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by: Al Backey

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6

# Chap. 7-13 Notes 672

Al Backey
CMU
Statistics
Dr. Ray Allen

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COURSE
Statistics
PROF.
Dr. Ray Allen
TYPE
Class Notes
PAGES
6
WORDS
KARMA
25 ?

## Popular in Professional Education Services

This 6 page Class Notes was uploaded by Al Backey on Monday October 19, 2015. The Class Notes belongs to 672 at Central Michigan University taught by Dr. Ray Allen in Fall 2015. Since its upload, it has received 27 views. For similar materials see Statistics in Professional Education Services at Central Michigan University.

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Date Created: 10/19/15
Factorial ANOVA Module 7 Review Comparative Statistics Three uses of Statistics Describe Compare Measure relationships When comparing two groups When comparing more than two groups Comparative Statistics Illustrated Review Critical Designations Samples Independent Related Variables Independent Number Dependent Number Three Kinds of Comparative Tests Two Groups t tests 1 One sample 2 Independent samples 3 Dependent sample gtTw0 Groups ANOVA 1 One way 2 Factorial 3 Repeated measures Review OneWay ANOVA One Independent Variable one way Multiple groups Divided into categories One Dependent Variable Normally distributed Interval data ANOVA Key Terminology Factor Independent or manipulated variable Usually a category or grouping designation Example education level or treatment type Level of the factor Variations in the factor Example HS degree BS degree graduate degree or treatment A vs treatment B vs treatment C Singlefactor design Study involves one factor Factorial design Study involves more than one factor OneWay ANOVA Compares the means of two or more groups of participants on a single FACTOR independent variable m categorical explanatory variable IVs m quantitative response variable DV H0 111 112 11k versus Ha at least one of the 113s differ Practice Exercise 1 and 2 Factorial ANOVA Used with two or more treatment independent variables Each Independent Variable has more than one level Value Assess effects of each independent variable Assess the interaction of each variable How does two variables together work vs each alone Factorial ANOVA 2x2 ANOVA Two independent variables Each has two levels or distinct values Example Teacher effectiveness Experience lt44 Degree minormajor 2x3 ANOVA Two independent variables One variable has two levels other has three 3X3X2 ANOVA TwoFactor ANOVA Used to study two factors simultaneously Uses separate samples for each treatment condition E g effect of heat and humidity on exercise performance Compare mean differences in heat levels Compare mean differences in humidity levels Search for an interaction between combinations specific heat and humidity levels Main Effects amp Interactions Main effect is the comparison of various levels of the same factor e g temperature level F ratios will be calculated for each of the possible main effects Interaction effects are differences that result from a combination of the factors A separate F ratio is calculated for the interaction as well Interactions will be present if The two factors are interdependent change in one depends on change in the other Data of the different factors converge graphically Main effects and interactions are independent of one another Calculation of Fratios Step 1 State the hypothesis Main Effects Interaction Step 2 Locate critical region Set alpha level Step 3 Perform the analysis Step 4 Make the hypothesis decision Main effects Interaction Demonstration Statistics teacher giving an essay final randomly divides the classes in half half the class writes with a blue book and half with computers The students are also designated by typing ability no typing ability some typing ability and highly skilled The dependent measure will be the score on the essay part of the final exam Considerations Dependent Variable Independent variables Levels groups Within variables 2X3 ANOVA Null Hypotheses Descriptive Statistics Table of Means Main Effects Main Effects Differences of one IV across the other IV Method 3033 and 3056 Statistically significant 0 Ability 0 2733 3338 3017 Statistically significant Simple Main Effects The effect of one factor at any given level of the second factor Ability s affect With bluebook 2667 31 3333 Method s effects at any ability 3333 27 Interaction Effects The change in the main effect of one variable over levels of the other unaccounted for by the two variables alone ANOVA PRINTOUT Dependert re39ieele i Te eef etueenSuhjeeteEffede Type III Neneerrt Deeerrr 5Lrn ef Meen Perernet eel Seuree Squares elf SE1 Llere F 5ig er F39errtera Cerreetezl 141 ejel 2334443 5 425 344 53 12232 231 Intercept 1553355 1 1553355 12E53 533 12II5343 1333 AEIIIJT r 122444 2 53222 4535 533 3213 554 141 ETHDD 222 1 222 315 331 315 352 AEIIIJTH WHEI39HDD 113223 2 553 4334 34 3353 533 Errer 155533 12 13333 Tetel 1233353 13 Cerreetezl Tetel 434444 1 El Cemented Lle39ng Emma 35 lit H Eiquereel 533 AdjueteUH Squared 4131 FACTORIAL ANOVA USING PASWSPSS ANALYZE GENERAL LINEAR MODEL Independent Variables entered into FIXED FACTORS OPTIONS DESCRIPTIVES Practice Analysis Exercises 3 through TASK EXERCISE 7

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