Ch 12 Understanding Research Results Description and Correlation

Ch 12 Understanding Research Results: Description and Correlation

Analyzing the results of research investigations § Three basic ways to describe results 1. Comparing group percentages 2. Correlating individual scores 3. Comparing group means

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

Descriptive statistics § Allow researchers to make precise statements about the data § Two types of stats are needed to describe data 1) Central tendency – tell us what the sample is as a whole § § § Mean. Median. Mode- 2) Variability

Descriptive statistics § Allow researchers to make precise statements about the data § Two types of stats are needed to describe data 1) Central tendency 2) 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

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

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

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

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 + b. X § Y = score we wish to predict § X = known score § a = a constant

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 + b 1*X 1 + b 2*X 2 +. . . + bn*Xn § § Y: criterion variable (predicted GPA) X: predictor variables a: constant b: scores on the predictor variables (grades, GRE score)