Understanding Research Results: Descriptive & Correlation Analysis

1. Ch 12 Understanding Research Results: Description and Correlation

2. Analyzing the results of research investigations • Three basic ways to describe results • Comparing group percentages • Correlating individual scores • Comparing group means

3. Frequency distributions • Indicates the # of individuals that receive each possible score on a variable • Graphing frequency distributions • Pie charts • Bar graphs • Used for nominal data • Frequency polygons • a.k.a. line graph • A line is drawn to represent the relationship between variables

4. Descriptive statistics • Allow researchers to make precise statements about the data • Two types of stats are needed to describe data • Central tendency – tell us what the sample is as a whole • Mean- • Median- • Mode- • Variability

5. Descriptive statistics • Allow researchers to make precise statements about the data • Two types of stats are needed to describe data • Central tendency • Variability – the amount of spread in a distribution of scores • Standard deviation -calculated by taking the square root of the arithmetic average of the squares of the deviations from the mean in a frequency distribution • Variance -the average squared deviation of each number from its mean

6. Correlation coefficients: describing the strength of relationships • Correlation coefficient – a statistic that describes how strongly variables are related to one another • Pearson r • Type of correlation coefficient • Designed to detect only linear relationships • Used when both variables have interval or ratio scale properties • Provides info about the strength of the relationship and the direction of the relationship • 0 = no relationship, 1 = strong positive relationship, -1 = strong negative relationship • The closer to 1, the stronger the relationship

7. Correlation coefficients: describing the strength of relationships • Correlation coefficient • Pearson r • Data can be visualized in a scatterplot • A scatterplot shows • An indicator of effect size; it indicates the strength of the linear association between two variables • Calculated using pairs of observations from each subject • Curvilinear relationship • A scatterplot can still be constructed

8. Effect size • A general term that refers to the strength of association between variables • Correlation coefficients are calculated to indicate the magnitude of the effect of the IV on the DV • Values range from ______________ • Provides a scale of values that is consistent across all types of studies

9. Regression equations • Calculations used to predict a person’s score on one variable when that person’s score on another variable is already known • For example, the use of SAT scores to predict college performance • General form is Y = a + bX • Y = score we wish to predict • X = known score • a = a constant

10. Multiple correlation • The correlation b/w a combined set of predictor variables and a single criterion variables • Used to combine a # of predictor variables to increase the accuracy of prediction of a given criterion or outcome variable • The resulting R value provides an indication of the goodness of fit of the model • Symbolized as R • Y = a + b1*X1 + b2*X2 + ... + bn*Xn • Y: criterion variable (predicted GPA) • X: predictor variables • a: constant • b: scores on the predictor variables (grades, GRE score)