Understanding Research Results: Description and Correlation

Analyzing the results of research investigations Three basic ways to describe results Comparing group percentages Correlating individual scores 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 Central tendency – tell us what the sample is as a whole Mean- Median- Mode- Variability

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

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 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 + bX 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 + 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)