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## Finishing up: Statistics & Developmental designs

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### Finishing up:Statistics & Developmental designs

Psych 231: Research Methods in Psychology

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 SummaryObserved difference

Computed

test statistic

=

Difference from chance

Make a decision: reject H0or fail to reject H0

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

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-testReporting 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.”

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 VarianceDo 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

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 ANOVAReporting 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”

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

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

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

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

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 designsAdvantages:

- 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

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

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 designsExample

- 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

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

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

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

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 designsAdvantages:

- 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

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