Statistics I Final

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Statistics I Final
2011-12-15 00:04:59

Statistics I
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  1. ANOVA
    • analyzing the variance
    • Compares 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
  2. Between Treatments
    how much difference exists between treatment conditions
  3. Within Treatments
    • measuring chance only
    • Denominator of F-Ratio: Error Term (uncontrolled and unexplained-unsystematic variability; provides a measure of the variance due to chance)
  4. Notations
    • k = number of treatment conditions
    • n = number of scores in each treatment
    • N = total number of scores in entire study
    • T = total for each treatment condition (EX)
    • G = ET = sum of all the scores in the study
  5. F-Ratio
    • MS Between
    • MS Within
  6. Post Hoc Tests
    Additional hypothesis tests that are done after ANOVA to determine which mean differences are significant and which are not
  7. 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 continuous
    • Depressed vs. Not Depressed
    • High SES vs. Low SES
    • More versatile and sensitive measure
    • Usually looking at a group of people rather than comparing groups of people
  8. Correlation
    • The relationship between variables
    • High blood pressure and age
    • Relation between times spent studying and GPA
    • Looking for a systematic relationship: how do variables more together
  9. Linear Relationships: 3 Types
    • Positive/Direct: values increase or decrease together
    • -Time spent studying and test performance
    • Negative/Inverse: as one variable increases, the other decreases (and vice versa)
    • -Rain and Driving Speed
    • No Relationship
  10. Explanation and Prediction
    • Go hand in hand
    • If two variables are systematically related, it is possible to use information about one of the variables to predict the other
    • If you can explain why, then we are likely to predict future behavior
  11. How do we measure relationships?
    • Covariance
    • Correlation Coefficient
    • Variance
  12. Covariance
    • whether two variables vary or change together
    • -Age and Memory
    • -Heat and Ice Cream Consumption
  13. Correlation Coefficient
    • Expresses the strength of the relationship between two variables (standardized covariance)
    • -Pearsons r
  14. Positive Covariance
    As one variable deviates from the mean, the other variable deviates in the same direction
  15. Negative Covariance
    As one variable deviates from the mean, the other deviates from the mean in the opposite direction
  16. Covariance is not a ______________. It is a _____________ and needs to be _________ for it to be interpretable.
    • Standardized Measure
    • Mathematical Abstraction
    • Standardized
  17. Correlation Coefficient: divide the ____________ by the ______.
    • Covariance
    • Standard Deviation
  18. Regression
    Tells us whether we can predict performance on one variable from another
  19. Regression: Outcome = _____ + _____
    Model + Error
  20. Independent Variable
    Predictor Variable
  21. Dependent Variable
    Criterion Variable
  22. Beta Coefficient
    The Slope and the Intercept of a Regression Analysis
  23. R2
    Percentage of variance accounted for
  24. What is calculated in Regression?
    Slope and an Intercept
  25. Slope Formula
    • n (sum of xy) - (sum x)(sum y)
    • n (sum x2) - (sum x)2
  26. Intercept Formula
    • Sum y - b (sum x)
    • n
  27. 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
  28. Pearson Correlation
    • Ranges from -1 to +1
    • Effect Sizes:
    • .1 = small
    • .3 = medium
    • .5 = large
  29. 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?
  30. Point-Biserial Correlation
    The relationship between a dichotomous variable (bad credit/good credit, happy/not happy) and a quantitative variable (age, years of education)
  31. Regression Formula
    • y = bx + a
    • b: slope
    • a: constant
  32. Concern about ____ is reason for ANOVA
    Type I Error
  33. Logic of ANOVA
    Goal is to measure amount of variability and explain where it comes from
  34. Purpose of the analysis of Between Treatments Variance is to distinguish between:
    • 1. differencees between treatments are simply due to chance
    • 2. diferences between treatments are significantly greater than can be explained by chance alone; that is, the differences have been caused by the treatment effects
  35. Two Explanations for the difference (variance) that exists between treatments:
    • 1. Treatment Effect (differences caused by treatments)
    • 2. Chance
  36. 2 Sources of Chance
    • 1. Individual Differences
    • 2. Experimental Error
  37. The Entire Process of ANOVA Requires:
    • 3 values for SS
    • 3 for df
    • 2 variances (between and within)
    • F-Ratio
  38. Posttests ______ risk of Type I Error
  39. Assumptions for Independent Measures ANOVA
    • 1. Observations within each sample must be independent
    • 2. Populations must be normal
    • 4. Homogeneity of Variance
  40. Mean Squared (MS) is also known as