Psyc 321_05 introduction to stats

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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