This is lecture notes on quantitative analysis approaches

Statistics

1. Chapter 12 Quantitative Approaches

2. Which Test to Use? You must identify: The number of variables in the analysis The level of measurement of the variables Whether variables are independent or dependent Whether the relationship is assumed to be linear

3. Hypothesis Testing Two basic elements: The test is based on the ratio of percentage of explained variance to the percentage of unexplained variance Variance is the basis of all analysis The variance explained is the variance in the dependent variable (explained by the independent variable) The relationship tested is generally a linear relationship

4. Two Basic Approaches to Analysis Group Differences Group differences use analysis of variance (ANOVA) Variable Relationships Within group variable relationships use correlation and regression

5. Translate the Measures Prepare the data set for a software program A rectangular matrix presents variables in columns and subjects in rows A column represents scores on a particular variable A record may refer to a single line of data A case (often the same as a record) is the set of data that represents a single subject

6. Group Difference Tests Generally, group differences have: Independent variables with a nominal or ordinal level of measurement, and A dependent variable measured at the interval or ratio level

7. Group Difference Tests T-test One way ANOVA ANOVA MANOVA

8. T-test The simplest of differences of means tests This difference of means test is an ANOVA ( an alysis o f va riance) with a single independent variable with only two levels and a single dependent variable; thus, there are only two groups to compare T to test explained variance

9. One Way ANOVA A one way ANOVA (analysis of variance) can be run wherever a difference of means t-test can be run This difference of means test has a single independent variable with two or more levels and a single dependent variable; thus, it can compare two or more groups F to test explained variance

10. ANOVA The general form of ANOVA; any t -test or one way ANOVA can be run as a general ANOVA This difference of means test can have more than one independent variable with two or more levels and a single dependent variable F to test explained variance

11. MANOVA M ultivariate An alysis o f Va riance An ANOVA that allows more than one dependent variable Beyond the scope of this text

12. Variable Relationship Tests Variables need to be interval or ratio level of measurement Correlation Simple correlation Multiple correlation/regression Canonical correlation

13. Correlation The most common associative measure, the Pearson Product Moment Correlation, is a description of the linear relationship between two variables No assumption that the two variables are independent or dependent

14. Simple Correlation/Regression Correlation with two variables; one designated independent, the other dependent b , β , a, 𝝰

15. Multiple Correlation/Regression Multiple regression is probably the most used statistical procedure in the world More than one independent variable and a single dependent variable R

16. Canonical Correlation Analogous to MANOVA, canonical correlation is multiple regression with multiple independent variables and more than one dependent variables Beyond the scope of this text

17. Descriptive Statistics Measures of central tendency: Mean: the arithmetic average Median: the middle score of the group (ordinal) Mode: the most frequent score The definition of a normal distribution: mean = median = mode

18. Descriptive Statistics Measures of dispersion: Range: calculated by taking the difference between the highest number in the group and the lowest Standard deviation: the average deviation a set of scores are from their mean

19. Statistical Difference Do the means likely come from different groups? Is there a real (statistical) difference between the groups being compared? We need a hypothesis and a test