KIN 4310 1nd Edition Lecture 19 Outline of Last Lecture I Two way ANOVA II Factors III Main Effects IV Interaction Effects V Example VI Interaction Effect of Factors VII F Statistic VIII ANOVA IX ANOVA SPSS Output X Example Two way ANOVA Outline of Current Lecture I Workshop II Testing the Significance of Correlations III Correlation Studies IV Correlation Studies Steps V Hand Study VI Review These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute Current Lecture I Workshop a Short term memory function versus temporal perception Are they related b H1 STM and TP are correlated c HO There is no correlation between STM and TP d Should we reject Ho Why or why not i We should not reject HO because r 0 01305 so it is not in the rejection zone because 1 n 40 2 df 38 3 critical values are 0 3044 and 0 3044 II Testing the Significance of Correlations a b Note If you have a population and there is no correlation then the null hypothesis is true c In this case they were unlucky with the sample they got which gave them a strong negative correlation which is also a type 1 error III Correlation Studies a We know how to calculate the linear correlation coefficient r b Testing the significance of a correlation i Determine critical values of r 1 Table B4 in book ii Calculate p values of r 1 Excel wont do this Need better stats software c Research Hypothesis i H1 r 0 ii H1 r 0 iii H1 does not equal 0 IV V d Null Hypothesis i H0 p 0 p is the greek letter row e Critical Value i Table B4 on page 379 f Degrees of Freedom i df total number of data pairs 2 ii n 2 g Note If the r is significant it is reasonable to assume it came from a population that was significant The r distribution has the values from 1 to 1 and you are more likely to get an r that equals around 0 if the null is true and the population is uncorrelated Correlation Studies Steps a Step 1 Calculate test statistic r b Step 2 Look up critical value of r c Step 3 Compare your r to rcrit d Step 4 Reject the null hypothesis Hand Study a b r 0 57 c df n 2 d 48 2 46 e Using a two tailed test with alpha 0 05 find rcrit i Rcrit 0 2875 0 2875 f Note There was a moderate correlation We re in the rejection zone So these sample data say it is unlikely to happen by random chance So there is a correlation in the population too VI Review a Which statement is true about the F distribution i It is negatively skewed No it is positively skewed ii 0 less than or equal to F less than or equal to 1 No F has positive values iii It can be approximated by the normal curve No this refers to t iv It is used in analysis of variance v The standard deviation is always 1 False b The variation BETWEEN groups represents i How much the individual data vary with respect to their group means No this is the variation within groups ii How much the group means vary with one another iii How much the individual data vary with respect to the mean value of all data iv The denominator of the F statistic No it s the numerator c In an experimental study 30 soldiers are randomly assigned to 4 groups Each group receives a different style of training The researchers want to know if the training style has an effect on the soldiers physical fitness test scores What is the critical value for F let alpha 0 05 i 2 69 No because F is positively skewed ii 0 No because F is positively skewed iii 2 98 iv There is not enough information No there is because we need df for the denominator df for the numerator and the type 1 error rate which is alpha we have all those for table B3 d There is no correlation between aerobic fitness and grip strength What is the probability of measuring r 0 7293 within a group of 6 randomly selected people Here the null is true which means there is no correlation i 0 ii 2 5 Would be the answer if it was a two tailed test iii 5 iv 10 v 95 vi Note n 6 df 4