Two Group Experimental Designs & t-tests

August 9, 2017 | Autor: Geoff Sutton | Categoria: Psychology, Social Psychology, Research Methodology, Psychology of Religion
Share Embed


Descrição do Produto

EXPERIMENTAL DESIGNS TWO GROUP DESIGNS & Statistical Inference

G. W. Sutton, Ph.D., 2010-2015

1

Two Group Designs The simplest experimental design is a two group design. The design may use two independent groups or two matched groups. Be sure to learn the difference.

G. W. Sutton, Ph.D., 2010-2015

2

Independent Groups We form independent groups when we randomly assign participants to one of two groups formed by the independent variable.

G. W. Sutton, Ph.D., 2010-2015

3

Independent Groups Consider an Example Suppose we want to study the willingness of congregants to restore to ministry a male or female youth pastor who abused alcohol.

G. W. Sutton, Ph.D., 2010-2015

4

Independent Groups Design Rather than having two pastors develop an alcohol problem to see how people respond, we can use a video case study method. Two groups of people view different but similar videos. Female pastor video Male pastor video

G. W. Sutton, Ph.D., 2010-2015

5

Two Group Designs A researchable problem stated in the form of a research question. Will Christian university students favor restoring one gender over another when considering restoring a youth pastor to ministry after she/he abused alcohol?

G. W. Sutton, Ph.D., 2010-2015

6

Two Group Designs Turn the question into a research hypothesis. There will be a significant difference in mean restoration ratings for youth pastor gender.

G. W. Sutton, Ph.D., 2010-2015

7

Two Group Designs You can use an If…then format.

If we expose participants to a video apology of male and female youth pastors who abused alcohol, then there will be a significant difference in attitudes toward restoration to ministry as measured on a rating scale.

G. W. Sutton, Ph.D., 2010-2015

8

Two Group Designs If we expose participants to a video apology of male and female youth pastors who abused alcohol… Notice that this part of the hypothesis identifies the independent variable.

G. W. Sutton, Ph.D., 2010-2015

9

Two Group Designs then there will be a significant difference in attitudes toward restoration to ministry Notice that this part of the hypothesis identifies the dependent variable

G. W. Sutton, Ph.D., 2010-2015

10

Two Group Designs as measured on a rating scale. Notice that this part of the hypothesis identifies how the dependent variable will be measured.

G. W. Sutton, Ph.D., 2010-2015

11

Two Group Designs then there will be a

significant

difference … Notice that this part of the hypothesis indicates the direction of the expected difference-- we do not mind which group mean is greater G. W. Sutton, Ph.D., 2010-2015

12

Two Group Designs a significant difference You can state that you expect one mean to be greater than another but, if you know the answer, why do the study? If you use a word like greater, you are stating a directional hypothesis.

G. W. Sutton, Ph.D., 2010-2015

13

Two Group Designs Write the null hypothesis. There is no significant difference in the population for mean restoration to ministry ratings of male and female pastors who abused alcohol and apologized for the abuse in a video (p < .05).

G. W. Sutton, Ph.D., 2010-2015

14

Two Group Designs There is no significant difference in the population for mean restoration to ministry ratings of male and female pastors who abused alcohol and apologized for the abuse in a video (p < .05). The null hypothesis is a NO difference hypothesis. We expect a null result.

G. W. Sutton, Ph.D., 2010-2015

15

Two Group Designs There is no significant difference in the population for mean restoration to ministry ratings of male and female pastors who abused alcohol and apologized for the abuse in a video (p < .05). The null hypothesis refers to POPULATION VALUES. Often, we compare group means but we can compare other values such as medians and variances.

G. W. Sutton, Ph.D., 2010-2015

16

Two Group Designs There is no significant difference in the population for mean restoration to ministry ratings of male and female pastors who abused alcohol and apologized for the abuse in a video (p < .05). The null hypothesis refers to a probability value, usually, p < .05. Note- italicize p and use spaces between algebraic values.

G. W. Sutton, Ph.D., 2010-2015

17

Two Group Designs Write the statistical null hypothesis. The Greek letter mu represents the population mean. The subscript identifies the group. You do not usually put the statistical null in a report.

μ1 = μ2 G. W. Sutton, Ph.D., 2010-2015

18

Design: Independent Groups Population of Volunteers

Male Pastor Case Group

Female Pastor Case Group

G. W. Sutton, Ph.D., 2010-2015

19

Two Group Designs

Procedure

G. W. Sutton, Ph.D., 2010-2015

20

Two Group Designs: Between Locate a population of volunteers. We expect to take a convenience sample.

G. W. Sutton, Ph.D., 2010-2015

21

Two Group Designs: Between Randomly select a sample of people from the defined population.

G. W. Sutton, Ph.D., 2010-2015

22

Two Group Designs: Between Divide the randomly selected sample into groups by randomly assigning people to two groups called A and B.

