Post on 21-Dec-2014
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04/10/2023 CEDP321 Ryan Sain, Ph.D. 1
Developmental Research MethodsTopic 5: Statistics
ProbabilityOnce we convert our raw scores
into Z-scoresAnd assuming our data is
normally distributedWe can now calculate the
probability of a given score.We use probability to test our
hypotheses!
The logicWe infer from
our sample to the population.
We do this using the tools we just talked about.
The 5% rule for statistical significance.
Confidence intervals How confident we are that the true population mean
falls within a given range of the sample mean Collect many samples (each one has a different
mean) CI of 95% - collecting 100 samples, 95% of them the
population mean will be within the CI constructed. Z score of -1.96 and 1.96 (95% of all data falls
between here) Reverse calculate to get the actual raw score. Range boundaries = M +/- (1.96 * SE)
SE is the standardized measure of how accurate our mean is.
SD/sqrt of the number of scores
Testing• Systematic variation–Variation due to a real effect – the
independent variable–confounds
• Unsystematic variation–Variation from individual differences
• Inferential stat = systematic/unsystematic
• If this falls below p=.05 then we are confident that the difference is not due to random error (known as α )
Gambler’s fallacy - independence
Last performance affects current performance
Not winning last time increases the probability that I will win this time
The roulette wheel – readouts!
Using the t-test• Used to detect differences between the
mean of two independent groups• Independent• The means from each group are compared• Assumptions– Normal distribution– Homogeneity of variance
• Error bars – plot the standard error of the mean.
04/10/2023 CEDP 596-04 Ryan Sain, Ph.D.
8
( )
The experimental hypothesis
The null hypothesis◦ The status quo◦ Mutually exclusive◦ Benchmark
Significance testing◦ h1 vs. h0
◦ probability
VariationRemember, we are interested in
two types of varaiationSystematic and unsystematic
(chance)There are two sources of
systematic variance◦Ones due to the IV◦Ones due to confounds
Types of Error
The Null Hypothesis Is …..
True False
Based on the Test, We
either…
Fail to Reject the Null
RESEARCH OBJECTIVE
TYPE II ERROR
β
Reject the NullTYPE I ERROR
α
RESEARCH OBJECTIVE
04/10/2023 CEDP 596-04 Ryan Sain, Ph.D.
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Effect Size
Significance ≠ Meaningfulness
Probability of result is <α◦Significant yes◦Meaningful?
Strength or magnitude◦Effect size (Cohen’s d)◦Linked to N
04/10/2023 CEDP 596-04 Ryan Sain, Ph.D.
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POWER
1 – βProbability of not making a
Type II error.◦ Sample size
Result 1
p = .03
r = .5
1-β= .35
Result 2
p = .4
r = .5
1-β= .17
04/10/2023 CEDP321 Ryan Sain, Ph.D. 13
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