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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
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