The Simpsons Sesame Street Lone Ranger Boys Girls Column total

27 Mathematical Solution H 0 : P boys who prefer Lone Ranger = P girls who prefer Lone Ranger H 0 : P boys who prefer Sesame Street = P girls who prefer Sesame Street H 0 : P boys who prefer The Simpsons = P girls who prefer The Simpsons H1: At least one of the null hypothesis statements is false. DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1) = 2 E r,c = (n r * n c ) / n E 1,1 = (100 * 100) / 300 = 10000/300 = 33.3 E 1,2 = (100 * 110) / 300 = 11000/300 = 36.7 E 1,3 = (100 * 90) / 300 = 9000/300 = 30.0 E 2,1 = (200 * 100) / 300 = 20000/300 = 66.7 E 2,2 = (200 * 110) / 300 = 22000/300 = 73.3 E 2,3 = (200 * 90) / 300 = 18000/300 = 60.0 Χ 2 = Σ [ (O r,c - E r,c ) 2 / E r,c ] Χ 2 = ( ) 2 / ( ) 2 / ( ) 2 /30 + ( ) 2 / ( ) 2 / ( ) 2 /60 Χ 2 = (16.7) 2 / (-6.7) 2 / (-10.0) 2 /30 + (-17.7) 2 / (3.3) 2 / (10) 2 /60 Χ 2 = = P(Χ 2 > 19.91) = Since the P-value (0.0000) is less than the significance level (0.05), we cannot accept the null hypothesis. Fadwa Flemban27

28 Homogeneity tests Example We have the following data: 1- Are two factories homogeneity ? 2-Test the hypothesis, the factories them the same calories (by million calories),Use a 0.05 level of significance? Fadwa Flemban28 Calories Factory Factory 2

29 Solution NOTE: we have two variables (scale & nominal). Hypotheses of Homogeneity test: H : σ²1 = σ²2 H1 : σ²1 ≠ σ²2 Fadwa Flemban29

30 Analyze  Compare means  Independent Samples Fadwa Flemban30

31 Fadwa Flemban31 Define Groups

32 Output : Fadwa Flemban32 P-value = P-value > α We don’t reject H The samples are Homogeneity P-value = P-value > α We don’t reject H The samples are Homogeneity

33 Also: From t-test of equality of means: Hₒ : µ1=µ2 H1 : µ1≠µ2 Sig. = 0.018, α = 0.05 Sig. < α we reject Hₒ, the means of two factories are not equal. Fadwa Flemban33

34 Summary In Nominal Variables Normality Test Data from Normal Dist. T test Data not from Normal Dist. Non Parametric Tests Fadwa Flemban34 Make Homogeneity Test Make Homogeneity Test

35 Regression & Correlation الانحدار و الارتباط 35Fadwa Flemban

36 Regression الانحدار استخدام معادلة خط الإنحدار في التنبؤ المستقبلي. معادلة خط الإنحدار تستخدم للتنبؤ لقيم ” ضمن “ قيم المتغير المستقل. Fadwa Flemban36

37 Fadwa Flemban37 يستخدم الانحدار الخطي لتقدير معامل المتغير المستقل للمعادلة الخطية بغرض تقدير المتغير التابع فى حالة وجود متغير مستقل واحد فإن معادلة الخط تأخذ الصورة : Y = a + b*X حيث تعبر X عن المتغير المستقل وتعبر Y عن المتغير التابع. الانحدار الخطي البسيط Simple linear Regression

38 Example Fadwa Flemban38 Suppose that X symbolize to the temperature between (3:00 pm & 4:00 pm) through the summer season, Y symbolize to electricity consumption representative by levels from 1 to 10 where level 10 is higher consumption. And the data were recorded during a period of 10 days: X: Y: Draw the scatter diagram for this data? 2-Estimate the linear regression equation between (X,Y) at a temperature ? 3- If X=35, then the level of electricity consumption =……

39 mathematical solution = 6.6 – (0.3073)(30.2) =

40 SPSS Solution 1- Graphs  Legacy Dialogs  Scatter/Dot  Fadwa Flemban40

41 Simple Scatter  Define  Fadwa Flemban41

42 Output : Fadwa Flemban42 To add the regression line on the chart: Double click on the chart  add fit line at total  linear  close

43 Fadwa Flemban43 Output :

44 2- Analyze  Regression  Linear Fadwa Flemban44

45 Fadwa Flemban45 Correlation Coefficient a = b = Output : the linear regression equation Yi = X i the linear regression equation Yi = X i

46 التنبؤ باستخدام معادلة الانحدار : تقدير الاستهلاك من الطاقة الكهربائية عندما تكون درجة الحرارة 35 درجة مئوية معادلة خط الانحدار هي Yi = Xi بما أن X = 35 إذن استهلاك الطاقة الكهربائية يقدّر بـ : Y = (35) Y = أ. فدوى فلمبان 46

47 Correlation الارتباط Can be used as another measure to determine strength of the relationship between and among phenomena, this measure is the correlation coefficient. Fadwa Flemban47

