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ANOVA
 analyzing the variance
 Compares all the individual mean differences (from all treatment conditions) within a single test
 •hypothesistesting 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 only
 Denominator of FRatio: Error Term (uncontrolled and unexplainedunsystematic variability; provides a measure of the variance due to chance)

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


Post Hoc Tests
Additional hypothesis tests that are done after ANOVA to determine which mean differences are significant and which are not

Problems with tTests 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

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

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

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

How do we measure relationships?
 Covariance
 Correlation Coefficient
 Variance

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 Measure
 Mathematical Abstraction
 Standardized

Correlation Coefficient: divide the ____________ by the ______.
 Covariance
 Standard 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

R^{2}
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 x^{2})  (sum x)^{2}


A main assumption of correlation is
 that the variables are bivarietly normally distributed (when two variables are linearly related)
 Do not want pvalue to be below .05: means that the distributions differ significantly from normality

Pearson Correlation
 Ranges from 1 to +1
 Effect 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?

PointBiserial 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 + a
 b: slope
 a: 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 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

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 SS
 3 for df
 2 variances (between and within)
 FRatio

Posttests ______ risk of Type I Error
increase

Assumptions for Independent Measures ANOVA
 1. Observations within each sample must be independent
 2. Populations must be normal
 4. Homogeneity of Variance

Mean Squared (MS) is also known as
Variance

