Statistical Tests for Independent GroupsELESTA2

Chi-square homogeneity Test for dependence of two variables Data are frequencies by categories

(nominal) Reject H0 If 2 computed > 2 critical

value Reject H0 if p value is less than (.05)

Wilcoxon Mann-Whitney U Test Tests the significant difference of two

independent ranks Data are ordinal (rankings) Reject H0 If U computed < U critical value

Reject H0 if p value is less than (.05)

t – test for Two Independent Samples Tests the significance difference of two

independent groups\ If X1 >< X2

Data are interval or ratio Reject H0 If t computed > t critical value

Reject H0 if p value is less than (.05)

t – test hypothesis testing Case: Third year high school males and

females are tested in their mathematical Ability

Males Females26 3824 2618 2417 2418 3020 2218

t – test hypothesis testing Males – Mean = 20.14 SD=3.48 Females – Mean = 27.33 SD = 5.89

Mean of Males and females in Math Box & Whisker Plot: Var2

Mean ±SD ±1.96*SD Males Females

Var1

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r2

t – test hypothesis testing H0= There is no significant difference between males

and females in their math scores H1= There is a significant difference between males

and females in their math scores 2. =.05 df = N1 + N2 –2 df = 7 + 6 –2 df = 11 t critical value = 2.201

t – test hypothesis testing 3. Computation

t = X1 - X2

x12 + x2

2 1 + 1

N1 + N2 – 2 N1 N2

t = - 2.73

t – test hypothesis testing4. Decision and Interpretation

Since the t obtained which is – 2.73 is greater than the t-critical which is 2.201, the null hypothesis is rejected.

This means that there is a significant difference between males and females in their math scores.

Females (M=27.33) significantly scored higher in math as compared to the males (M=20.14)

t – test hypothesis testing4. Decision and Interpretation (another way using p

values)

Since the p value obtained which is 0.0195 is less than the alpha level which is .05, the null hypothesis is rejected.

This means that there is a significant difference between males and females in their math scores.

Females (M=27.33) significantly scored higher in math as compared to the males (M=20.14)

Testing for Independent Groups t – test for two independent samples is only limited

with 2 samples. What if your data have three independent groups?

What statistical test will be used? Use Analysis of Variance (ANOVA)for testing the

difference of more than three groups

Sample Case for ANOVA In an experiment done by dela Cruz, Cagandahan and

Arciaga (2004), the effect of nonbehavioral intervention techniques was investigated on the computational abilities of fourth year high school students. The non-behavioral intervention techniques has three levels, bibliotherapy, small group interaction and games. These techniques were used as a teaching strategy in a lesson in a math class for three sections. Each of the strategy was used for each section. One section did not receive any strategy which served as the control group. After undergoing the strategy, the students were tested where they answered a series of computation items.

Sample Case for ANOVABibliotherapy Small group

interactionGames Control Group

X1 X2 X3 X4

X1 X2 X3 X4

X1 X2 X3 X4

X1 X2 X3 X4

ANOVA Hypothesis Testing1. H0: The non-behavioral intervention techniques have no

significant effect on computational ability

H0: There are no significant differences among the groups receiving bibliotherapy, small group interaction, games and control in their computational ability.

2. =.05 df between = groups – 1 = (4-1=3) df within = (N – 1) – df between ((209-1)-3)=205 df total = df between + df within (3 + 205) F ratio critical value = 2.65

ANOVA Hypothesis Testing3. Computation

F ratio computed = 4.62

4. Decision and Interpretation

Since the F ratio obtained which is 4.62 is greater than the F ratio critical which is 2.65, the null hypothesis is rejected. The non-behavioral intervention techniques have a significant effect on computational ability.

ANOVA Hypothesis TestingIntervention techniques; LS Means

Current effect: F(3, 205)=4.6819, p=.00347Effective hypothesis decomposition

Vertical bars denote 0.95 confidence intervals

controlGames

BibliotherapySmall group interaction

Intervention techniques

3.5

4.0

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5.0

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6.0

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The group who received the small group interaction significantly scored the highest among other intervention techniques.

Factorial ANOVA 1 IV – One way ANOVA 2 IV – Two way ANOVA 3 IV – Three way ANOVA Able to test the:

Main effects Interaction Effects

Factorial ANOVA  

Independent Variable B

  A1 A2 A3   

B1 A1 B1 A2 B1 A3 B1 B1 Mean  

Main Effect for BB2 A1 B2 A2 B2 A3 B2 B2 Mean

  A1 Mean A2 Mean A3 mean  

 

  Main Effect for A  

Main effect of A

Main Effect of B

Interaction effect of A and B (A X B)

Talent

Achievement

Effect of Achievement and Type of school on Talent

Low Achievers

High Achievers

Type of school

Public school

Private School

Ho: Achievement does not have a significant main effect on

talent (there is no significant difference between high and low

achievers on talent) Type of school does not have a significant main effect

on talent (there is no significant difference between public and

private school students in their talent) There is no significant interaction effect between

achievement and type of school (there are no significant differences among high

achievers in public, high achievers in private, low achievers in public, and low achievers in private in their talent

Effect of Achievement and Type of school on Talent

H1: Achievement have a significant main effect on talent (there is a significant difference between high and low

achievers on talent) Type of school have a significant main effect on talent (there is a significant difference between public and

private school students in their talent) There is a significant interaction effect between

achievement and type of school (there are significant differences among high

achievers in public, high achievers in private, low achievers in public, and low achievers in private in their talent

Effect of Achievement and Type of school on Talent

Effect of Achievement and Type of school

on Learning Approach

Achievement Type of School

Low

achievers

High

achievers

Public private

Deep approach Surface approach

Learning Approach

Effect of Achievement and Type of school on Learning Approach

H0: Achievement does not have a significant main effect on

Learning approach as a whole Type of school does not have a significant main effect

on learning approach as a whole Achievement and type of school have no significant

interaction effect on learning approach as a whole Univariate Analysis Achievement does not have a significant main effect on

deep approach Type of school does not have a significant main effect

on deep approach Achievement and type of school have no significant

interaction effect on deep approach

Achievement does not have a significant main effect on surface approach

Type of school does not have a significant main effect on surface approach

Achievement and type of school have no significant interaction effect on surface approach

Alternative Hypothesis

Achievement have a significant main effect on Learning approach as a whole

Type of school have a significant main effect on learning approach as a whole

Achievement and type of school have a significant interaction effect on learning approach as a whole

Univariate Analysis Achievement have a significant main effect on deep

approach Type of school have a significant main effect on deep

approach Achievement and type of school have a significant

interaction effect on deep approach

Achievement have a significant main effect on surface approach

Type of school have a significant main effect on surface approach

Achievement and type of school have a significant interaction effect on surface approach

Talent, Context and Effort as Predictors of Deep approach

Talent

Context

Effort

Deep approach

Talent, Context and Effort as Predictors of Deep approach

H0: Talent, context, and effort does not significantly

predict deep approach H1 Talent, context, and effort significantly predicts deep

approach