Research in Social Work Practice Salem State University Jeff Driskell, MSW, PhD

Agenda Check-in/announcements Lecture/activities Correlations

4 basic categories of statistical tests Mean, standard deviation Median, Mode Percentage, frequency Description Pearson’s correlation Correlation Student’s t tests Chi-square tests ANOVA Odds ratios Comparison OLS regression Logit regression Prediction

What are Correlations? DEFINITION:

Correlation tests FYI – also known as: Pearson product-moment correlation coefficient Pearson’s r Pearson’s test Pearson correlation/s Correlation coefficient

Statistical Strategy for Assessing Correlations Known as Pearson’s correlation coefficient. A parametric test represented by r Statistical significance- An insignificant correlation is one that is not very reliable Easier to obtain significance with a larger sample size. You could have a statistical significant finding but then have a low correlation of .20 which is not very meaningful.

Correlation Examples Example 1- As a student- It might be interesting to look at the relationship between the amount of time spent reading (IV) the course text and your exam scores (DV) Example 2- You may want to know the relationship between exam scores (DV) and test anxiety (IV).

Why are Calculating Correlations Important? Helps to identify early on any potential relationships between variables. These significant correlations are often the variables that are controlled for in multivariate analysis. Helps answer any initial hypotheses. Allows you to quantify the strength of the relationship between two variables .

Interpreting Correlations The type of relationship between variables Positive Relationship Negative Relationship Not related at all-

Range of Values- SPSS Output Always will be between -1 to +1 (if you find a correlation less than -1 or more than +1 something has seriously gone wrong) r=+1 this is a perfect positive linear association between two variables and all data points lie exactly on the line of best fit. They are positively correlated. r= -1 this is a perfect negative linear association between two variables…They are negatively correlated. r= 0 there is no relationship between the two variables.

Strength of the Linear Relationship Range Strength Less than .20 Extremely low .20-.40 Small/very low .40-.70 Moderate .70-.90 Strong .90-1.00 Very strong

Correlation test: A measure of association Years of employment variable 11-20 years 0-5 years 6-10 years The longer you work at the Department of Children and Families… 60 (Mid) 90 (High) Burnout score variable 30 (Low) Moving apart? ..the more likely you are to experience “burnout”

Correlation test: A measure of association Caseload variable 23-30 0-18 19-22 The lower your caseload at the Department of Children & Families… 60 (Mid) 90 (High) 30 (Low) Burnout score variable Moving apart? ..the less likely you are to experience “burnout”

Correlation test: A measure of association Job satisfaction variable High Mid Low The higher your job satisfaction at the Department of Children & Families… High Mid Low Burnout score variable Moving apart? ..the less likely you are to experience “burnout”

Look for the “r” and “p” values Statistically significant association between variables p-level should be between .05-.001 p<.05* p<.01** p<.001

Correlation Matrix

Narrative: Table 1

Using R2 for to Boost Interpretations We can figure out the amount of variability of the explanation. IE: That is, how much does test anxiety contribute to poor exam scores. We know that there are other possible factors that impact exam scores (length of time studying, memory)

Calculating R2 (This has to be done manually) (-.4410-)2= .194. Take Pearson’s r from SPSS output and square it-(r)2 (This has to be done manually) Exam Score and Anxiety example- (-.4410-)2= .194. Interpretation 1: Exam anxiety accounts for 19% of the variability in exam scores. Although correlated, it only accounts for 19.4% of the variation in exam scores. Interpretation 2: This leaves another 80.6% that is unexplained and is accounted for by other variables.

Marziali et al (2008) Correlation Matrix Interpretation Which variable had the strongest positive significant relationship? Which variable had the weakest negative significant relationship? Which variable is the only one that is significantly correlated with self-efficacy?

Exercise Identify an article of your choice that contains correlation analyses….preferably a correlation matrix How would you interpret the findings?