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Analyze Statistic by Using SPSS

Analyze Statistic by Using SPSS. 2 nd Day. الإعجاز الإحصائي للقرآن.

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Analyze Statistic by Using SPSS

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  1. Analyze Statistic by Using SPSS 2nd Day Fadwa Flemban

  2. الإعجاز الإحصائي للقرآن الإعجاز الإحصائي للقرآن يعني أننا عاجزون عن تأليف كتاب فيه نظام رقمي دقيق لتكرار الكلمات مثل القرآن .} إِنَّ هَذِهِ تَذْكِرَةٌ فَمَنْ شَاءَ اتَّخَذَ إِلَى رَبِّهِ سَبِيلاً} هذه الآية الكريمة نجدها في موضعين فقط من القرآن :1 ـ { إن هذه تذكرة فمن شاء اتخذ إلى ربه سبيلاً } [ المزمل : 19 [2 ـ { إن هذه تذكرة فمن شاء اتخذ إلى ربه سبيلاً } [ الإنسان : 29[1 ـ لماذا تكررت هذه الآية مرتين في القرآن ؟2 ـ لماذا كان رقم الآيتين : 19 ـ 29 ؟ 3 ـ لماذا كان تسلسل سورة المزمل قبل سورة الإنسان ؟ سوف نجيب على هذه الأسئلة وغيرها بلغة الأرقام ، فتكرار هذه الآية في القرآن مرتين له حكمة ، وقد اختار اللّه تعالى لهذه الآية رقمين 19 و 29 وذلك لحكمة أيضاً ، ويمكن استنتاج جزء من هذه الحكمة بالاعتماد على الرقم 7 . والفكرة الأساسية في هذا البحث تعتمد على صَفّ أرقام الآيات بجانب بعضها وذلك حسب تسلسل هذه الآيات في القرآن (وليس جَمع الأرقام ) وعندما نصُفّ أرقام الآيتين19ـ 29 ينتج عدد جديد هو 2919 هذا العدد يُقرأ : ألفان وتسعمئة وتسعة عشر ، وهو من مضاعفات الرقم 7 ، أي يقبل القسمة تماماً على 7 من دون باقٍ: 417 × 7 = 2919 Fadwa Flemban

  3. Probability Distributions بعض التوزيعات الاحتمالية • The normal distribution • The Standard normal distribution • T distribution • Chi-square distribution Fadwa Flemban

  4. (1)Normal Distribution • The normal distribution is a probability distribution that associates the normal random variable X with a cumulative probability . The normal distribution is defined by the following equation: Y = [ 1/σ * sqrt(2π) ] * e -(x - μ)2/2σ2 • the sampling distribution of a statistic will follow normal distribution, as long as : 1- the sample size is sufficiently large. 2-we know the standard deviation of the population. Fadwa Flemban

  5. The Curve of Normal Distribution: • = P(Z <z) • Find P(Z > a)? • P(Z > a) = 1 - P(Z < a) • Find P(a < Z < b)? • P(Z < b) - P(Z < a) Fadwa Flemban

  6. Difference between these curves: The curve on the left is shorter and wider than the curve on the right, because the curve on the left has a bigger standard deviation. Fadwa Flemban

  7. (2)The standard normal distribution • The standard normal distribution is a special case of the normal distribution. • the following equation: z = (X - μ) / σ • Z ~ N ( μ , σ ) in standard normal distribution: Z ~ N ( 0 , 1 ) Fadwa Flemban

  8. Standard Normal Distribution Table The table shows that the probability that a standard normal random variable will be less than -1.31, that is, P(Z < -1.31) = 0.0951. • Find the cumulative probability of a z-score equal to -1.31? Fadwa Flemban

  9. قال تعالى : (اللَّهُ الَّذِي خَلَقَكُم مِّن ضَعْفٍ ثُمَّ جَعَلَ مِن بَعْدِ ضَعْفٍ قُوَّةً ثُمَّ جَعَلَ مِن بَعْدِ قُوَّةٍ ضَعْفاً وَشَيْبَةً يَخْلُقُ مَا يَشَاءُ وَهُوَ الْعَلِيمُ الْقَدِيرُ) [الروم : 54] قـوة ضعف ضعف Fadwa Flemban

  10. (3) t Distribution • sample sizes are sometimes small, and often we do not know the standard deviation of the population. When either of these problems occur, statisticians rely on the distribution of the t statistic. • The equation : t = [ x - μ ] / [ s / sqrt( n ) ] • Degrees of Freedom: the sample size minus one (n-1,α). Fadwa Flemban

  11. Curve of t Distribution Fadwa Flemban

  12. (4)Chi-Square Distribution • using the following equation: Χ2 = [ ( n - 1 ) * s2 ] / σ2 • degrees of freedom Χ2: n - 1 Fadwa Flemban

  13. Curve of Chi-Square As the degrees of freedom increase, the chi-square curve approaches a normal distribution. Fadwa Flemban

  14. Inferential Statisticsالاحصاء الاستدلالي Fadwa Flemban

  15. The First Topic inInferential Statistics Estimation Fadwa Flemban

  16. Estimation التقدير • When a parameter is being estimated, the estimate can be either a single number or it can be a range of scores. • When the estimate is a single number, the estimate is called a "point estimate" • When the estimate is a range of scores, the estimate is called an interval estimate. Confidence interval are used for interval estimates. Fadwa Flemban

