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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.

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finishing up statistics developmental designs

Finishing up:Statistics & Developmental designs

Psych 231: Research Methods in Psychology

statistics summary

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





  • 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


set α-level

Statistics Summary

Observed difference


test statistic


Difference from chance

Make a decision: reject H0or 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
Some inferential statistical tests
t test

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:



Computation differs for

between and within t-tests

t test1
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

Observed variance

F-ratio =




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
1 factor anova

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




Null hypothesis:

H0: all the groups are equal

Alternative hypotheses

  • HA: not all the groups are equal
1 factor ANOVA
1 factor anova1

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
1 factor anova2
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
factorial anovas1
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
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
Non-Experimental designs
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
developmental designs1
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
developmental designs2
    • 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
developmental designs3
    • 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
developmental designs4
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


Age 11

Age 15

Age 20

Developmental designs
longitudinal designs
    • 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
developmental designs5
    • 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
developmental designs6
    • 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
developmental designs7
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
developmental designs8

Cohort-sequential design

Time of measurement




Cohort A


Age 5

Age 5

Age 5

Cross-sectional component

Cohort B


Age 15

Age 15

Cohort C


Age 25

Longitudinal component

Developmental designs
developmental designs9
    • 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