understanding research results: statistical inference

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