statistical tests for independent groups
Post on 26-May-2015
220 Views
Preview:
TRANSCRIPT
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
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
Va
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
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
co
mp
uta
tio
n
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
top related