48 Fadwa Flemban48 ان واحدا من اهم اهداف اى بحث هى إيجاد علاقات بين المتغيرات وذلك هو هدف أساسي لعلم الاحصاء. ويجب قبل حساب معاملات الارتباط للبيانات الكمية مشاهدة البيانات من خلال شكل الانتشار Scatter diagram وذلك لملاحظة طبيعة العلاقة ( خطية او غير ذلك ) او لملاحظة وجود قيم شاذة outliers والتى قد يؤدى وجودها الى نتائج مضللة. تنحصر قيمة معامل الارتباط بين 1- و 1+. إذا كانت قيمة معامل الإرتباط مساوية 1+ عندها يكون الإرتباط طردي تام، وكذلك عندما تكون قيمة معامل الإرتباط مساوية 1 - عندها يكون الإرتباط عكسي تام. Correlation الارتباط

49 Scatter Diagram Fadwa Flemban49 this scatter diagram means the coefficient of correlation ( r=0) : There is no relationship between the variables or there is relationship but not linear. this scatter diagram means the coefficient of correlation (r=-1 or r=+1) : Of all points on the regression line which is the relationship between the variables (x,y). this scatter diagram means the coefficient of correlation (0 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/3385648/12/slides/slide_48.jpg", "name": "Scatter Diagram Fadwa Flemban49 this scatter diagram means the coefficient of correlation ( r=0) : There is no relationship between the variables or there is relationship but not linear.", "description": "this scatter diagram means the coefficient of correlation (r=-1 or r=+1) : Of all points on the regression line which is the relationship between the variables (x,y). this scatter diagram means the coefficient of correlation (0

50 Values of the correlation coefficients rIts meanr +1Perfect positive correlationPerfect negative correlation 0.99 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/3385648/12/slides/slide_49.jpg", "name": "Values of the correlation coefficients rIts meanr +1Perfect positive correlationPerfect negative correlation 0.99

51 Fadwa Flemban51 معاملات الارتباط تبعاً لقياس المتغيرات

52 Two different correlation techniques are available: for quantitative variables 1- Pearson correlation coefficient for ordinal scales 2- Spearman correlation coefficient Fadwa Flemban52

53 Fadwa Flemban53 for quantitative variables 1- Pearson correlation coefficient

54 Fadwa Flemban54 Example Find the correlation between the outside temperature (y) and the height by thousands of foot (x) for a plane in different times. Height (x) Temperature (y) Calculate the coefficient of correlation between the height & the temperature?

55 mathematical solution Fadwa Flemban55 No.xyx²y²xy ∑ =18.4; = 4.8Sx=3.2496;Sy=  It means there is strong negative correlation between the height & the temperature

56 1- Graphs  Legacy Dialogs  Scatter/Dot  Simple Scatter Fadwa Flemban56 SPSS Solution

57 Fadwa Flemban57 To add the regression line on the chart: Double click on the chart  add fit line at total  linear  close Output :

58 Fadwa Flemban58 Output :

59 2- Analyze  Correlate  Bivariate Fadwa Flemban59

60 Bivariate Correlations Windows: Fadwa Flemban60

61 Fadwa Flemban61 Output : From Output of correlation:r= It means there is strong negative correlation between the height & the temperature.

62 Fadwa Flemban62 for ordinal scales 2- Spearman correlation coefficient

63 Example Fadwa Flemban63 If we have the grade of 5 students in both articles : StatisticsACDFB MathematicsBCFDA Find the correlation between the students' grade in the statistics and the mathematics?

64 mathematical solution Fadwa Flemban64 There is strong positive correlation between the students' grade in the statistics and the mathematics. d squared d Rank of Stat Rank of Math StatMath 112AB 0033CC 1 45DF 1154FD 1121BA 40Total

65 By same steps in the previous example: Fadwa Flemban65 Solution by SPSS

66 Fadwa Flemban66 Analyze  Correlate  Bivariate

67 Fadwa Flemban67 Output : From this table we find the same result: r=0.8, there is strong positive correlation.

68 1) استخدام معامل بيرسون للإرتباط لبيانات غير خطية لذلك يجب التأكد من ” خطية “ العلاقة بين الظاهرتين. 2) معامل بيرسون للإرتباط يعكس ” خطية العلاقة “. Fadwa Flemban68 أخطاء شائعة

69 Question ??? A national consumer magazine reported the following correlations. 1-The correlation between car weight and car reliability is The correlation between car weight and annual maintenance cost is Which of the following statements are true? I. Heavier cars tend to be less reliable. II. Heavier cars tend to cost more to maintain. III. Car weight is related more strongly to reliability than to maintenance cost. Fadwa Flemban69

70 Fadwa Flemban70 Statistical Humor A ONE-WAY ANOVA shouted at a TWO-WAY ANOVA: "STOP! Turn around - You are going the wrong way!" The TWO-WAY ANOVA yelled back: "Sorry! I will turn when I see an interaction!"


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