Inferential Statistics

The Logic of Inferential Statistics Makes inferences about a population from a sample Makes inferences about a population from a sample Assumes a random sample to estimate error Assumes a random sample to estimate error Uses tests of significance which are rooted in the logic of probability sampling 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 1: Establishing Type I and Type II Error Risk Levels Step 2: Selecting the appropriate statistical test Step 2: Selecting the appropriate statistical test –Parametric and Nonparametric Statistics –Statistics of Difference and Relationship Step 3: Computing the test statistic Step 3: Computing the test statistic Step 4: Consulting the appropriate statistical table Step 4: Consulting the appropriate statistical table Step 5: Deciding whether or not to reject the null hypothesis. Step 5: Deciding whether or not to reject the null hypothesis.

Chi Square Nonparametric Statistic of difference Nonparametric Statistic of difference Used to identify differences in frequency data. Used to identify differences in frequency data. One Sample Chi Square compares the frequency of attributes of a variable measured at the nominal level. 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. 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 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. 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 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. The Paired Samples T-test is used when the two groups (independent variable) are related.

Analysis of Variance (ANOVA) Parametric test of difference 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. 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 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. 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 Parametric statistic of relationship Assess the degree to which two variables measured at the interval or ratio level are linearly related to one another. 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 (a perfect negative relationship) to (perfect positive relationship) A correlation coefficient can range from (a perfect negative relationship) to (perfect positive relationship) The coefficient of determination indicates the percentage of variation of one variable that is predicted by knowledge of the other variable. The coefficient of determination indicates the percentage of variation of one variable that is predicted by knowledge of the other variable.