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UNDERSTANDING RESEARCH
RESULTS: STATISTICAL
INFERENCE
Probabilistic Reasoning
• Most results are in probabilistic terms
• Exceptions to the rule
• The ‘Person Who’ argument
• Misuse of probabilistic information
• Base rates = the natural occurrence of some
phenomenon with no other information
• Sample size
Probabilistic Reasoning
• People aren’t very good at probabilistic
reasoning
• Gamblers fallacy
• iPod shuffle
SAMPLES AND POPULATIONS
Inferential statistics are necessary because
the results of a given study are based on
data obtained from a single sample of
researcher participants
Allows conclusions on the basis of sample
data
INFERENTIAL STATISTICS
Allows researchers to make inferences
about the true difference in the population
on the basis of the sample data
Gives the probability that the difference
between means reflects random error rather
than a real difference
NULL AND RESEARCH
HYPOTHESES
Null Hypothesis: Population Means are
Equal
Research Hypothesis: Population Means are
Not Equal
Statistical significance
PROBABILITY AND SAMPLING
DISTRIBUTIONS
Probability: The Case of knocking ability
Significance level
Sample Size
The larger the sample size, the more confidence
you have in rejecting the null hypothesis
THE t TEST
t value is a ratio of two aspects of the data:
the difference between the group means and
the variability within groups
t=
group difference
within group variability
The t-test
• t=
X1 – X2
√s21/N1 + s22/N2
• t = 5.27
Critical values of t-test
Significance level
df
1
2
3
4
18
.05
.10
6.314
2.920
2.353
2.132
1.734
.025
.05
12.706
4.303
3.182
2.776
2.101
.01
.02
31.821
6.965
4.541
3.747
2.552
SAMPLING DISTRIBUTION OF
t VALUES
The t-test
Degrees of Freedom
df = N1 + N2 - # of groups
One-Tailed Versus Two-Tailed Tests
One-tailed = directional hypothesis
Two-tailed = no directional hypothesis
SAMPLING DISTRIBUTION OF
t VALUES
-1.734
Critical values of t-test
Significance level
df
1
2
3
4
18
.05
.10
6.314
2.920
2.353
2.132
1.734
.025
.05
12.706
4.303
3.182
2.776
2.101
.01
.02
31.821
6.965
4.541
3.747
2.552
The F-test
F Test (analysis of variance) – ANOVA
Used when you have 2 or more levels of an IV
or when a factorial design with 2 or more levels
Systematic variance = variability of scores
between groups
Error variance = variability of scores within
groups