Exam 4 notes and Plous Readings

# Exam 4 notes and Plous Readings - Hypothesis Testing with...

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Hypothesis Testing with Correlation and Regression Plous (17,18) I believe r is how precise the line is. Examples are -.2, .8 etc Five Steps to Hypothesis Testing Step 1: Identify the research problem (hypothesis) o Describe the null and alternative hypotheses o For correlation null is that r=0 (no relationship) Step 2: Decision Rule o Alpha level (.05 or .01) o Critical Statistic (e.g. critical r) value form table? Step 3: Calculations Step 4: Make decision whether r not to reject the null hypothesis o If observed r is bigger then critical r then reject null Step 5: Conclusion o Tie findings back into research problem Finding a Statistically Significant Correlation The result is “statistically significant” if: o The observed correlation is larger than the critical correlation We want our r to be big if we want it to be significantly different form zero. It can be either negative or positive but just as far away from zero o The p value is less than .05 (which is our alpha) o We reject the null hypothesis o Then we have support for our alternative hypothesis Correlation Measure of how two variable co-occur and also can be used for prediction Range is between -1 and +1 The closer to zero the weaker the relationship and the worse the prediction Positive of negative Positive Correlation As values on one variable go up, so do values for other variable Pairs of observations tend to occupy similar relative positions Higher scores on one variable tend to co-occur with higher scores on the second variable

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Lower scores on one variable tend to co-occur with lower scores on the second variable Scatter plot shows clusters of point from lower left to upper right Negative Correlation As values on one variable go up, values for the other variable go down Pairs of observation tend to occupy dissimilar relative position Higher scores on one variable tend to co-occur with lower scores on the second variable Scatter plot shows clusters of point from upper left to lower right Zero Correlation As values on one variable go up, values for the other variable go…anywhere Pairs of observation tend to occupy seemingly random relative position Scatter plot shows no apparent slope Correlation The more closer the dots approximate a straight line, the stronger the relationship is Perfect correlation= + or – 1.00 o One variable perfectly predicts the other o No variability in the scatter plot o The dots approximate a straight line Correlation Matrices Correlation Matrix o Table showing correlations for all possible pairs of variables
Finding a statistically significant correlation The result is “statistically significant” if: o The observed correlation is larger than the critical correlation We want our r to be big if we want it to be significantly different from zero. This can be negative or positive. They are both equally far from 0 o The p value is less than 0.05 (which is our alpha)

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