Statistics I Final

• 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

how much difference exists between treatment conditions

• measuring chance only
• Denominator of F-Ratio: Error Term (uncontrolled and unexplained-unsystematic variability; provides a measure of the variance due to chance)

• 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

• MS Between
• MS Within

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

• 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

• 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

• 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

• 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

• Covariance
• Correlation Coefficient
• Variance

• whether two variables vary or change together
• -Age and Memory
• -Heat and Ice Cream Consumption

• Expresses the strength of the relationship between two variables (standardized covariance)
• -Pearsons r

As one variable deviates from the mean, the other variable deviates in the same direction

As one variable deviates from the mean, the other deviates from the mean in the opposite direction

• Standardized Measure
• Mathematical Abstraction
• Standardized

• Covariance
• Standard Deviation

Tells us whether we can predict performance on one variable from another

Model + Error

Predictor Variable

Criterion Variable

The Slope and the Intercept of a Regression Analysis

Percentage of variance accounted for

Slope and an Intercept

• n (sum of xy) - (sum x)(sum y)
• n (sum x²) - (sum x)²

• Sum y - b (sum x)
• n

• 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

• Ranges from -1 to +1
• Effect Sizes:
• .1 = small
• .3 = medium
• .5 = large

• 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?

The relationship between a dichotomous variable (bad credit/good credit, happy/not happy) and a quantitative variable (age, years of education)

• y = bx + a
• b: slope
• a: constant

Type I Error

Goal is to measure amount of variability and explain where it comes from

• 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

• 1. Treatment Effect (differences caused by treatments)
• 2. Chance

• 1. Individual Differences
• 2. Experimental Error

• 3 values for SS
• 3 for df
• 2 variances (between and within)
• F-Ratio

increase

• 1. Observations within each sample must be independent
• 2. Populations must be normal
• 4. Homogeneity of Variance

Variance