QTIA Report 2012 IQRA UNIVERSITY

IQRA UNIVERSITY (IU)

Quantitative Techniques In Analysis

Report of about

Tests of Regression Analysis and Differences Between Groups

Submitted To: Syed Hammad Ali

Submitted By: Syed Asfar Ali Kazmi (14807)

Date of Submitted: 13-05-2012

http://en.wikipedia.org/wiki/Regression_analysis


CONTENTS:

Other Test

1. Test of Normality ………………………… 3 - 5

2. Test of linearity ………………………… 6 – 7

Tests of Regression Analysis

3. Linear Regression ………………………… 8 - 11

4. Multiple Regression ………………………… 12 – 15

Differences Between Groups

5. One Sample T Test ………………………… 16 – 18

6. Independent Sample T Test ………………. 18 – 21

7. Paired Sample T Test ………………………… 22 – 23

8. One-Way ANOVA ………………………… 23 – 25

9. Two-Way ANOVA …………………………. 25 – 27

10. SPANOVA ………………………… 27 – 29

11. MANOVA …………………………. 30 - 40

OTHER TESTS


Test of Normality:

Normality tests are used to determine whether a data set is well-modeled by a normal distribution or not, or to compute how likely an underlying random variable is to be normally distributed.

Question:Is the variable ‘’ AGE OF RESPONDENT ’’ of GSS2000R.sav is normally distributed or not?

Hypothesis:

HO: The null hypothesis states that the data is normally distributedHA: The alternative hypothesis states that the data is not normally distributed

Interpretation:Case Processing Summary

Cases

Valid Missing Total

N Percent N Percent N Percent

AGE OF RESPONDENT 270 100.0% 0 .0% 270 100.0%

This Table show us that sample size caese N=270, there is no missing cases and the data

is 100% valid.

Tests of Normality

Kolmogorov-Smirnova Shapiro-Wilk

Statistic df Sig. Statistic df Sig.

AGE OF RESPONDENT .083 270 .000 .957 270 .000

a. Lilliefors Significance Correction

Decision:

http://en.wikipedia.org/wiki/Random_variable

http://en.wikipedia.org/wiki/Normal_distribution

http://en.wikipedia.org/wiki/Data_set

The test statistics are shown in the third table. Here two tests for normality are run. In our case, since we have N= 270 elements sample size,for AGE OF RESPONDENT data set which is greather than 51 elements, we use the Kolmogorov-Smirnov test .From A, the p-value is 0.000 is less than 0.05.

So we can reject the null hypothesis and conclude the sample is not normally distributed.

The histogram plot indicates the shape of the distributed data have a “ bell” shape These data are clearly Not normally distributed.

From this graph we can conclude that the data appears is not to be normally distributed as it follows the diagonal line closely and does appear to have a non-linear pattern.

Test of Linearity:

Linearity means that the amount of change, or rate of change, between scores on two variables are constant for the entire range of scores for the variables.when one variable( X ) increases and the other variable(Y) is also be increased in the same way.we check through linearity test that there relationships are linear not linear.

Question:

hypothesis test of the correlation coefficient, the relationship between "total hours spent on the chat" and "total hours spent on the Internet" is not linear. However, the square transformation of the independent variable "total hours per spent on the Internet" does result in a relationship that is linear.

Interpretation:

The value of R2 Linear (0.656) suggests that the relationship between “total time spent on the internet” and “the total hours spent on chat” is strong. R= 0.8099

Tests for Regression Analysis

Regression analysis is used to measure the re la t ionship be tweent w o o r m o r e variables. One variable is called dependent (response, or outcome) variable and the other is called Independent (explanatory or predictor) variables.It is used to check that due to one unit change in the independent variable(s) how much change occurs in dependent variable.

Or

The use of regression to make quantitative predictions of one variable from the values of another variable is called regression analysis. There are following several types of regression, which may be used by the researcher.

Linear regression Multiple linear regression Quadratic / Curvilinear regression Logistic / Binary logistic regression Multivariate logistic regression

Linear Regression:

When one dependent variable depends on single independent variable then their dependency called linear regression it is a measure of how strongly the independent variable predicts the dependent variable and its model is given by

y = a + bx

Assumptions:

Variables are measured at the interval or ratio level (continuous). Variables are approximately normally distributed There is a linear relationship between the two variables.

