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in Quantitative Research B E.Shehniyilagh Ph.D

in Quantitative Research B E.Shehniyilagh Ph.D. The Role of Statistics. t-Static. 1. Single Sample or One Sample t-Test AKA student t-test. 2. Two Independent sample t-Test, AKA B etween S ubject D esigns or Matched subjects Experiment.

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in Quantitative Research B E.Shehniyilagh Ph.D

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  1. inQuantitative Research BE.ShehniyilaghPh.D The Role of Statistics

  2. t-Static 1. Single Sample or One Sample t-Test AKA student t-test. 2. Two Independent sample t-Test, AKA BetweenSubject Designs or Matched subjects Experiment. 3. Related Samples t-test or Repeated Measures Experiment AKA Within Subject Designs or Paired Sample T-Test .

  3. CHAP 9 t-Static Single Sample or One Sample t-Test t-testis used to test hypothesis about an unknown population mean, µ, when the value of σor σ² is unknown. Ex. Is this class know more about STATS than the last year class? Mean for the last year class µ=80 Mean for this year class M=82 Note: We don’t know what the average STATS score should be for the population. We compare this year scores with the last year.

  4. Degrees of Freedomdf=n-1

  5. Assumption of the t-test (Parametric Tests) • 1.The Values in the sample must consist of independent observations • 2. The population sample must be normal • 3. Use a large sample n ≥ 30

  6. Inferential Statistics • t-Statistics: • There are different types of t- Statistic • 1. Single (one) Sample t-statistic/Test (chap 9) • 2. Two independent sample t-test, Matched-Subject Experiment, or Between Subject Design t-test (chap10) • 3.RepeatedMeasure Experiment, or Related/Paired Sample t-test (chap11)

  7. FYI Steps in Hypothesis-TestingStep 1: State The Hypotheses • H0 : µ ≤ 100 average • H1 : µ> 100 average • Statistics: • Because the Population mean or µ is known the statistic of choice is • z-Score

  8. FYI Hypothesis TestingStep 2: Locate the Critical Region(s) or Set the Criteria for a Decision

  9. FYI Directional Hypothesis Test

  10. FYI None-directional Hypothesis Test

  11. FYI Hypothesis Testing Step 3: Computations/ Calculations or Collect Data and Compute Sample StatisticsZ Score for Research • ZZZ

  12. FYI Hypothesis TestingStep 3: Computations/ Calculations or Collect Data and Compute Sample Statistics

  13. Hypothesis TestingStep 4: Make a Decision

  14. Calculations for t-testStep 3: Computations/ Calculations or Collect Data and Compute Sample Statistics M-μ • t= s Sm Sm= or Sm=M-μ √n t M=t.Sm+μ μ=M- Sm.t Sm= estimated standard error of the mean

  15. FYI VariabilitySS,Standard Deviations and Variances • X σ² = ss/N Pop 1 σ = √ss/N 2 4 s = √ss/df 5 s² = ss/n-1 or ss/dfSample SS=Σx²-(Σx)²/N SS=Σ(x-μ)² Sum of SquaredDeviationfrom Mean

  16. FYI d=Effect Size for ZUse S instead of σ for t-test

  17. Cohn’s d=Effect Size for tUse S instead of σ for t-test • d = (M - µ)/s • S= (M - µ)/d • M= (d . s) + µ • µ= (M – d) s

  18. Percentage of Variance Accounted for by the Treatment (similar to Cohen’s d) Also known as ω² Omega Squared

  19. percentage of Variance accounted for by the Treatment • Percentage of Variance Explained • r²=0.01-------- Small Effect • r²=0.09-------- Medium Effect • r²=0.25-------- Large Effect

  20. Problems • Infants, even newborns prefer to look at attractive faces (Slater, et al., 1998). In the study, infants from 1 to 6 days old were shown two photographs of women’s face. Previously, a group of adults had rated one of the faces as significantly more attractive than the other. The babies were positioned in front of a screen on which the photographs were presented. The pair of faces remained on the screen until the baby accumulated a total of 20 seconds of looking at one or the other. The number of seconds looking at the attractive face was recorded for each infant.

  21. Problems • Suppose that the study used a sample of n=9 infants and the data produced an average of M=13 seconds for attractive face with SS=72. • Set the level of significance at α=.05 for two tails • Note that all the available information comes from the sample. Specifically, we do not know the population mean μor the population standard deviation σ. • On the basis of this sample, can we conclude that infants prefer to look at attractive faces?

