understanding research results: statistical inference
Post on 15-Jan-2016
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UNDERSTANDING RESEARCH UNDERSTANDING RESEARCH RESULTS: STATISTICAL RESULTS: STATISTICAL
INFERENCEINFERENCE
Probabilistic ReasoningProbabilistic 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 ReasoningProbabilistic Reasoning
• People aren’t very good at probabilistic reasoning• Gamblers fallacy• iPod shuffle
SAMPLES AND POPULATIONSSAMPLES 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 STATISTICSINFERENTIAL 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 NULL AND RESEARCH HYPOTHESESHYPOTHESES
Null Hypothesis: Population Means are Equal
Research Hypothesis: Population Means are Not Equal
Statistical significance
PROBABILITY AND SAMPLING PROBABILITY AND SAMPLING DISTRIBUTIONSDISTRIBUTIONS
Probability: The Case of knocking abilitySignificance level
Sample SizeThe larger the sample size, the more confidence
you have in rejecting the null hypothesis
THE THE tt TEST 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-testThe t-test
• t = X1 – X2
√s21/N1 + s2
2/N2
• t = 5.27
Critical values of t-testCritical values of t-test
Significance level
.05 .025 .01
df .10 .05 .02
1 6.314 12.706 31.821
2 2.920 4.303 6.965
3 2.353 3.182 4.541
4 2.132 2.776 3.747
18 1.734 2.101 2.552
SAMPLING DISTRIBUTION OF SAMPLING DISTRIBUTION OF tt VALUES VALUES
The The t-t-testtest
Degrees of Freedomdf = N1 + N2 - # of groups
One-Tailed Versus Two-Tailed TestsOne-tailed = directional hypothesisTwo-tailed = no directional hypothesis
SAMPLING DISTRIBUTION OF SAMPLING DISTRIBUTION OF tt VALUES VALUES
-1.734
Critical values of t-testCritical values of t-test
Significance level
.05 .025 .01
df .10 .05 .02
1 6.314 12.706 31.821
2 2.920 4.303 6.965
3 2.353 3.182 4.541
4 2.132 2.776 3.747
18 1.734 2.101 2.552
The F-testThe F-test
F Test (analysis of variance) – ANOVAUsed when you have 2 or more levels of an IV
or when a factorial design with 2 or more levelsSystematic variance = variability of scores
between groupsError variance = variability of scores within
groups