Finishing up: Statistics & Developmental designs Psych 231: Research Methods in Psychology

Announcements Remember to turn in the second group project rating sheet in labs this week

Statistics Summary Real world (‘truth’) H 0 is correct H 0 is wrong Experimenter’s conclusions Reject H 0 Fail to Reject H 0 Type I error Type II error  Example Experiment:  Group A - gets treatment to improve memory  Group B - gets no treatment (control)  After treatment period test both groups for memory  Results:  Group A’s average memory score is 80%  Group B’s is 76%  Example Experiment:  Group A - gets treatment to improve memory  Group B - gets no treatment (control)  After treatment period test both groups for memory  Results:  Group A’s average memory score is 80%  Group B’s is 76% XAXA XBXB 76%80%  Is the 4% difference a “real” difference (statistically significant) or is it just sampling error? Two sample distributions H 0 : there is no difference between Grp A and Grp B H 0 : μ A = μ B About populations Observed difference Difference from chance Computed test statistic = set α-l evel Make a decision: reject H 0 or fail to reject H 0

Some inferential statistical tests The Design of the study determines what statistical tests are appropriate 1 factor with two groups T-tests Between groups: 2-independent samples Within groups: Repeated measures samples (matched, related) 1 factor with more than two groups Analysis of Variance (ANOVA) (either between groups or repeated measures) Multi-factorial Factorial ANOVA

T-test Design 2 separate experimental conditions Degrees of freedom Based on the size of the sample and the kind of t-test Formula: T = X 1 - X 2 Diff by chance Based on sample error Observed difference Computation differs for between and within t-tests XAXA XBXB

T-test Reporting your results The observed difference between conditions Kind of t-test Computed T-statistic Degrees of freedom for the test The “p-value” of the test “The mean of the treatment group was 12 points higher than the control group. An independent samples t-test yielded a significant difference, t(24) = 5.67, p < 0.05.” “The mean score of the post-test was 12 points higher than the pre-test. A repeated measures t-test demonstrated that this difference was significant significant, t(12) = 5.67, p < 0.05.”

Analysis of Variance Designs More than two groups 1 Factor ANOVA, Factorial ANOVA Both Within and Between Groups Factors Test statistic is an F-ratio Degrees of freedom Several to keep track of The number of them depends on the design XBXB XAXA XCXC Observed variance Variance from chance F-ratio = Can’t just compute a simple difference score since there are more than one difference A - B, B - C, & A - C

1 factor ANOVA Null hypothesis: H 0 : all the groups are equal X A = X B = X C Alternative hypotheses H A : not all the groups are equal X A ≠ X B ≠ X C X A ≠ X B = X C X A = X B ≠ X C X A = X C ≠ X B The ANOVA tests this one!! Do further tests to pick between these XBXB XAXA XCXC

1 factor ANOVA Planned contrasts and post-hoc tests: - Further tests used to rule out the different Alternative hypotheses X A ≠ X B ≠ X C X A ≠ X B = X C X A = X B ≠ X C X A = X C ≠ X B Test 1: A ≠ B Test 2: A ≠ C Test 3: B = C

Reporting your results The observed differences Kind of test Computed F-ratio Degrees of freedom for the test The “p-value” of the test Any post-hoc or planned comparison results “The mean score of Group A was 12, Group B was 25, and Group C was 27. A 1-way ANOVA was conducted and the results yielded a significant difference, F(2,25) = 5.67, p < Post hoc tests revealed that the differences between groups A and B and A and C were statistically reliable (respectively t(8) = 5.67, p < 0.05 & t(9) = 6.02, p <0.05). Groups B and C did not differ significantly from one another” 1 factor ANOVA

Factorial ANOVAs We covered much of this in our experimental design lecture More than one factor Factors may be within or between Overall design may be entirely within, entirely between, or mixed Many F-ratios may be computed An F-ratio is computed to test the main effect of each factor An F-ratio is computed to test each of the potential interactions between the factors

Factorial ANOVAs Reporting your results The observed differences Because there may be a lot of these, may present them in a table instead of directly in the text Kind of design e.g. “2 x 2 completely between factorial design” Computed F-ratios May see separate paragraphs for each factor, and for interactions Degrees of freedom for the test Each F-ratio will have its own set of df’s The “p-value” of the test May want to just say “all tests were tested with an alpha level of 0.05” Any post-hoc or planned comparison results Typically only the theoretically interesting comparisons are presented

Non-Experimental designs Sometimes you just can’t perform a fully controlled experiment Because of the issue of interest Limited resources (not enough subjects, observations are too costly, etc). Surveys Correlational Quasi-Experiments Developmental designs Small-N designs This does NOT imply that they are bad designs Just remember the advantages and disadvantages of each

Developmental designs Used to study changes in behavior that occur as a function of age changes Age typically serves as a quasi-independent variable Three major types Cross-sectional Longitudinal Cohort-sequential

Developmental designs Cross-sectional design Groups are pre-defined on the basis of a pre- existing variable Study groups of individuals of different ages at the same time Use age to assign participants to group Age is subject variable treated as a between-subjects variable Age 4 Age 7 Age 11

Cross-sectional design Developmental designs Advantages: Can gather data about different groups (i.e., ages) at the same time Participants are not required to commit for an extended period of time

Cross-sectional design Developmental designs Disavantages: Individuals are not followed over time Cohort (or generation) effect: individuals of different ages may be inherently different due to factors in the environmental context Are 5 year old different from 15 year olds just because of age, or can factors present in their environment contribute to the differences? Imagine a 15yr old saying “back when I was 5 I didn’t have a Wii, my own cell phone, or a netbook” Does not reveal development of any particular individuals Cannot infer causality due to lack of control

Longitudinal design Developmental designs Follow the same individual or group over time Age is treated as a within-subjects variable Rather than comparing groups, the same individuals are compared to themselves at different times Changes in dependent variable likely to reflect changes due to aging process Changes in performance are compared on an individual basis and overall Age 11 time Age 20Age 15

Longitudinal Designs Example Wisconsin Longitudinal Study (WLS) Wisconsin Longitudinal Study Began in 1957 and is still on-going (50+ years) 10,317 men and women who graduated from Wisconsin high schools in 1957 Originally studied plans for college after graduation Now it can be used as a test of aging and maturation

Longitudinal design Developmental designs Advantages: Can see developmental changes clearly Can measure differences within individuals Avoid some cohort effects (participants are all from same generation, so changes are more likely to be due to aging)

Longitudinal design Developmental designs Disadvantages Can be very time-consuming Can have cross-generational effects: Conclusions based on members of one generation may not apply to other generations Numerous threats to internal validity: Attrition/mortality History Practice effects Improved performance over multiple tests may be due to practice taking the test Cannot determine causality

Developmental designs Measure groups of participants as they age Example: measure a group of 5 year olds, then the same group 10 years later, as well as another group of 5 year olds Age is both between and within subjects variable Combines elements of cross-sectional and longitudinal designs Addresses some of the concerns raised by other designs For example, allows to evaluate the contribution of cohort effects Cohort-sequential design

Developmental designs Cohort-sequential design Time of measurement Cohort A Cohort B Cohort C Cross-sectional component 1970s 1980s 1990s Age 5 Age 15Age 25 Age 5 Age 15 Age 5 Longitudinal component

Developmental designs Advantages: Get more information Can track developmental changes to individuals Can compare different ages at a single time Can measure generation effect Less time-consuming than longitudinal (maybe) Disadvantages: Still time-consuming Need lots of groups of participants Still cannot make causal claims Cohort-sequential design