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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. - PowerPoint PPT Presentation
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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’)
H0 is correct
H0 is wrong
Experimenter’s conclusions
Reject H0
Fail to Reject H0
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%
XAXB
76% 80%
Is the 4% difference a “real” difference (statistically significant) or is it just sampling error?
Two sampledistributions
H0: there is no difference between Grp A and Grp B
H0: μA = μB
About populations
Observed difference
Difference from chance
Computed test statistic
=
set α-level
Make a decision: reject H0 or fail to reject H0
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 = X1 - X2
Diff by chance
Based on sample error
Observed difference
Computation differs for between and within t-tests
XAXB
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
XBXA XC
Observed variance
Variance from chanceF-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: H0: all the groups are equal
XA = XB = XC
Alternative hypotheses
HA: not all the groups are equal
XA ≠ XB ≠ XC XA ≠ XB = XC
XA = XB ≠ XC XA = XC ≠ XB
The ANOVA tests this one!!
Do further tests to pick between these
XBXA XC
1 factor ANOVA
Planned contrasts and post-hoc tests:
- Further tests used to rule out the different Alternative
hypothesesXA ≠ XB ≠ XC
XA ≠ XB = XC
XA = XB ≠ XC
XA = XC ≠ XB
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 < 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
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
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)
• 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 designTime of measurement
1975 1985 1995
Cohort A
Cohort B
Cohort CCro
ss-s
ectio
nal c
ompo
nent
1970s
1980s
1990s
Age 5 Age 15 Age 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