G. W. Sutton, Ph.D., 2010-2015

23

Two Group Designs: Between Divide the randomly selected sample into groups by randomly assigning people to two groups called A and B.



Note the two different uses of the word,

randomly.

G. W. Sutton, Ph.D., 2010-2015

24

Two Group Designs: Between Provide one group with a case of a female youth pastor and another group with a case of a male youth pastor. Keep other variables constant.

G. W. Sutton, Ph.D., 2010-2015

25

Two Group Designs: Between Measure the attitudes of each group using a restoration rating scale.

G. W. Sutton, Ph.D., 2010-2015

26

Two Group Designs: Between Compare the results by looking at the mean scores and the data. Then, test for significant differences using an

Independent Samples t-test.

G. W. Sutton, Ph.D., 2010-2015

27

Two Group Designs: Between Independent Samples t-test. t = the difference between the two means divided by the standard error of the difference between the means.

G. W. Sutton, Ph.D., 2010-2015

28

Two Group Designs: Between Independent Samples t-test. M (male) – M (female) – (μ1 – μ2)

t=

__________________________  s2/ df + s2/df

G. W. Sutton, Ph.D., 2010-2015

29

Two Group Designs: Between

Independent Samples t-test. Differences between groups due to IV

t=

__________________________ Score Variations Within a group--- error

G. W. Sutton, Ph.D., 2010-2015

30

Two Group Designs: Between Independent Samples t-test. If the samples were from the same population, the difference between the means would be zero. Some slight differences will occur due to error. This error is called error variance.

G. W. Sutton, Ph.D., 2010-2015

31

Two Group Designs: Between Independent Samples t-test. A large difference between groups and small variations within a group leads to a large t-value.

G. W. Sutton, Ph.D., 2010-2015

32

Two Group Designs: Between If the t value is large and the p-value is less than .05 then, conclude that there is a reliable (or significant) difference between the groups.

G. W. Sutton, Ph.D., 2010-2015

33

Two Group Designs: Between If the differences between the mean ratings are reliable (significant), then reject the null hypothesis of no difference and conclude that there is a statistically significant difference. Some differences are likely reliable but of no practical value.

G. W. Sutton, Ph.D., 2010-2015

34

Two Group Designs: Between Statistically significant differences are not necessarily valuable or important. They may just be reliable differences but so small as to have no practical value.

G. W. Sutton, Ph.D., 2010-2015

35

Two Group Designs: Between In a well designed study, a statistically significant t-value indicates that the specific differences, or more extreme differences, between the two means are likely reliable differences. The differences are likely true and not due to chance.

G. W. Sutton, Ph.D., 2010-2015

36

Two Group Designs: Between An error could occur. If alpha = .05, we assume that we could make a mistake about 5% of the time. The mistake would be to reject the null when it was true. This is a Type I error. Some writers refer to a Type I error as an alpha error.

G. W. Sutton, Ph.D., 2010-2015

37

Two Group Designs: Between Sometimes we may make a beta, or Type II, error. There may be a real difference between the groups but we did not find it. Therefore, we failed to reject the null hypothesis.

G. W. Sutton, Ph.D., 2010-2015

38

Two Group Designs: Between We commit a Type II error when we retain a false null hypothesis. A power analysis can help us reject the null hypothesis. Power = 1 - beta.

G. W. Sutton, Ph.D., 2010-2015

39

Two Group Designs: Between Power and research Power increases as the difference between the sample means increases. A powerful independent variable has an effect on the treatment group mean but the control group mean should remain unchanged.

G. W. Sutton, Ph.D., 2010-2015

40

Two Group Designs: Between Power and research Power increases with sample size. Larger samples allow us to have more confidence in the results and the statistical tests are more sensitive.

G. W. Sutton, Ph.D., 2010-2015

41

Two Group Designs: Between Power and research

Lower sample variance increases power. We want to reduce the score differences within the groups. Score variation within a group is error variance because all members of a group receive the same treatment. Homogeneity of variance is important to analyzing the effects of independent variables. G. W. Sutton, Ph.D., 2010-2015

42

Two Group Designs: Between Power and research Power increases with alpha. The larger the alpha level (e.g., .05 instead of .01), the more likely we will detect a difference between the means.

G. W. Sutton, Ph.D., 2010-2015

43

Two Group Designs: Between Effect Size (ES) If there is a significant difference between the means then, the IV affected the DV. How large was the effect? The p-value does not tell us about the effect size.