Question:

Can we predict math achievement from grades in high school?


Variables:

D.V= Math achievement

I.V = grades in high school

Hypothesis:

H0: there is the relationship b/w V1 and V2HA: there is no relationship b/w V1 and V2

Interpretation:

Variables Entered/Removedb

Model Variables

Entered

Variables

Removed Method

dim

ensi

on0

1 grades in h.s.a . Enter

a. All requested variables entered.

b. Dependent Variable: math achievement test

The above table tells us about the independent variable and the regression method used.

Here we see that the independent variable i.e. grads in high school is entered for the

analysis as we selected the Enter method.

Model Summary

Model

R R Square

Adjusted R

Square

Std. Error of the

Estimate

dime

nsio

1 .504a .254 .244 5.80018

a. Predictors: (Constant), grades in h.s.

This table gives us the R-value, which represents the correlation between the

observed values and predicted values of the dependent variable. R-Square is called

the coefficient of determination and it gives the adequacy of the model. Here the

value of R-Square is 0.504 that means the independent variable in the model can

predict 50% of the variance in dependent variable. Adjusted R-Square gives the

more accurate information about the model fitness if one can further adjust the

model by his own.

ANOVAb

Model Sum of Squares df Mean Square F Sig.

1 Regression 836.606 1 836.606 24.868 .000a

Residual 2455.875 73 33.642

Total 3292.481 74

a. Predictors: (Constant), grades in h.s.

b. Dependent Variable: math achievement test

The above table gives the test results for the analysis of one-way ANOVA. The results are given in three rows. The first row labeled Regression gives the variability in the model due to known reasons. The second row labeled Residual gives the variability due to random error or unknown reasons. F-value in this case is 24.868 and the p-value is given by 0.000 which is less that 0.05, so we reject our null hypothesis and conclude that there is no relationship between math achievement and grades in high school.

Coefficientsa

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig.B Std. Error Beta

1 (Constant) .397 2.530 .157 .876

grades in h.s. 2.142 .430 .504 4.987 .000

a. Dependent Variable: math achievement test

The above table gives the regression constant and coefficient and their significance. These regression coefficient and constant can be used to construct an ordinary least squares (OLS) equation and also to test the hypothesis of the independent variable. Using the regression coefficient and the constant term given under the column labeled B; one can construct the OLS equation for predicting the math achievement i.e.

Math achievement = .397 + (2.1242) (grades in h.s)

Multiple Regression (Hierarchical Method)

Multiple regression is the most commonly used technique to assess the relationship between one dependent variable and several independent variables. There are three major types of multiple regression i.e.

Simultaneous regression. Hierarchical or Sequential regression. Stepwise or statistical regression.

Assumptions:

1) Dependent variables should be scale.2) The relationship between the predictor variable and the dependent variable in linear.3) The error/residual4) Multicollinearity should not be exist5) Homogenity should be exist

Question :

How well can we predict current salary from a combination of three variables Beginning salary, Educational Level, and Month since hire?

Variables:

Dependent variable = Current Salary

Indendepent Variable = (1) Beginning salary

(2) Educational Level

(3) Month since hire

Interpretation:

Descriptive Statistics

Mean Std. Deviation N

Current Salary $34,419.57 $17,075.661 474

Beginning Salary $17,016.09 $7,870.638 474

Months since Hire 81.11 10.061 474

Educational Level (years) 13.49 2.885 474

Correlations

Current Salary

Beginning

Salary

Months since

Hire

Educational

Level (years)

Pearson Correlation Current Salary 1.000 .880 .084 .661

Beginning Salary .880 1.000 -.020 .633

Months since Hire .084 -.020 1.000 .047

Educational Level (years) .661 .633 .047 1.000

Sig. (1-tailed) Current Salary . .000 .034 .000

Beginning Salary .000 . .334 .000

Months since Hire .034 .334 . .152

Educational Level (years) .000 .000 .152 .

