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```Experimental Psychology
PSY 433
Appendix B
Statistics
Goals for the Experimenter
 Create the strongest effect possible:
 Increase the number of subjects
 Improve the stimuli and task (e.g., increase
trials, change manipulation)
 Reduce “noise” – unwanted variance:
 Control as much as possible
 Make sure all subjects have the same
experience (except for the manipulation)
 Eliminate confounds – the only explanation
should be the “alternative explanation
Descriptive & Inferential Statistics
 Descriptive statistics -- organize,
summarize & describe data.
 Inferential statistics -- make inferences
about a large group based on data from a
small portion of those people
 The large group is called the population.
 The small portion is called the sample.
 We generalize from the sample to the
population.
Samples and Populations
 Example: Randomly assign 100 students
to 2 groups of 50



One group gets a drug and the other a
placebo.
Test both groups’ memory for 80 words.
Mean # of words recalled: drug = 48,
placebo = 42.
 What are the samples and what are the
populations?
 What can be inferred about the population?
Null & Alternative Hypotheses
 Does the drug improve memory in students?
 There are two possibilities:
 The drug has no effect and the difference
between sample means reflects random
chance (null hypothesis)
 The drug improves memory and the
difference between sample means reflects
the presence of two different populations
(alternative hypothesis).
Hypothesis Testing
 We first assume there is no effect of the
drug on memory (null hypothesis)
 We then look at the difference between
sample means & ask: how likely is this
difference if the null hypothesis is true?
 Small differences are likely (due to chance),
so the null hypothesis (no difference) could
be true.
 Large differences are unlikely, so we reject
the null hypothesis and decide the drug
most likely did affect memory.
Significance Level
 We reject the null hypothesis if there is a
“large difference” between sample means
 But what’s a “large difference?”
 A “large difference” is one that would occur
less than 5% of the time by chance alone
(significance level, or p < .05)
 This is called a significant difference.
Kinds of Descriptive Statistics
 Measures of central tendency – use a single
number to describe the group.


Useful for comparing between multiple groups.
Mean, median, mode.
 Measures of dispersion – quantifies how
much the values are spread out or distant
from the mean.



Range
Variance
Standard deviation
Inferential Statistics
 Used to test difference between means or
between a mean and some other number.
 Answers the question: could this result have
occurred due to chance (normal variability)?
 Compares the observed values against what
typically occurs with repeated sampling – the
normal distribution.

Standard error of the mean – a standard
deviation for the means of all possible
samples from a population.
Kinds of Inferential Tests
 Tests for a single group against a known
value:

Single group z-test or t-test
 Tests for differences between two groups:
 Independent groups t-test
 Repeated measures (paired groups) t-test
 Tests for difference between several groups:
 ANOVA – for one IV (one-way)
 Repeated measures ANOVA
 Multi-factor ANOVA
Nonparametric Tests
 When data is not normally distributed then
the assumptions about what might occur due
to chance are different.
 Two choices:


Convert data to normal distribution.
Minimize the odd distribution and make it more
closely normal by using the rank orders of the
observations instead of their actual values.
 Slightly different tests are required -- each
test has a non-parametric equivalent.
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