G. W. Sutton, Ph.D., 2010-2015

44

Two Group Designs: Between Effect Size Effect sizes are about relationships. Some measures of effect size include Pearson’s r2 Cohen’s d2 Omega squared ω2 Eta squared (2) G. W. Sutton, Ph.D., 2010-2015

45

Two Group Designs: Between Effect sizes are about relationships between IV and DV. Pearson r2 and t- test.

r= 

t2 ______ t2 + df

[r2 = r x r]

G. W. Sutton, Ph.D., 2010-2015

46

Two Group Designs: Between If you graph the means of the IV groups as X variables against scores on the Y axis you can connect the Means with a line and examine the relationship between the effect variable (X) and the outcome (Y) variable.

G. W. Sutton, Ph.D., 2010-2015

47

Two Group Designs: Between In our research design model, the outcome of restoration attitude depends on the effect of the IV in our research model.   

Outcome = model + error Y=X+e Y is a function of X plus some error

G. W. Sutton, Ph.D., 2010-2015

48

Two Group Designs: Between Effect Size SPSS provides eta squared for many data analyses.

G. W. Sutton, Ph.D., 2010-2015

49

Experimental Power 

SPSS provides a checkbox to obtain the observed power value for your study.

G. W. Sutton, Ph.D., 2010-2015

50

APA Reporting of Results 

We analyzed the scores from the two groups. Male pastors received higher scores (M = 53, SD = 4.2) than did female pastors (M = 35, SD = 3.6). Using an independent samples t-test we found significant differences for restoration attitude (t (24) = 5.02, p = .01, r2 = .74, OP = .85). Thus, we rejected the null hypothesis. For our sample, the participants favored restoring male rather than female youth pastors who had abused alcohol. [Fictitious data]

G. W. Sutton, Ph.D., 2010-2015

51

Two Group Designs: Within Now, change your thinking… We want to perform the same experiment using a

within-subjects design.

G. W. Sutton, Ph.D., 2010-2015

52

Two Group Designs: Within In a within-subjects design each person receives each level (group, condition, treatment) of the independent variable. Therefore, everybody in the sample will read both cases (male and female youth pastor) and complete two ratings.

G. W. Sutton, Ph.D., 2010-2015

53

Two Group Designs: Within Participant

Case 1

G. W. Sutton, Ph.D., 2010-2015

Case 2

54

Two Group Designs: Within Notice how we counterbalance the independent variable conditions to examine any effect that may be due to reading one case before the other.

G. W. Sutton, Ph.D., 2010-2015

55

Two Group Designs: Within At the end of each condition (Male or Female Youth Pastor), the participants completed their ratings. We examined the scores for errors and replaced missing data with series means.

G. W. Sutton, Ph.D., 2010-2015

56

Two Group Designs: Within Look at the wording on the next slide to see how we would write the results using APA style.

G. W. Sutton, Ph.D., 2010-2015

57

Two Group Designs: Within We analyzed the scores from the two conditions. Male pastors received higher scores (M = 45, SD = 4.2) than did female pastors (M = 37, SD = 3.6). Using a paired samples t-test we found significant differences for restoration attitude (t (25) = 4.02, p = .02, r2 = .64, OP = .80). Thus, we rejected the null hypothesis. For our sample, the participants favored restoring male rather than female youth pastors who had abused alcohol.

G. W. Sutton, Ph.D., 2010-2015

58

Two Group Designs: Within The within-subjects designs are valuable because we only need half as many people to conduct the study. The design controls for differences (variance) due to participant effects because each person participates in every condition. Each person is his/her own “control group”. G. W. Sutton, Ph.D., 2010-2015

59

Two Group Designs: Within The order of treatment effects is a problem in within groups designs. Attitudes can change as a result of viewing one case first.

G. W. Sutton, Ph.D., 2010-2015

60

Two Group Designs: Within We counterbalance the order of the stimulus (treatment, condition) to control the effects of order. Note that we do not eliminate the effects of order. The effects occur but we hope the counterbalanced design controls the effects.

G. W. Sutton, Ph.D., 2010-2015

61

Two Group Designs: Within We could introduce a time lapse between the presentations of the two cases. Sometimes it is a good idea to conduct a study both ways (between and within) as a way to increase our confidence in the results.

G. W. Sutton, Ph.D., 2010-2015

62

Two Group Designs: Within If you prescribe medicine or other therapy you will need to understand the lasting effects of the first treatment to appreciate the effects of the next treatment.

G. W. Sutton, Ph.D., 2010-2015

63

Two Group Designs: Summary  



Between-Subjects Design Two Groups Use the Independent Samples t-test also called a betweensubjects t-test.

 



Within-Subjects Design One group: each person gets two levels of IV. Use the Paired Samples or WithinSubjects t-test.

G. W. Sutton, Ph.D., 2010-2015

64

Two Group Designs Statistics review note… Refer to your Statistics text and SPSS manual so you know how to perform and interpret the t-tests discussed in the text. You may ask the lab and research assistants for help.

G. W. Sutton, Ph.D., 2010-2015

65

Lihat lebih banyak...

Comentários

Copyright © 2017 DADOSPDF Inc.