N Current Salary 474 474 474 474

Beginning Salary 474 474 474 474

Months since Hire 474 474 474 474

Educational Level (years) 474 474 474 474

Variables Entered/Removedb

Model Variables

Entered

Variables

Removed Method

dim

ensi

on0

1 Educational

Level (years),

Months since

Hire, Beginning

Salarya

. Enter

a. All requested variables entered.

b. Dependent Variable: Current Salary

Model Summary

Model

R R Square

Adjusted R

Square

Std. Error of the

Estimate

dim

ensi

on0

1 .895a .801 .800 $7,645.998

a. Predictors: (Constant), Educational Level (years), Months since Hire,

Beginning Salary

ANOVAb

Model Sum of Squares df Mean Square F Sig.

1 Regression 1.104E11 3 3.681E10 629.703 .000a

Residual 2.748E10 470 5.846E7

Total 1.379E11 473

a. Predictors: (Constant), Educational Level (years), Months since Hire, Beginning Salary

b. Dependent Variable: Current Salary

Coefficientsa

Model Unstandardized

Coefficients

Standardized

Coefficients

t Sig.

Collinearity

Statistics

B Std. Error Beta Tolerance VIF

1 (Constant) -19986.502 3236.616 -6.175 .000

Beginning Salary 1.689 .058 .779 29.209 .000 .597 1.676

Months since Hire 155.701 35.055 .092 4.442 .000 .994 1.006

Educational Level

(years)

966.107 157.924 .163 6.118 .000 .595 1.679

a. Dependent Variable: Current Salary

Collinearity Diagnosticsa

Model Dimension

Eigenvalue

Condition

Index

Variance Proportions

(Constant)

Beginning

Salary

Months since

Hire

Educational

Level (years)

dimension0

1

dimension1

1 3.847 1.000 .00 .01 .00 .00

2 .125 5.542 .01 .57 .02 .00

3 .020 13.734 .02 .42 .12 .92

4 .007 23.392 .97 .00 .86 .08

a. Dependent Variable: Current Salary

Result:Simultaneously multiple regression was conducted to investigate the best predictors of current salary. The means, standard deviation and inter correlations can be found in table. The combination of variables to predict current salary from Beginning salary,Educational Level ,& Month since hire was statistically significant, F =629.703., p<0.05 . The be ta coef f ic ien ts a re presented in las t t ab le . Note tha t a l l indenpent var iab les Beginning salary,Educational Level ,& Month since hire are significantly predicts on current salary when all three variables are included. The adjusted R2 value was 0.800. This indicatesthat 80 % of the variance in current salary is a large effect.

( Differences Between Groups )

T-TEST Statistics:

The t test is used to compare to groups to answer the differential research questions. Its values determines the difference by comparing means.

Hypothesis for T-test:

HO: there is no difference between variable 1 and variable 2 (Accept when the significant value is greater than 0.05)

H1:There is difference between variable 1 and variable 2 (Accept when the significant value is less than 0.05)

Types of T-testThere are three types of T-tests.

1) One sample t-test.2) Independent sample t-test.3) Paired sample t-test

1) ONE SAMPLE T-TEST:

One sample t-test is used to determine if there is difference between population mean(Test value) and the sample mean (X)

Assumptions and conditions of sample t-test:1.The dependent variable should be normally distributed within the population2.The data are independent.(scores of one participant are not depend on scores of the other:participant are independent of one another )

Question:

Is the average salary of employee in the ( employee data.sav ) is equal or more than $ 30000 ( per month ) in US?

The hypotheses are:

1)The null hypothesis states that the average salary of the employee is equal to “30000”

H0: 30000

2) The alternative hypothesis states that the average salary of the employee is not equal to “30000”

HA: 30000

Interpretation:0

One-Sample Statistics

N Mean Std. Deviation Std. Error Mean

Current Salary 474 $34,419.57 $17,075.661 $784.311

In above table “N” shows the total number of observation.(sample Size N=474 employees) The

average salary of total employees is “34,419.57”.

The standard deviation of the data is “17,075.661”and the standard error of the mean is

“784.311”.

One-Sample Test

Test Value = 30000

T df Sig. (2-tailed) Mean Difference

95% Confidence Interval of the

Difference

Lower Upper

Current Salary 5.635 473 .000 $4,419.568 $2,878.40 $5,960.73

Through above table we can observe that,

i. “T” value(5.635) is positive which show that our estimated mean value is less than actual value of mean.

ii. Degree of freedom is (N – 1) = 473.

iii. `````The “P-value” is “0.000” which is less than “0.05”.

iv. The difference between the estimated & actual mean is “4,419.568”.

v. Confidence interval has the lower & upper limit 2,878.40 & 5,960.73respectively. The confidence interval limits does not contains zero.

