research design exam 3

what is the purpose of an experiment

to test a hypothesis

Two-group Design

• the simplest design

• 1 IV (2 levels)

• 1 DV

inferential statistics

• allow us to determine whether the alternative (experimental) hypothesis is true

dependent T-test

• compares two means on data from the same people measured at different times

independent t-tests

• compares two means on data from different groups of people

what is the rationale behind a t-test

• Compare the means of two samples.

• The standard error measures the expected variability between sample means.

• If the observed difference is larger than expected from standard error alone, then either:

  1. The difference occurred by random chance (null hypothesis is true), or

  2. The samples come from different populations (null hypothesis is false).

• The t-test helps determine which explanation is more likely.

t = ____

t = (observed difference between sample means - expected difference between population means (0) ) / estimate of the standard error of the difference between two sample means

multiple-group design

• comparing several means

• 1 IV (3 or more levels)

• 1 DV

what are limitations of a multi-group design

• can only compare 2 means when we often want to compare means from 3 or more groups

• can only be used with one IV / predictor variable

ANOVA

• compares several means

• can be used when we have manipulated more than one IV

• it is an extension of regression

what does ANOVA tell us

• tests the null hypothesis that the means are the same

• it is an omnibus test

• it tests for an overall difference between groups

• it tells us that the group means are different, but it doesn’t tell us exactly which means differ

Theory of ANOVA

• calculate how much variability there is between scores

• then calculate how much of this total variability can be explained by the model we fit to the data

• and how much cannot be explained

SS_T = _____

SS_M + SS_R

what if the ANOVA experiment is successful?

• the model will explain more variance than it can’t explain

• SS_M will be greater than SS_R

degrees of freedom

• the number of values that are free to vary

• one less than the number of values used to calculate the SS

model degrees of freedom

• df_M = (k-1)

why use follow up tests?

• the f-ratio tells us that the experiment was successful (the group means were different)

follow up tests

• multiple t-tests

  • this is a bad idea

  • possible to inflate type 1 error

planned contrasts

• hypothesis driven

• planned a priori

planned contrast rules

• variables not included in the contrast are coded as zero

• positive values are compared to negative values

• entire row must sum to zero

post hoc tests

• not planned (no hypothesis)

• compare all pairs of means

total sum of squares

• total variability

model sum of squares

• how much variability is due to the experimental manipulation

residual sums of squares

• how much variability is due to individual differences in performance