Pred 354 teach probility statis for primary math
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PRED 354 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH. Lesson 13 Two-factor Analysis of Variance (Independent Measures). Two-factor ANOVA. ANOVA is a hypothesis-testing procedure that is used to evaluate mean differences between two or more treatments (or populations).

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PRED 354 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH

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Pred 354 teach probility statis for primary math

PRED 354 TEACH. PROBILITY & STATIS. FOR PRIMARY MATH

Lesson 13

Two-factor Analysis of Variance (Independent Measures)


Two factor anova

Two-factor ANOVA

ANOVA is a hypothesis-testing procedure that is used to evaluate mean differences between two or more treatments (or populations)

A research study with two independent variables: The effects of two different teaching methods and three different class size are evaluated. DV: math achievement test score


Two factor anova1

Two-factor ANOVA

levels

levels

A two-by-three factorial design

2X3= 6 different treatments


Two factor anova2

Two-factor ANOVA

Two factor ANOVA will allow researcher to test for mean differences in the experiment:

  • Mean difference between teaching methods.

  • Mean differences between the three class sizes.

  • Any other mean differences that may result for unique combinations of a specific teaching method and a specific class size.


Two factor anova3

Two-factor ANOVA

Main effect:

The mean differences among the levels of one factor are referred to as main effect of that factor.

Main effect for class size (factor B)

Main effect for methods (factor A)


Two factor anova4

Two-factor ANOVA


Two factor anova5

Two-factor ANOVA

Interaction effect:

There is an interaction between factors if the effect of one factor depends on the levels of the second factor. The interaction is identified as the AXB interaction.


Two factor anova6

Two-factor ANOVA


Two factor anova7

Two-factor ANOVA

There is no interaction between factors A and B. The effect of factor A does not depend on the levels of factor B (and B does not depend on A)


Two factor anova8

Two-factor ANOVA

It is composed of three distinct hypothesis tests:

  • The main effect of factor A (The A-effect)

  • The main effect of factor B (The B-effect)

  • The interaction (AXB interaction)


Two factor anova9

Two-factor ANOVA


Two factor anova10

Two-factor ANOVA

  • Treatment effect (factor A, factor B and AXB)

  • Individual differences (there are different subjects for each trwatment condition)

  • Experimental error


Two factor anova11

Two-factor ANOVA


Two factor anova12

Two-factor ANOVA


Distribution of f ratios

Distribution of F-ratios

Table B.4 The F-Distribution


Pred 354 teach probility statis for primary math

Example (Do these data indicate that the size of the class and /or programs has a significant effect on test performance?)


Assumptions

Assumptions

1. The observations within each sample must be independent.

2. The populations from which the samples are selected must be normal.

3. The populations from which the samples are selected must have equal variances.


Example

Example

In 1968, Schachter published an article in Science reporting a series of experience on obesity and eating behavior. One of these studies examined the hypothesis. One of these studies examined the hypothesis that these individuals do not respond to internal , biological signals of hunger. In simple terms, this hypothesis says that obese individuals tend to eat whether or not their bodies are actually hungery.

In Shachter’s study, subjects were led to believe that they were taking part in a “taste test.” All subjects were told to come to the experiment wthout eating for several hours beforehand.


Example1

Example

  • The study used two indepedent variables or factors:

  • Weights (obese versus normal subjects)

  • Full stomach versus empty stomach

  • All subjects were then invited to taste and rate five different types crackers. The dependent variables was the number of crackers eaten by each subject.


Example2

Example


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