Decision:-On the basis of following observation I reject my “Null hypothesis” and accept the “Alternative hypothesis”. I am almost “100%” sure on my decision.

i. The “P-value” is “0.000” which is less than “0.05”.ii. The confidence interval limits does not contains zero.

Therefore the average salary of employees is not equal to “30000”.

2) INDEPENDENT SAMPLE T-TEST:

Independent sample T-test is used to compare two independent groups (Male and Female) with respect to there effect on same dependent variable.

Assumptions and conditions of Independent T-test:

1.Variance of the dependent variable for two categories of the independent variableshould be equal to each other.

2.Dependent variable should be scale

3.Data on dependent variable should be independent.

Question:

Are the mean differences average salaries of male & female employees differ significantly or equal to their current salary in US?

( employee data.sav)

The hypotheses are:

1) The null hypothesis states that the average salary of the male employee is equal to average salary of the female employee.

H0 :

2) The alternative hypothesis states that the average salary of the male employee is not equal to average salary of the female employee.

HA :

Interpretation:-

Group Statistics

Gender N Mean Std. Deviation Std. Error Mean

Current Salary Female 216 $26,031.92 $7,558.021 $514.258

Male 258 $41,441.78 $19,499.214 $1,213.968


i. Total number of male is “258” and the female is “216”.ii. The mean value of salaries of male employee is 41,441.78 & the female employee is

26,031.92.

iii. Standard deviation of salaries of male employee is 19,449.214 & the female employee is 7,558.021.

iv. Standard error of mean of salaries of male employees is 1,213.968 & the Standard error of mean of salaries of female employees is 514.258.

Independent Samples Test

Levene's Test

for Equality of

Variances t-test for Equality of Means

F Sig. t df

Sig.

(2-

tailed)

Mean

Difference

Std. Error

Difference

95% Confidence Interval

of the Difference

Lower Upper

Current

Salary

Equal

variance

s

assumed

119.669 .000 10.94

5

472 .000 $15,409.86

2

$1,407.90

6

$12,643.32

2

$18,176.40

1

Equal

variance

s not

assumed

11.68

8

344.26

2

.000 $15,409.86

2

$1,318.40

0

$12,816.72

8

$18,002.99

6

Interpretation:-

In above table we have two parts (a) f-test, (b) t-test, through which we can observe that,

i. “F” value is “119.669” with significant value of “0.00” which is less than “0.05”.ii. On the basis of P-value of F-test part we assume that the variance of the two populations

is not equal. iii. “T” value is positive which show that the mean value of salaries of male employees is

greater than the mean value of salaries of female employeesiv. Degree of freedom is “344.262”.v. The “P-value” is “0.000” which is less than “0.05”.

vi. The difference between the two population mean is “15,409.862”.vii. The standard error difference between the two population mean is “1,318.400”.

viii. Confidence interval has the lower & upper limit “12,816.728” & “18,002.996” respectively. The confidence interval limits does not contains zero.

Decision:-

On the basis of following observation I reject my “Null hypothesis” and accept the “Alternative hypothesis”. I am almost “100%” sure on my decision.

i. The “P-value” is “0.000” which is less than “0.05”.ii. The confidence interval limits does not contains zero.

The average salaries of male & female employees are not equal.

3) Paired t-test : A paired (samples) t-test is used when you have two related observations (i.e., two observations per subject) and you want to see if the means on these two normally distributed interval variables differ from one another.

Assumptions and conditions of Paired sample T-test :

1)The independent variable is dichotomous and its levels (or groups) are paired, or matched, in some way (husband-wife, pre-post etc)

2) The dependent variable is normally distributed in the two conditions

Question:

The mean difference of the two paired variables ( current and beginning salary) is significant or equal?

