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UA / Economics / CS 211 / What are planned contrasts in anova?

# What are planned contrasts in anova? Description

##### Description: Final Study guide for Stats. PY 211 w/Kyle Kramer
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PY 211 Final Study Guide

## What are planned contrasts in anova?

-003 Kyle Kramer

Analysis of Variance (PPT 1):

Variability: measures the level of differences between scores/data.

ANOVA: Analysis of Variance (F-test)

-Determines whether there is a difference among 2 or more groups.

-compares the differences between the groups and differences  within each group.

Between Groups Variance: variability due to the grouping factor  (i.e. control vs. experimental)

-We want this number to be large

Within Groups Variance: variability between the individuals within  each group.

-error

-This number should be small (error!)

## How do you determine if a change is statistically significant?

F= Between Groups Variance / Within Groups Variance

Finding Between Groups Variance: We also discuss several other topics like What is an example of self­enhancement in the us?

-Find the mean of each set of data

-Find the total mean of all data

-subtract total mean by indivudal means (add each together)  -Divide the SS by the number of variables (points where the data came from i.e. people) -1.

-Multiply this number by the total number of variables

Or

1.Calculate the Variance using group means

2. Multiply each by the number of people in each group

Finding Within Groups Variance

-like pooled variance

-find the variance of each group

-average them

OR

## How do you control the effects of extraneous variables?

(SSwithin 1 + SSwithin 2 + SSwithin3) / dfwithin

ANOVA part 2 (2nd PPT)

There are two ways to calculate S^2 (variance)If you want to learn more check out How many west point graduates fought for the confederacy?

1. Calculate Variances Directly

2. Calculate Sum of Squares→ Then divide to get the variance

Planned Contrasts: An analysis planned ahead of time, that  compares two groups in an ANOVA.  We also discuss several other topics like Is tongue rolling homozygous or heterozygous?

-you take the between variance between the two groups you are  looking to compare.

(Between group: find the mean of each group, average them. -subtract the average of the two means, from the mean of each  group

-divide by the df (2 groups -1)

-multiple by the total # groups, 3

-Divide the Between Variance of the Two Groups by the Within Variance of all the groups. )

-Run the test to see if their is a difference between the groups. -There is a different cutoff value, because the df of Between Groups is  different.  Don't forget about the age old question of What differentiates an acute from a persistent viral infection?

-Performing a test more than once decreases the chance of at least  one random result of happening.

-We don’t want differences do to chance…. sooo we have the  Bonferroni Correction.

Bonferroni Correction: a procedure that adjusts the alpha when  multiple analyses are run.

-Divide alpha by the # of tests performed.

-i.e. 2 tests, divide alpha (.05) by 2 = .025

Post Hoc Tests: group comparisons tested AFTER the ANOVA.  -perform these to see how ALL the groups differ from each  other.

“are their any comparisons you want to know about after the  other analyses?” If you want to learn more check out Who is louis xiv's great-grandson?

ANOVA (factors, levels, & effect size)

Assumptions for Anova: Don't forget about the age old question of What is the meaning of nerve regeneration?

-Normal Distribution

-Independence of Observations

-Homogeneity of Variance

(These are all the same assumptions as an Independent T-test)

Factor: an independent variable

-i.e. type of car

Levels: variations of a given factor

-i.e. Chevy, Honda, Dodge

-there are at least 2 factors for each level

-levels = # of groups in a one way ANOVA

Power:

-in ANOVA….

-having more participants INCREASES power

-having more groups DECREASES power

Factors in ANOVA:

Between Subjects: each level is different

ex. gender

Within Subjects (each participant is in all the levels) -repeated measures

“Mixed” ANOVA

-an ANOVA with at least one Between Subjects factor AND at  least one WIthin subjects factor

Effect Size: tells us how significant the effect of a variable is. -variability explained by group/total variability

R^2= SS between/SS total

Independent variable explains the significance of variance

Analysis of Covariance (ANCOVA)

-ran when you think you know what part of the unexplained  variance is

-controls for at least one variable (takes affect of that variable out of  the analysis)

Covariates:

-A variable that relates to the dependent variable, and can  help explain some of its variability

-it is neither an independent or dependent variable.  M&M DAY PPT~~~~~~~~~~~~~~~~~

-no new info a review of what is discussed above

Two-Way ANOVA (factorial)

PPT~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Factorial ANOVA: an ANOVA with at least two factors (independent  variables)

ex: the effect of both greek status and gender on drinking -2x2x2= 3 way anova

Two reasons why one way ANOVA isn’t a good test to run for 2  independent variables:

1. experiment-wise alpha (multiple tests increase the chance of  seeing a difference that is actually random)

2. More detailed conclusions

Main Effect: source of variation associated with mean difference  across the levels of a single factor.

-what is received if you ran two separate tests

-effect of both independent variables on the dependent

Interaction: source of variation associated with the variance of group means across the combination of levels of two factors.  -this occurs when you have to say the effect of one variable  depends on that of another

-. i.e “the effect of intelligence on GPA, depends on study habits”

Graphing Interactions:

-Parallel Lines: no interaction (a significant interaction is not likely) -Touching or Crossing Lines: There is a good chance of a significant  interaction

Regression

PPT~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Correlation: Tells us by how much two variable vary together -correlation does not equal causation

-correlates make good predictors

Mean: guess that gives the least wrong answer

Regression= Prediction

-Best fit line, used to predict values of predictors

y=mx+b

y=predicted values, m=slope of the line , x=independent variable , b= where line crosses y axis

-We use Fraction of Explained variability (r^2) when using regression.

-More explained variance = less error

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