ANALISIS UNIVARIAT

1. ANALISIS UNIVARIAT

2. Statistik Univariat • Menguji Keertian Statistik • Menguji Hipotesis satu pembolehubah per satu (tiap kali).

3. Hipotesis • Proposisi ( cadangan) yang belum terbukti • Andaian bagi menerangkan sesuatu fakta atau • Andaian mengenai keadaan dunia • (Dalam ertikata yang lain hipotesis adalah jangkaan)

4. Hipotesis • Proposisi atau andaian belum terbukti bagi menerangkan sesuati fakta atau fenomena. • Hipootesis Nol • Hipotesis Alternatif • Hoptesis nol adalah hipotesis yang status quo atau kedudukan semasa, tidak berubah. • Hipotesis alternatif adalah hipotesis yang bertentangan. • Contoh: Aras jualan mingguan tidak berbeza dengan purata jualan mingguan dengan penawaran diskaun harga 20 sen. • Jumlah pembelian menggunakan kad keredit tidak berbeza dengan bayaran secara tunai.

5. Proses Menguji Hipotesis • Menentukan apakah hipotesis yang hendak diuji secara statistik. • Menggambarkan apakahtaburan persampelan mean jika pernyataan hipotesis adalah benar menerangkan tetang keadaan populasi. • Mendapatkan sampel sebenar dan menentukan mean sampel tersebut(atau statistik yang sesuai)

6. Kita memang menjangkakan bahawa memang wujud perbezaan kecil diantara sampel dan populasi. Namun begitu kita pelu menguji sama ada perbezaan ini kecil atau sangat ketara dengan mean dari taburan persampelan mean. Jika wujud perbezaan yang ketara, kita tidak boleh membuat kesimpulan begitu sahaja sama ada memerima atau menolak hipotesis nol. Kita harus merujuk kepada peraturan membuat keputusan yang terpiawai. Ini dipanggil dalam bidang statistik sebagai aras keertian.

7. 3. Keputusan menerima atau menolak hipotesi nol akan dibuat jika perbezaan tersebut diperingkat keertian kurang daripada 0.05 ( <0.05) atau diluar diluar kawasan penerimaan.

8. Aras Keertian • Kebangkalian kritikal sama ada memilih hipotesis nol atau hipotesis alternatif

9. Aras Keertian • Kebangkalian kritikal • Aras keyakinan • Alpha • Aras Kebarangkalian yang dipilih biasanya .05 atau .01 • Terlalu rendah untuk menyokong hipotesis nol

10. Example: A study on consumer perception of service quality- friendly or not friendly. Measurement 5 point-point scale, assumed to be an interval scale. 5- very friendly and 1- very unfriendly. A sample of 225 respondents were taken. The mean score from the sample equaled 3.75 and sample standard deviation S=1.5 The null hypothesis that the mean is equal to 3.0:

11. The alternative hypothesis that the mean does not equal to 3.0:

12. A Sampling Distribution m=3.0

13. A Sampling Distribution a=.025 a=.025 m=3.0

14. A Sampling Distribution UPPER LIMIT LOWER LIMIT m=3.0

15. Standardized Sampling Distribution Z=1.96 UPPER LIMIT LOWER LIMIT -1 1 m=0 Z

16. Critical values ofm Critical value - upper limit

17. Critical values ofm

18. Critical values ofm Critical value - lower limit

19. Critical values ofm

20. Region of Rejection LOWER LIMIT m=3.0 UPPER LIMIT

21. Hypothesis Test m =3.0 2.804 3.78 m=3.0 3.196

22. Type I and Type II Errors Accept null Reject null Null is true Correct- no error Type I error Null is false Type II error Correct- no error

23. Type I and Type II Errors in Hypothesis Testing State of Null Hypothesis Decision in the Population Accept Ho Reject Ho Ho is true Correct--no error Type I error Ho is false Type II error Correct--no error

24. Calculating Zobs

25. Alternate Way of Testing the Hypothesis

26. Alternate Way of Testing the Hypothesis

27. Choosing the Appropriate Statistical Technique • Type of question to be answered • Number of variables • Univariate • Bivariate • Multivariate • Scale of measurement

28. NONPARAMETRIC STATISTICS PARAMETRIC STATISTICS

29. t-Distribution • Symmetrical, bell-shaped distribution • Mean of zero and a unit standard deviation • Shape influenced by degrees of freedom

30. Degrees of Freedom • Abbreviated d.f. • Number of observations • Number of constraints

31. or Confidence Interval Estimate Using the t-distribution

32. Confidence Interval Estimate Using the t-distribution = population mean = sample mean = critical value of t at a specified confidence level = standard error of the mean = sample standard deviation = sample size

33. Confidence Interval Estimate Using the t-distribution

36. Hypothesis Test Using the t-Distribution

37. Univariate Hypothesis Test Utilizing the t-Distribution Suppose that a production manager believes the average number of defective assemblies each day to be 20. The factory records the number of defective assemblies for each of the 25 days it was opened in a given month. The mean was calculated to be 22, and the standard deviation, ,to be 5.

40. Univariate Hypothesis Test Utilizing the t-Distribution The researcher desired a 95 percent confidence, and the significance level becomes .05.The researcher must then find the upper and lower limits of the confidence interval to determine the region of rejection. Thus, the value of t is needed. For 24 degrees of freedom (n-1, 25-1), the t-value is 2.064.

43. Univariate Hypothesis Test t-Test

44. Testing a Hypothesis about a Distribution • Chi-Square test • Test for significance in the analysis of frequency distributions • Compare observed frequencies with expected frequencies • “Goodness of Fit”

45. Chi-Square Test

46. Chi-Square Test x² = chi-square statistics Oi = observed frequency in the ith cell Ei = expected frequency on the ith cell

47. Chi-Square Test Estimation for Expected Number for Each Cell

48. Chi-Square Test Estimation for Expected Number for Each Cell Ri = total observed frequency in the ith row Cj = total observed frequency in the jth column n = sample size

49. Univariate Hypothesis Test Chi-square Example

50. Univariate Hypothesis Test Chi-square Example