UNDERSTANDING RESEARCH RESULTS: STATISTICAL INFERENCE

1

• UNDERSTANDING RESEARCH RESULTS STATISTICAL
  INFERENCE

2
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

3
Probabilistic Reasoning

• People arent very good at probabilistic
  reasoning
• Gamblers fallacy
• iPod shuffle

4
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

5
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

6
NULL AND RESEARCH HYPOTHESES

• Null Hypothesis Population Means are Equal
• Research Hypothesis Population Means are Not
  Equal
• Statistical significance

7
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

8
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

9
The t-test

• t X1 X2
• vs21/N1 s22/N2
• t 5.27

10
Critical 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

11
SAMPLING DISTRIBUTION OF t VALUES
12
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

13
SAMPLING DISTRIBUTION OF t VALUES
-1.734
14
Critical 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

15
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