Chapter 13: Understanding Results—Statistical InferencesChapter 14: Generalizing Results

Descriptive Statistics Used to present data in summary

form.

Inferential statistics

Used to determine whether an independent variable had a reliable effect on a dependent variable

Replication: repeating experiment to try to get the same results second time

Groups must be equivalentAchieved by experimental control and/or

randomization

Random error

Variation due to differences among subjects within each group

Responsible for some difference in the means

Research and Null Hypotheses Research hypothesis

H1: Population means are not equal

Null hypothesis HO: Population means are equalThe assumption that the independent variable has had no effect

Statistical significance

The probability the difference in sample means is due to error

Statistically significant outcome: has a small likelihood of occurring if the null hypothesis is true

Level of significance

Probability of error chosen by researcher

Usually set at .05 or less Alpha level indicated by Greek letter α

Noted as p .05; p .01, etcp: probability

Null-Hypothesis Significance Testing

Null-hypothesis significance testing assesses the probability of obtaining a given difference between sample means

t-test: commonly used significance test

The t-test

Interpreting the t-test value:If probability is high (over .05), fail to

reject the null hypothesisIf probability is low (.05 or less), reject

the null hypothesis

Do we have a winner?Data Analysis for an Experiment Comparing Means

Round Chopsticks?

Did the independent variable (shape of chopsticks) have an effect on the dependent variable (number of pasta pieces transferred)?

Square Chopsticks?

Null Hypothesis Significance Testing: The t Test

One-tailed versus two-tailed testsOne-tailed test =

research hypothesis specified a direction of difference between the groups

Two-tailed test = research hypothesis did not predict direction of difference

Chopsticks Challenge Hypothesis #1: Performance when

using round chopsticks is different (better or worse) than performance when using square chopsticks(two-tailed) = .19

Hypothesis #2: Performance when using round chopsticks is better than performance when using square chopsticks(one-tailed) = .09

Do we accept the null hypothesis if the independent variable did not have an effect? No! Instead we fail to reject the null

hypothesis.

Type I and Type II Errors Decision to reject the null hypothesis is

based on probabilities rather than certainties. Decision may or may not be correct

Type I error

Occurs when the null hypothesis is rejected, but the null hypothesis is true

Type II error

Occurs when the null hypothesis is false, but it is not rejected

Experimental sensitivity

Occurs when an experiment detects an effect of the independent variable (when, in fact, the independent variable truly has an effect)

Experimental power

Occurs when a statistical test allows researchers to correctly reject the null hypothesis

Determined by 3 factors:Size of the effectSample sizeLevel of statistical significance