Interpretation:

Paired Samples Statistics

Mean N Std. Deviation Std. Error Mean

Pair 1 Current Salary $34,419.57 474 $17,075.661 $784.311

Beginning Salary $17,016.09 474 $7,870.638 $361.510


i. The mean value of current & beginning salary is “34,419.57” & “17,016.09” respectively.

ii. Total number of both groups is “474” individually.

iii. The standard deviation of current & beginning salary is “17,075.661” & “7,870.638” respectively

iv. The standard error mean of current & beginning salary is “784.331” & “361.510” respectively

Paired Samples Correlations

N Correlation Sig.

Pair 1 Current Salary & Beginning

Salary

474 .880 .000


i. The total number of pair is “474”.ii. “0.88” show that the both values of group are highly co-related, which indicate that the

employees who has greater begging salary has also greater current salary.

iii. The P-value is “0.00” which is less than “0.05”

Paired Samples Test

Paired Differences

t df

Sig. (2-

tailed)Mean

Std.

Deviation

Std. Error

Mean

95% Confidence Interval of

the Difference

Lower Upper

Pair

1

Current Salary -

Beginning

Salary

$17,403.481 $10,814.620 $496.732 $16,427.407 $18,379.555 35.036 473 .000

Interpretation:-

In above table we have two parts (a) f-test, (b) t-test, through which we can observe that,

i. The mean value of pair is “17,403.481”.ii. The standard deviation of pair is “10,814.620”.

iii. The standard error mean of pair is “496.732”.

iv. Confidence interval has the lower & upper limit “16,427.407” & “18,379.555” respectively. The confidence interval limits does not contains zero.

v. T- Value is “35.036”.

vi. Degree of freedom is (N-1) = “473”.

vii. P-vale is “0.00” which is less than “0.05”.

Decision:-

On the basis of following observation I reject my “Null hypothesis” and accept the “Alternative hypothesis”. I am almost “100%” sure on my decision.

iii. The “P-value” is “0.000” which is less than “0.05”.iv. The confidence interval limits does not contains zero.

The mean difference of the two paired variables i.e. current and beginning salary is

significant or not same.

One-way ANOVA:A one-way analysis of variance (ANOVA) is used when you have a categorical independent variable (with two or more categories) and a normally distributed interval dependent variable and you wish to test for differences in the means of the dependent variable broken down by the levels of the independent variable.

Assumptions:

Independent variable consists of two or more categorical independent groups.

Dependent variable is either interval or ratio (continuous).

Dependent variable is approximately normally distributed for each category of the independent variable.

Equality of variances between the independent groups (homogeneity of variances).

Observations are independent.

Question:

Are there difference among the ethnicity groups(Euro-American, African-American, Latino-American, Asian-American ) on competence scale?

Dependent variable : Competence scaleIndependent variable : Ethnicity groups

Interpretation:

Descriptives

competence scale

N Mean

Std.

Deviation Std. Error

95% Confidence Interval for

Mean

Minimum MaximumLower Bound Upper Bound

Euro-Amer 40 3.4000 .54243 .08577 3.2265 3.5735 1.75 4.00

African-

Amer

14 3.1786 .90101 .24080 2.6583 3.6988 1.00 4.00

Latino-Amer 10 2.8750 .72887 .23049 2.3536 3.3964 1.00 3.50

Asian-Amer 7 3.3214 .51467 .19453 2.8454 3.7974 2.50 4.00

Total 71 3.2746 .66300 .07868 3.1177 3.4316 1.00 4.00

The descriptives table provides us the descriptive statistics.

mean, standard deviation and 95% confidence intervals for the dependent variable

(competence scale ) for each separate groups of ethnicity ( Euro-American,

African-American, Latino-American, Asian-American ) as well as when all groups

are combined (Total ).

Test of Homogeneity of Variances

competence scale

Levene Statistic df1 df2 Sig.

1.323 3 67 .274

The assumption of equal variances (Homogeneity ) has been met,because the sig.

value =.274 is more than 0.05 .(we accept the Null hypothesis )

ANOVA

competence scale

Sum of Squares df Mean Square F Sig.

Between Groups 2.370 3 .790 1.864 .144

Within Groups 28.399 67 .424

Total 30.769 70

The above table gives the test results for the analysis of one-way ANOVA. The results are given in three rows. The first row labeled between groups gives the variability due to the different designations of the ethnicity groups (known reasons). The second row labeled within groups gives the variability due to random error (unknown reasons), and the third row gives the total variability. In this case, F-value is 1.864, and the corresponding p-value=0.144 is greather than 0.05. Therefore we accept the null hypothesis and conclude that the no difference among the ethnicity groups are not the same in all four categories

There is no difference between the ethnicity groups and the competence scale.

