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**Chapter 13: Understanding Results—Statistical Inferences Chapter 14: Generalizing Results**

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**Descriptive Statistics**

Used to present data in summary form.

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**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 equivalent Achieved by experimental control and/or randomization

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Random error Variation due to differences among subjects within each group Responsible for some difference in the means

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**Research and Null Hypotheses**

Research hypothesis H1: Population means are not equal Null hypothesis HO: Population means are equal The assumption that the independent variable has had no effect

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**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

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**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, etc p: probability

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**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

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**The t-test Interpreting the t-test value:**

If probability is high (over .05), fail to reject the null hypothesis If probability is low (.05 or less), reject the null hypothesis

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**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?

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**Null Hypothesis Significance Testing: The t Test**

One-tailed versus two-tailed tests One-tailed test = research hypothesis specified a direction of difference between the groups Two-tailed test = research hypothesis did not predict direction of difference

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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

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**Do we accept the null hypothesis if the independent variable did not have an effect?**

Instead we fail to reject the null hypothesis.

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**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

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Type I error Occurs when the null hypothesis is rejected, but the null hypothesis is true

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

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**Experimental sensitivity**

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

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Experimental power Occurs when a statistical test allows researchers to correctly reject the null hypothesis Determined by 3 factors: Size of the effect Sample size Level of statistical significance

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