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Finishing up: Statistics & Developmental designs

Finishing up: Statistics & Developmental designs. Psych 231: Research Methods in Psychology. Remember to turn in the second group project rating sheet in labs this week. Announcements. About populations. Real world ( ‘ truth ’ ). H 0 is correct. H 0 is wrong. Type I error. Reject H 0.

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Finishing up: Statistics & Developmental designs

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

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

  3. About populations Real world (‘truth’) H0 is correct H0 is wrong Type I error Reject H0 Experimenter’s conclusions Fail to Reject H0 Type II error 76% 80% XB XA • 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% H0: μA = μB H0: there is no difference between Grp A and Grp B • Is the 4% difference a “real” difference (statistically significant) or is it just sampling error? Two sample distributions set α-level Statistics Summary Observed difference Computed test statistic = Difference from chance Make a decision: reject H0or fail to reject H0

  4. 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 Some inferential statistical tests

  5. Observed difference X1 - X2 T = Diff by chance Based on sample error • Design • 2 separate experimental conditions • Degrees of freedom • Based on the size of the sample and the kind of t-test • Formula: XB XA Computation differs for between and within t-tests T-test

  6. 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.” T-test

  7. Observed variance F-ratio = XA XC XB Variance from chance • 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 Can’t just compute a simple difference score since there are more than one difference A - B, B - C, & A - C Analysis of Variance

  8. The ANOVA tests this one!! Do further tests to pick between these XA = XB = XC XA ≠ XB ≠ XC XA ≠ XB = XC XA = XB ≠ XC XA = XC ≠ XB XA XC XB Null hypothesis: H0: all the groups are equal Alternative hypotheses • HA: not all the groups are equal 1 factor ANOVA

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

  10. 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 < 0.05. 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

  11. 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

  12. 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 Factorial ANOVAs

  13. 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 Non-Experimental designs

  14. 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

  15. 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 Developmental designs

  16. 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

  17. 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 • Cross-sectional design Developmental designs

  18. 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 • Longitudinal design time Age 11 Age 15 Age 20 Developmental designs

  19. Example • Wisconsin Longitudinal Study(WLS) • 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 Designs

  20. 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

  21. 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 • Longitudinal design Developmental designs

  22. 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

  23. Cohort-sequential design Time of measurement 1975 1985 1995 Cohort A 1970s Age 5 Age 5 Age 5 Cross-sectional component Cohort B 1980s Age 15 Age 15 Cohort C 1990s Age 25 Longitudinal component Developmental designs

  24. 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 Developmental designs

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