Two-way ANOVA:The two-way ANOVA compares the mean differences between groups that have been split on two independent variables (called factors). You need two independent, categorical variables and one continuous, dependent variable

Assumptions to use two-way ANOVA:

As with other parametric tests, we make the following assumptions when using two-way ANOVA:

Dependent variable is either interval or ratio (continuous).

Dependent variable is approximately normally distributed for each category of the independent variable.

The variances among populations must be equal (homogeneity).

Data are interval or nominal.

Interpretation:

Between-Subjects Factors

Value Label N

math grades 0 less A-B 43

1 most A-B 30

father's educ

revised

1.00 HS grad or

less

38

2.00 Some College 16

3.00 BS or More 19

This table is provide us the sample size N of our independent variables ( math grades and

Father’s educations revised groups ).


Dependent Variable:math achievement test

math grades father's educ revised Mean Std. Deviation N

dimension1

less A-B

dimension2

HS grad or less 9.8261 5.03708 23

Some College 12.8149 5.05553 9

BS or More 12.3636 7.18407 11

Total 11.1008 5.69068 43

most A-B

dimension2

HS grad or less 10.4889 6.56574 15

Some College 16.4284 3.43059 7

BS or More 21.8335 2.84518 8

Total 14.9000 7.00644 30

Total

dimension2

HS grad or less 10.0877 5.61297 38

Some College 14.3958 4.66544 16

BS or More 16.3509 7.40918 19

Total 12.6621 6.49659 73

This table is very useful as it provides the mean and standard deviation for the groups that have been split by both independent variables. In addition, the table also provides "Total" rows, which allows means and standard deviations for groups only split by one independent variable or none at all to be knownThere are six-cell means will be shown in the plot.

Levene's Test of Equality of Error Variancesa

Dependent Variable:math achievement test

F df1 df2 Sig.

2.548 5 67 .036

Tests the null hypothesis that the error variance

of the dependent variable is equal across groups.

a. Design: Intercept + mathgr + faedRevis +

mathgr * faedRevis

The Levene Statistic p-value = 0.36 is greater than α = 0.05 ,so we fail toreject the null hypothesis that the variances are all equal. Since the variances appear to be equal (and we have random/independent samples), the assumption of homogeneity has been met we may continue with ANOVA .

One-way repeated measures ANOVA:one-way repeated measures analysis of variance if you had onecategorical independent variable and a normally distributed interval dependentvariable that was repeated at least twice for each subject. This is the equivalent of the paired samples t-test, but allows for two or more levels of the categorical variable.This tests whether the mean of the dependent variable differs by the categoricalvariable.

SPANOVA / MIXED ANOVA: (split plot ANOVA)

Robust: if the assumptions are not met even though we run the test.

Anova = difference between the groups (boys & Girls) (couples, non couples)Spanova = difference with in the groups. (1st class to last class anxiety level of boys)(time intervals)

Question: which intervention develop maths skill or develop confidence building in more effective in reducing students fear of statistics test score across the three time period:(pre-intervention, post intervention and follow up(three month later)

Assumptions:

One variable between the group One variable within the group Continuous variable Homogeniety of variance co-variance (will find through box m test) More assumptions like the ANOVA Homogeniety of variance co-variance:

Changes between the two groups are the same in the three time intervals.(through genereal liner model)

Procedure:Analyze>general linera model> repeated measeuretype: Time, factor 3shift with in group Fear 1, fear 2, fear 3intervals add 03 and between subject: types of classOptions: Check Estimation, effect size, homogenietyplots: groups = separate line, time = horizontal

Interpretation:


Value Label N

type of

class

1 maths skills 15

2 confidence

building

15

Three dependent variables are there.


type of class

Mean

Std.

