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Inferential Statistics. The Logic of Inferential Statistics. Makes inferences about a population from a sample Assumes a random sample to estimate error Uses tests of significance which are rooted in the logic of probability sampling. Making a Statistical Decision.

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## Inferential Statistics

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**The Logic of Inferential Statistics**• Makes inferences about a population from a sample • Assumes a random sample to estimate error • Uses tests of significance which are rooted in the logic of probability sampling**Making a Statistical Decision**• Step 1: Establishing Type I and Type II Error Risk Levels • Step 2: Selecting the appropriate statistical test • Parametric and Nonparametric Statistics • Statistics of Difference and Relationship • Step 3: Computing the test statistic • Step 4: Consulting the appropriate statistical table • Step 5: Deciding whether or not to reject the null hypothesis.**Chi Square**• Nonparametric Statistic of difference • Used to identify differences in frequency data. • One Sample Chi Square compares the frequency of attributes of a variable measured at the nominal level. • Chi Square for Contingency Tables compares the frequency of attributes of two or more variables measured at the nominal level.**T-test**• Parametric statistic of difference • Measures the difference between attributes of an independent variable measured at the nominal level on some dependent variable measured at the interval or ratio level. • The Independent Samples T-test is used when the two groups (independent variable) are independent. • The Paired Samples T-test is used when the two groups (independent variable) are related.**Analysis of Variance (ANOVA)**• Parametric test of difference • Assesses the extent to which attributes of independent variables measured at the nominal level differ on some dependent variable measured at the interval or ratio level. • A one-way ANOVA is used when there are more than two attributes of a single independent variable measured at the nominal level. • A factorial ANOVA is used when there are more than one independent variables measured at the nominal level.**Pearson Product-Moment Correlation**• Parametric statistic of relationship • Assess the degree to which two variables measured at the interval or ratio level are linearly related to one another. • A correlation coefficient can range from -1.00 (a perfect negative relationship) to +1.00 (perfect positive relationship) • The coefficient of determination indicates the percentage of variation of one variable that is predicted by knowledge of the other variable.

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