  22. Null Hypothesis • t-Statistic: • If the Population mean or µ and the sigma are unknown the statistic of choice will be t-Static • 1. Single (one) Sample t-statistic (test) • Step 1 • H0 : µattractive = 10 seconds • H1 : µ attractive≠ 10 seconds

  23. None-directional Hypothesis Test

  24. None-directional Hypothesis Test

  25. Calculations for t-testStep 3: Computations/ Calculations or Collect Data and Compute Sample Statistics M-μ • t= s Sm Sm= or Sm=M-μ √n t M=t.Sm+μ μ=M- Sm.t Sm= estimated standard error of the mean

  26. Problems • A psychologist has prepared an “Optimism Test” that is administered yearly to graduating college seniors. The test measures how each graduating class feels about its future. The higher the score, the more optimistic the class. Last year’s class had a mean score of μ=15. A sample of n=9 seniors from this year’s class was selected and tested..

  27. Problems • The scores for these seniors are 7, 12, 11, 15, 7, 8, 15, 9, and 6, which produced a sample mean of M=10withSS=94. • On the basis of this sample, can the psychologist conclude that this year’s class has a differentlevel of optimism? • Note that this hypothesis test will use a t-statistic because the population variance σ² is not known. USE SPSS • Set the level of significance at α=.01 for two tails

  28. Null Hypothesis • t-Statistic: • If the Population mean or µ and the sigma are unknown the statistic of choice will be t-Static • 1. Single (one) Sample t-statistic (test) • Step 1 • H0 : µoptimism = 15 • H1 : µ optimism≠ 15

  29. None-directional Hypothesis Test • Step 2

  30. Calculations for t-testStep 3: Computations/ Calculations or Collect Data and Compute Sample Statistics M-μ • t= s Sm Sm= or Sm=M-μ √n t M=t.Sm+μ μ=M- Sm.t Sm= estimated standard error of the mean

  31. t-Static 1. Single Sample or One Sample t-Test AKA student t-test. 2. Two Independent sample t-Test, AKA BetweenSubject Designs or Matched subjects Experiment. 3. Related Samples t-test or Repeated Measures Experiment AKA Within Subject Designs or Paired Sample T-Test .

  32. Chapter 10TwoIndependent Sample t-test Matched-Subject Experiment, or Between Subject Design • An independent-measures study uses a separate sample to represent each of the populations or treatment conditions being compared.

  33. Independent Sample t-test • An independent measures study uses a separate group of participants to represent each of the populations or treatment conditions being compared.

  34. TwoIndependent Sample t-test • Null Hypothesis: • If the Population mean or µ is unknown the statistic of choice will be t-Static • Two independent sample t-test, Matched-Subject Experiment, or Between Subject Design Step 1 • H0 : µ1 -µ2= 0 • H1: µ1 -µ2 ≠ 0

  35. None-directional Hypothesis Test • Step 2

  36. STEP 3

  37. Estimated Standard ErrorS(M1-M2) • The estimated standard error measures how much difference is expected, on average, between a sample mean difference and the population mean difference. In a hypothesis test, µ1 -µ2 is set to zero and the standard error measures how much difference is expected between the two sample means.

  38. Estimated Standard Error S(M1-M2)=

  39. Pooled Variance s²P

  40. Pooled Variance s²P

  41. Step 4

  42. Measuring d=Effect Size for the independent measures

  43. Estimated d

  44. Estimated d

  45. Percentage of Variance Accounted for by the Treatment (similar to Cohen’s d) Also known as ω² Omega Squared

  46. FYI in Chap 15 We use the Point-Biserial Correlation (r) when one of our variable is dichotomous, in this case (1) watched Sesame St. (2) and didn’t watch Sesame St.

  47. Problems • Research results suggest arelationship Between the TV viewing habits of 5-year-old children and their future performance in high school. For example, Anderson, Huston, Wright & Collins (1998) report that high school students who regularly watched Sesame Street as children had better grades in high school than their peers who did not watch Sesame Street.

  48. Problems • The researcher intends to examine this phenomenon using a sample of 20 high school students. She first surveys the students’ s parents to obtain information on the family’s TV viewing habits during the time that the students were 5 years old. Based on the survey results, the researcher selects a sample of n1=10

  49. Problems • students with a history of watching “Sesame Street“ and a sample of n2=10 students who did not watch the program. The average high school grade is recorded for each student and the data are as follows: Set the level of significance at α=.05 for two tails

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