Deviation N

fear of stats

time1

maths skills 39.87 4.596 15

confidence

building

40.47 5.817 15

Total 40.17 5.160 30

fear of stats

time2


confidence

building

37.33 5.876 15

Total 37.50 5.151 30

fear of stats

time3


confidence

building

34.40 6.631 15

Total 35.23 6.015 30

Range is 20-60, 60 is the highst fear of mean we see here the aveerage of the means and which says that in Time1: they are very

much fear Time2: they are not very much fear Time3: they are very much fear

Box's Test of

Equality of

Covariance

Matricesa

Box's M 1.520

F .224

df1 6

df2 5680.302

Sig. .969

Tests the null

hypothesis that

the observed

covariance

matrices of the

dependent

variables are

equal across

groups.

a. Design:

Intercept + group

Within Subjects

Design: time

If it is > 0.05 Null hypotheses is equal, assumpition of co-variance is met

Multivariate Testsc

Effect

Value F

Hypothesi

s df

Error

df Sig.

Partial

Eta

Squared

Noncent.

Paramete

r

Observed

Powerb

time Pillai's

Trace

.663 26.59

3a

2.000 27.00

0

.00

0

.663 53.185 1.000

Wilks'

Lambda

.337 26.59

3a

2.000 27.00

0

.00

0

.663 53.185 1.000

Hotelling's

Trace

1.970 26.59

3a

2.000 27.00

0

.00

0

.663 53.185 1.000

Roy's

Largest

Root

1.970 26.59

3a

2.000 27.00

0

.00

0

.663 53.185 1.000

time *

group

Pillai's

Trace

.131 2.034a 2.000 27.00

0

.15

0

.131 4.067 .382

Wilks'

Lambda

.869 2.034a 2.000 27.00

0

.15

0

.131 4.067 .382

Hotelling's

Trace

.151 2.034a 2.000 27.00

0

.15

0

.131 4.067 .382

Roy's

Largest

Root

.151 2.034a 2.000 27.00

0

.15

0

.131 4.067 .382

a. Exact statistic

b. Computed using alpha = .05

c. Design: Intercept + group

Within Subjects Design: time

Time: Wilks Lambda: Significance is < than 0.05 and which means there are

differences in the fear scale of 03 dimension / time intervals.

Then we seee time * groups(time depends on groups): in here significane value is >

than 0.05 which means there is no differences. If the changes same over time for the

two different groups.

Partial Eta Squared(it is predicting dependent variable in time interval)(it tells us the

effect size of differences / relationship):we square root 0.663 = 0.81is is largely

effective and give the very large differences b/w the time interval for the dependent

variable FEAR. it will explain the 0.663 the time.

Mauchly's Test of Sphericityb

Measure:MEASURE_1

Within Subjects

Effect Mauchly's

W

Approx. Chi-

Square df Sig.

Epsilona

Greenhouse-

Geisser

Huynh-

Feldt

Lower-

bound

dimension1 time .348 28.517 2 .000 .605 .640 .500

Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent

variables is proportional to an identity matrix.

a. May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are

displayed in the Tests of Within-Subjects Effects table.

b. Design: Intercept + group


Are the variance of the student remain same during the interval 1st time student get the marks (like = 1st student is 10, 2nd is 20, 3rd is 30, 4th is 40, 5th is 50)

Are the variance of the student remain same during the interval 2st time student get the marks (like = 1st student is 20, 2nd is 30, 3rd is 40, 4th is 50, 5th is 60)

Are the variance of the student remain same during the interval 3rd time student get the marks (like = 1st student is 30, 2nd is 40, 3rd is 50, 4th is 60, 5th is 70)

Here above variance are the same than we met the assumption of spersity (if the intervals have same variance / range it is called spercity)

Tests of Within-Subjects Effects

Measure:MEASURE_1

Source Type III

Sum of

Square

s df

Mean

Square F Sig.

Partial

Eta

Square

d

Noncent.

