Statistics I Final

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ANOVA analyzing the varianceCompares all the individual mean differences (from all treatment conditions) within a single test•hypothesis-testing procedure that is used to evaluate mean differences between two or more txs (or populations), and uses sample data as the basis for drawing general conclusions about populations•Goal of ANOVA is to determine whether the mean differences observed among the samples provide evidence to conclude that there are mean differences among the populations Between Treatments how much difference exists between treatment conditions Within Treatments measuring chance onlyDenominator of F-Ratio: Error Term (uncontrolled and unexplained-unsystematic variability; provides a measure of the variance due to chance) Notations k = number of treatment conditionsn = number of scores in each treatmentN = total number of scores in entire studyT = total for each treatment condition (EX)G = ET = sum of all the scores in the study F-Ratio MS BetweenMS Within Post Hoc Tests Additional hypothesis tests that are done after ANOVA to determine which mean differences are significant and which are not Problems with t-Tests and ANOVA We lose a lot of information since the groups are treated as qualitative categorical variables even when they are inherently quantitative and continuousDepressed vs. Not DepressedHigh SES vs. Low SESMore versatile and sensitive measureUsually looking at a group of people rather than comparing groups of people Correlation The relationship between variablesHigh blood pressure and ageRelation between times spent studying and GPALooking for a systematic relationship: how do variables more together Linear Relationships: 3 Types Positive/Direct: values increase or decrease together-Time spent studying and test performanceNegative/Inverse: as one variable increases, the other decreases (and vice versa)-Rain and Driving SpeedNo Relationship Explanation and Prediction Go hand in handIf two variables are systematically related, it is possible to use information about one of the variables to predict the otherIf you can explain why, then we are likely to predict future behavior How do we measure relationships? CovarianceCorrelation CoefficientVariance Covariance whether two variables vary or change together-Age and Memory-Heat and Ice Cream Consumption Correlation Coefficient Expresses the strength of the relationship between two variables (standardized covariance)-Pearsons r Positive Covariance As one variable deviates from the mean, the other variable deviates in the same direction Negative Covariance As one variable deviates from the mean, the other deviates from the mean in the opposite direction Covariance is not a ______________. It is a _____________ and needs to be _________ for it to be interpretable. Standardized MeasureMathematical AbstractionStandardized Correlation Coefficient: divide the ____________ by the ______. CovarianceStandard Deviation Regression Tells us whether we can predict performance on one variable from another Regression: Outcome = _____ + _____ Model + Error Independent Variable Predictor Variable Dependent Variable Criterion Variable Beta Coefficient The Slope and the Intercept of a Regression Analysis R2 Percentage of variance accounted for What is calculated in Regression? Slope and an Intercept Slope Formula n (sum of xy) - (sum x)(sum y) n (sum x2) - (sum x)2 Intercept Formula Sum y - b (sum x) n A main assumption of correlation is that the variables are bivarietly normally distributed (when two variables are linearly related)Do not want p-value to be below .05: means that the distributions differ significantly from normality Pearson Correlation Ranges from -1 to +1Effect Sizes: .1 = small.3 = medium.5 = large Partial Correlation Indicates the degree that two variables are linearly related with the exception that the effects of a confounding variable are controlled for (they are partialed out)Does a relationship exist between Music and Mood even after taking into consideration the influence of Commute time? Point-Biserial Correlation The relationship between a dichotomous variable (bad credit/good credit, happy/not happy) and a quantitative variable (age, years of education) Regression Formula y = bx + ab: slopea: constant Concern about ____ is reason for ANOVA Type I Error Logic of ANOVA Goal is to measure amount of variability and explain where it comes from Purpose of the analysis of Between Treatments Variance is to distinguish between: 1. differencees between treatments are simply due to chance2. diferences between treatments are significantly greater than can be explained by chance alone; that is, the differences have been caused by the treatment effects Two Explanations for the difference (variance) that exists between treatments: 1. Treatment Effect (differences caused by treatments)2. Chance 2 Sources of Chance 1. Individual Differences 2. Experimental Error The Entire Process of ANOVA Requires: 3 values for SS3 for df2 variances (between and within)F-Ratio Posttests ______ risk of Type I Error increase Assumptions for Independent Measures ANOVA 1. Observations within each sample must be independent2. Populations must be normal4. Homogeneity of Variance Mean Squared (MS) is also known as Variance Authorshelbymailho ID123781 Card SetStatistics I Final DescriptionStatistics I Updated2011-12-15T05:04:59Z Show Answers