Statistics for the Social Sciences Psychology 340 Spring 2005 Hypothesis testing with Correlation and Regression

Statistics for the Social Sciences Outline Hypothesis testing with: –Correlation (effect sizes too) See textbook Chapter 3 appendix (pgs ) –Regression analyses Bi-variate & Multiple regression

Statistics for the Social Sciences Hypothesis testing with Pearson’s r Recall our previous example Y X Appears linear Positive relationship Fairly strong relationship.89 is far from 0, near +1 Fairly strong, but stronger than you’d expect by chance? X Y

Statistics for the Social Sciences Hypothesis testing with Pearson’s r Hypothesis testing –Core logic of hypothesis testing Considers the probability that the result of a study could have come about if the experimental procedure had no effect If this probability is low, scenario of no effect is rejected and the theory behind the experimental procedure is supported Step 1: State your hypotheses Step 2: Set your decision criteria Step 3: Collect your data Step 4: Compute your test statistics Step 5: Make a decision about your null hypothesis –A five step program

Statistics for the Social Sciences –Step 1: State your hypotheses : as a research hypothesis and a null hypothesis about the populations Null hypothesis (H 0 ) Research hypothesis (H A ) Hypothesis testing with Pearson’s r There are no correlation between the variables (they are independent) Generally, the variables correlated (they are not independent)

Statistics for the Social Sciences Hypothesis testing with Pearson’s r r ≥  r <  H0:H0: HA:HA: – Our theory is that the variables are negatively correlated –Step 1: State your hypotheses One -tailed Note: sometimes the symbol  (rho) is used Note: sometimes the symbol  (rho) is used

Statistics for the Social Sciences Hypothesis testing with Pearson’s r r > r >  r <  H0:H0: HA:HA: – Our theory is that the variables are negatively correlated –Step 1: State your hypotheses One -tailed r =  r ≠  H0:H0: HA:HA: – Our theory is that the variables are not correlated Two -tailed

Statistics for the Social Sciences Hypothesis testing with Pearson’s r –Step 2: Set your decision criteria Your alpha (  ) level will be your guide for when to reject or fail to reject the null hypothesis. –Based on the probability of making making an certain type of error

Statistics for the Social Sciences Hypothesis testing with Pearson’s r –Step 3: Collect your data Descriptive statistics (Pearson’s r) Compute your degrees of freedom (df) r = 0.89 df = n - 2 = = X Y

Statistics for the Social Sciences Hypothesis testing with Pearson’s r –Step 4: Compute your test statistics r = 0.89 Descriptive statistics (Pearson’s r) Inferential statistics: 2 choices (really the same): –A t-test & the t-tablet-table –Use the Pearson’s r table (if available)Pearson’s r table

Statistics for the Social Sciences Hypothesis testing with Pearson’s r –Step 4: Compute your test statistics Descriptive statistics (Pearson’s r) Inferential statistics: 2 choices (really the same): –A t-test & the t-tablet-table –Use the Pearson’s r table (if available)Pearson’s r table From table, with df = n - 2 = 3: t crit = 3.18 Reject H 0 Conclude that the correlation is ≠0 –Step 5: Make a decision about your null hypothesis r = 0.89

Statistics for the Social Sciences Hypothesis testing with Pearson’s r –Step 4: Compute your test statistics From table –  -level = 0.05 –Two-tailed –df = n - 2 = 3 – r crit = Reject H 0 Conclude that the correlation is ≠0 –Step 5: Make a decision about your null hypothesis Descriptive statistics (Pearson’s r) Inferential statistics: 2 choices (really the same): –A t-test & the t-tablet-table –Use the Pearson’s r table (if available)Pearson’s r table r = 0.89

Statistics for the Social Sciences Effect sizes with Pearson’s r Smallr = 0.10 Mediumr = 0.30 Larger = 0.50

Statistics for the Social Sciences Hypothesis testing with Regression A brief review of regression Y = (X)(slope) + (intercept) Y X Hypothesis testing on each of these Hypothesis testing on each of these

Statistics for the Social Sciences Hypothesis testing with Regression H 0 : Slope = 0 H 0 : Intercept (constant) =0 Both: –Standardized coefficients –Unstandardized coefficients These t-tests test hypotheses

Statistics for the Social Sciences Hypothesis testing with Regression Multiple Regression –Typically researchers are interested in predicting with more than one explanatory variable –In multiple regression, an additional predictor variable (or set of variables) is used to predict the residuals left over from the first predictor. “residual” “fit”

Statistics for the Social Sciences Hypothesis testing with Regression First Explanatory Variable Second Explanatory Variable Fourth Explanatory Variable Third Explanatory Variable Multiple Regression –We can test hypotheses about each of these explanatory hypotheses within a regression model So it’ll tell us whether that variable is explaining a “significant”amount of the variance in the response variable

Statistics for the Social Sciences Multiple Regression in SPSS Null Hypotheses H 0 : Coefficient for var1 = 0 p < 0.05, so reject H 0, var1 is a significant predictor H 0 : Coefficient for var2 = 0 p > 0.05, so fail to reject H 0, var2 is a not a significant predictor

Statistics for the Social Sciences Hypothesis testing with Regression Multiple Regression –We can test hypotheses about each of these explanatory hypotheses within a regression model So it’ll tell us whether that variable is explaining a “significant”amount of the variance in the response variable –We can also use hypothesis testing to examine if the change in r 2 is statistically significant

Statistics for the Social Sciences Hypothesis testing with Regression Method 2 cont: –Enter: Second Predictor variable into the Independent Variable field Click Statistics

Statistics for the Social Sciences Hypothesis testing with Regression –Click the ‘R squared change’ box

Statistics for the Social Sciences Hypothesis testing with Regression The variables in the first model (math SAT) r 2 for the first model Coefficients for var1 (var name) Shows the results of two models The variables in the second model (math and verbal SAT) Model 1

Statistics for the Social Sciences Hypothesis testing with Regression The variables in the first model (math SAT) Coefficients for var1 (var name) Coefficients for var2 (var name) Shows the results of two models r 2 for the second model The variables in the second model (math and verbal SAT) Model 2

Statistics for the Social Sciences Hypothesis testing with Regression The variables in the first model (math SAT) Shows the results of two models The variables in the second model (math and verbal SAT) Change statistics: is the change in r 2 from Model 1 to Model 2 statistically significant? The change in r 2 is not statistically significant (p = 0.46) The change in r 2 is not statistically significant (p = 0.46)

Statistics for the Social Sciences Next week Review for the exam (Oct. 31) –I’ll put together two review labs

Statistics for the Social Sciences Relating Critical t’s and r’s Inferential statistics: 2 choices (really the same): –A t-test & the t-tablet-table –Use the Pearson’s r table (if available)Pearson’s r table