STUDY QUESTIONS FINAL EXAM COMM 301 1 How does the conceptual interpretation of r 2 change when we come from relationship to explanation prediction Why is this THE most important statistical concept for the social sciences R2 can only range from 0 to 1 and can be interpreted as the variance that X and Y share You can see magnitude and now of shared variance so now you have knowledge We start to think about the shared variance as knowledge or the variance that we can explain We know information about Y because the information about X is available The parts we can t explain is ignorance Seeking if they re related index of standardized covariation r Seeking to explain them r 2 shared variance Shared variance is explained variance Observed changes in one variable are accompanied by concomitant change in the other 2 What is Y hat What is its relationship to Y What would its relationship be if r 1 00 In words what is the principle of least squares error How does this relate to the graphical depiction of the model through the scatterplot of data points How does this relate to SS error Y hat the predicted value for Y gives us the line of best fit sample regression line Relation to Y Y is the criterion variable and Y hat symbolizes all of these predicted values The goal of the model is to make the difference between the ith Y score and its corresponding predicted value Y hat i as small as possible to minimize error of prediction Yi is the linear model y hat i is the line of best fit r 1 00 the line of best fit will connect Y the relationship will be perfect and X Y hat are exactly the same Least Squares Error a k a Sum of Squares Error goal of the linear model is to produce Y predictions which minimize this quantity The model s inaccuracy or error of prediction the of Y s variance that cannot be explained by X goals to minimize error of prediction and maximize shared variance happen simultaneously Relates to the graphical depiction of the model through the scatterplot of data points The best fit in the least squares sense minimizes the sum of squared residuals the difference between an observed value and the fitted value provided by a model models inaccuracy or error of prediction Relation to SS Error SS Error is the actual quantity of the Y variation that is unexplained or unaccounted for It is the Error Sum of Squares calculated differently by taking the we can t explain and multiplying by SS Y the total variation of the criterion variable 3 What is the null hypothesis What is statistical significance How does statistical significance differ from relevance or meaningfulness What is a useful statistical index of meaningfulness Logical Concepts of Statistical Inference Null Hypothesis the prediction that the two variables of interest are totally unrelated in the population all statistical inference is based on a direct test of this prediction p 05 true less than 5 times out of 100 reject null hypothesis as false Statistical Significance maximum probability of committing an inferential error that a researcher is willing to accept usually small probability magnitude large enough to reject beyond a reasonable doubt the hypothesis of no relationship researcher is confident that relationship exists in the population labeling something as significant implies that it exists in the population Statistical Significance vs Relevance Meaningfulness Test of significance provides info concerning the probability of committing and error in rejecting the null hypothesis a test statistic declared significant tells and experimenter nothing regarding the magnitude of the relationship or the practical importance or usefulness of the results Sample Size larger sample size smaller the finding can be to still be considered statistically significant larger the relationship less reasons a researcher needs to come up with to say it s meaningful Statistical Index of Meaningfulness r 2 4 For a bivariate model what is the relationship between r 2 and SS model What is the relationship between SS model SS error and SS Y r 2 and SS model SS model r 2 SS Y both get same F ratio and t test both have same quantity and explanatory and predictor information but r 2 has better quality because it s in SS model SS error and SS Y SS for Y and Error are numerical equivalents of which the variance can be divided into explained and unexplained They can be added in this manner and are considered independent or non overlapping components of the Y variation not related in any way SS Error 1 r 2 SS Y SS Y Total SS Model SS Error 5 What is the relationship between SS model and SS error and r 2 and 1 r 2 Which is more heuristic Why r 2 and 1 r 2 multiplied by SS Y SS Model and SS Error r 2 and 1 r 2 is more heuristic because represented as a percentage SS Model and SS Error combine to equal SS Y which is equivalent to asserting that r 2 1 r 2 1 0 or 100 of the variance 6 What is the F ratio How do we estimate it from the data Make certain to understand the concept of the critical value F ratio Measure which tells us how many times larger the systematic variance is than the random variance critical value p is the of explanatory predictor variables in the model p is always one in bivariate linear model look at Appendix C and use N p 1 degrees freedom to find critical value that F ratio test statistic must surpass to be considered significant 7 What are the four origins of categorical data as defined in Chapter 12 Be certain to know which one is undesirable and why 1 Data are inherently normal gender religion political preference 2 Subjects refuse to provide continuous data forced to classify observations into broader categories ex personal income ranges or age ranges researcher not overjoyed in this case but has no other choice 3 Experimental studies most prevalent situation categorical variables are obtained in analysis of data from experiments 4 Poor empirical procedures negative consequences discarding information by placing variables into a few vague categories like heavy readers and light readers 8 Understand the concept of dummy coding Does it make any difference which codes are used Statistical procedures are applied to numbers not letters Researcher must label discrete classes of a categorical variable with numerical rather than alphabetic symbols This substitution is referred to as dummy coding Dummy refers to these numbers not really being numbers but surrogate symbols which possess numerical properties that make them able to be