basic statistics in the social sciences - not a full blown analysis, just a presentation about the topic(s) in research methods.

1. Developmental Research
Methods
Topic 5: Statistics
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2. Probability
 Once we convert our raw scores into
Z-scores
 And assuming our data is normally
distributed
 We can now calculate the probability
of a given score.
 We use probability to test our
hypotheses!

3. The logic
 We infer
from our
sample to
the
population.
 We do this
using the
tools we just
talked about.
 The 5% rule
for statistical
significance.

4. 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

5. 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 )

6. 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!

7. 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.

8. ( )
 The experimental
hypothesis
 The null hypothesis
◦ The status quo
◦ Mutually exclusive
◦ Benchmark
 Significance testing
◦ h1 vs. h0
◦ probability
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9. Variation
 Remember, we are interested in two
types of varaiation
 Systematic and unsystematic (chance)
 There are two sources of systematic
variance
◦ Ones due to the IV
◦ Ones due to confounds

10. 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 Null
TYPE I
ERROR
α
RESEARCH
OBJECTIVE

11. Effect Size
 Significance ≠
Meaningfulness
 Probability of result is <α
◦ Significant yes
◦ Meaningful?
 Strength or magnitude
◦ Effect size (Cohen’s d)
◦ Linked to N
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12. POWER
 1 – β
 Probability of not making a
Type II error.
◦ Sample size
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Result 1
p = .03
r = .5
1-β= .35
Result 2
p = .4
r = .5
1-β= .17

13. Credits
 www.sxc.hu
◦ Spices – pape2000
◦ Black hole - zakeros
◦ Beer - dreamjay
◦ Roulette wheel - rasto
◦ DNA - flaivoloka
◦ Dice – thegnome54
◦ Darts 195617
 Raptor – USAF
 Mt. Rainier – Ryan Sain
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