  17. Estimation by SPSS Analyze  Descriptive Statistics  Explore Fadwa Flemban

  18. Statistics Fadwa Flemban

  19. Output: All the estimations at Confidence interval 95% µ = 112.2 105.42 < µ < 118.98 σ² = 89.73 Fadwa Flemban

  20. The Second Topic inInferential Statistics Testing Hypotheses Fadwa Flemban

  21. Inferential Statisticsالاحصاء الاستدلالي Fadwa Flemban

  22. Tests Concerning a Single Mean اختبارات الفروض حول متوسط المجتمع Fadwa Flemban

  23. Summary of Computational Steps • Specify the null hypothesis and an alternative hypothesis. • Compute M = ΣX/N. • Compute , if σ unknown compute • Compute , if n<30 compute • where M is the sample mean and µ is the hypothesized value of the population. • Use a z table to determine p from z , or Use a t table to compute p from t and df (df=N-1). Fadwa Flemban

  24. Testing Hypothesesاختبارات الفروض Consider an experiment designed to test the null hypothesis that µ = 10. The test would be conducted with the following formula: where M (the statistic) is the samplemean. Fadwa Flemban

  25. Tests Concerning a Single Mean Example n > 30 A random sample of 100 deaths in the Philippines last year showed an average life span of 69.3 years. Assuming a population standard deviation of 7.8 years. • does this seem to indicate that the life span today is lesser than 70 years? • Use a 0.01 level of significance? Fadwa Flemban

  26. Solution: • We will solve this testing problem in 5 steps: • 1. H0:  = 70 years. • H1:  < 70 years. • 2. Use a = 0.01. • Since we are testing the mean life span and the population standard deviation is known • ( / = • 0.78). Using normal distribution , Rejection Region • At 0.01 level of significance, we reject • if and only if Z < z 0.01= -2.33 • 5.Based from the rejection region (and critical value –2.33), • we see that the z value is outside the rejection region • (or –0.90 is greater than –2.33). Thus, • we do not reject the null hypothesis and conclude that the life expectancy of Filipinos is 70 years. Z = -0.90 -2.33 Fadwa Flemban

  27. Note The previous Example We cannot use SPSS because: 1- the standard deviation is known . 2- and we haven’t data . Fadwa Flemban

  28. Tests Concerning a Single Mean Example n ≤ 30 A teacher of Arabic language was assumed that the mean of students' degree is 68, drew a sample from the students' degree as follows (n=30): 80 85 75 65 55 52 44 33 30 25 45 80 95 50 30 95 88 90 77 72 75 60 40 57 55 52 48 84 87 78 Is teacher's claim is true at 0.01 level of significance? Fadwa Flemban

  29. SPSS Solution: H0: µ = 68 H1:µ 68 Fadwa Flemban

  30. Analyze  compare mean  One-sample test Fadwa Flemban

  31. Option Fadwa Flemban

  32. Output (P-value) 0.240 > 0.01 (α) don't reject Hₒ the teacher's claim is true. Fadwa Flemban

  33. Tests of Differences between Means اختبارات الفروض حول متوسطي مجتمعين Fadwa Flemban

  34. Tests of Differences between Means,Independent Samples Example: If we have the following marks for students (male & female): Is there a difference between the mean of marks at level of significant 0.05? Fadwa Flemban

  35. SPSS Solution H0: µ1 = µ2 H1:µ1  µ2 Fadwa Flemban

  36. Analyze  Compare means  Independent Samples T Test Fadwa Flemban

  37. Press Define Groups Fadwa Flemban

  38. Press Option Fadwa Flemban

  39. Inside the Box: T-Test for Equality of means t= .045, df =(33+35)-2 =68-2= 66 Sig.=0.964> α=0.05 Don’t reject Hₒ Confidence Interval of the difference (-9.949,10.412) Output : 0.771 > 0.05 Equal Variance Assumed Fadwa Flemban

  40. What is learned: • Test of Hypotheses : T-Test of two Independent Samples. • Estimate : Confidence Interval of the difference between means. • Mean difference : • µ1-µ2 = 64.69 – 64.45 = 0.24 (from Group Statistics Table) • Or mean difference = 0.23 1 (fromIndependent samples test Table ) Fadwa Flemban

  41. Make a decision : Fadwa Flemban

  42. Tests of Differences between Means,dependent Samples Example : We have the data of 20 students in two courses (Arabic & English): Examine if there is difference between the mean of students’ marks in two courses, at level of significant 0.10? Fadwa Flemban

  43. SPSS Solution H0: µ1 = µ2 H1:µ1  µ2 Fadwa Flemban

  44. Analyze  Compare means  Paired Samples T Test Fadwa Flemban

  45. Press Option Fadwa Flemban

  46. t= 2.309, df=20-1=19 Sig.=0.032 < α=0.10 Reject Hₒ Confidence Interval of the difference (1.796,12.504) Note: the interval doesn’t contain ZERO Output: Fadwa Flemban

  47. اخطاء شائعة • استخدام اختبارات t :لبيانات صغيرة غير مسحوبة من مجتمع طبيعي Fadwa Flemban

  48. Statistical Humor A boy asked his statistician father, "Why is my body not well proportioned just like my brother's?" His father's response, "Because, when your mother had your pregnancy, itsdistribution was skewed!!" Fadwa Flemban

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