Paramete

r

Observe

d Powera

time Sphericity

Assumed

365.86

7

2 182.93

3

43.28

6

.00

0

.607 86.571 1.000

Greenhouse

-Geisser

365.86

7

1.210 302.24

7

43.28

6

.00

0

.607 52.397 1.000

Huynh-Feldt 365.86

7

1.281 285.63

2

43.28

6

.00

0

.607 55.445 1.000

Lower-

bound

365.86

7

1.000 365.86

7

43.28

6

.00

0

.607 43.286 1.000

time *

group

Sphericity

Assumed

19.467 2 9.733 2.303 .10

9

.076 4.606 .449

Greenhouse

-Geisser

19.467 1.210 16.082 2.303 .13

4

.076 2.788 .342

Huynh-Feldt 19.467 1.281 15.198 2.303 .13

2

.076 2.950 .352

Lower-

bound

19.467 1.000 19.467 2.303 .14

0

.076 2.303 .311

Error(tim

e)

Sphericity

Assumed

236.66

7

56 4.226

Greenhouse

-Geisser

236.66

7

33.89

4

6.983

Huynh-Feldt 236.66

7

35.86

5

6.599

Lower-

bound

236.66

7

28.00

0

8.452

a. Computed using alpha = .05

There are difference b/w faer scale when effecting time.

Tests of Within-Subjects Contrasts

Measure:MEASURE_1

Source Time Type III

Sum of

Squares df

Mean

Square F Sig.

Partial

Eta

Squared

Noncent.

Paramete

r

Observed

Powera

time Linear 365.067 1 365.06

7

49.22

2

.000 .637 49.222 1.000

Quadratic .800 1 .800 .772 .387 .027 .772 .136

time *

group

Linear 19.267 1 19.267 2.598 .118 .085 2.598 .344

Quadratic .200 1 .200 .193 .664 .007 .193 .071

Error(tim

e)

Linear 207.667 28 7.417

Quadratic 29.000 28 1.036



F df1 df2 Sig.

fear of stats

time1

.893 1 28 .353

fear of stats

time2

.767 1 28 .389

fear of stats

time3

.770 1 28 .388

Tests the null hypothesis that the error variance of the

dependent variable is equal across groups.

a. Design: Intercept + group


Here assumption are met that the variances are same for 1st, 2nd & 3rd time interval

Tests of Between-Subjects Effects

Measure:MEASURE_1

Transformed Variable:Average

Source Type III

Sum of

Squares df

Mean

Square F Sig.

Partial Eta

Squared

Noncent.

Parameter

Observed

Powera

Intercept 127464.10

0

1 127464.100 1531.757 .000 .982 1531.757 1.000

Group 4.900 1 4.900 .059 .810 .002 .059 .056

Error 2330.000 28 83.214


Here we see signifiacnce level which is >0.05 says that with in the group both are

effecting the fear level in the same way and have no differences

Its partial ETA iafter squaring is 0.04 which is very small hich says that there is no

efect of group on the fear

Here lines are in same direction in all 3rd intervals which says that there are no differences

One-way MANOVA:

Multivariate Analysis of Variance ( Manova ) is used to model two or more dependent variables that are continuous with one or more categorical predictor variables.

Assumptions:

One independent variable consists of two or more categorical independent groups. Two or more dependent variables that are either interval or ratio (continuous) Multivariate Normality Equality of variances between the independent groups (homogeneity of variances). Independence of cases.

Question:

Do male and female differ in terms of overall well being in other words are males better adjusted than female in term of their positive and negative mood stats and levels of perceived stress ?

Interpretion:


Value Label N

sex 1 MALES 184

2 FEMALES 248

This table show us the independent variable which gender sex

the sample size cases of males are N= 184

and females cases areN= 248


sex Mean Std. Deviation N

Total positive affect MALES 33.62 6.985 184

FEMALES 33.69 7.439 248

Total 33.66 7.241 432

Total negative affect MALES 18.71 6.901 184

FEMALES 19.98 7.178 248

Total 19.44 7.082 432

Total perceived stress MALES 25.79 5.414 184

FEMALES 27.42 6.078 248

Total 26.72 5.854 432

the Descriptive Statistics table show us the samples sizes of all dependent variables

means and standard deviations.

Box's Test of Equality of

Covariance Matricesa

Box's M 6.942

F 1.148

df1 6

df2 1074771.869

Sig. .331

Tests the null hypothesis that

the observed covariance

matrices of the dependent

variables are equal across

groups.

a. Design: Intercept + sex

One of the assumptions of the MANOVA is homogeneity of covariances, which is

tested for by Box's Test of Equality of Covariance Matrices. If the "Sig." value

is less than .005 (P < 0.05) then the assumption of homogeneity of covariances was

violated. Then we can say this the assumption of homogeneity of covaiances has

been met (P = .331).

Multivariate Testsc

Effect

Value F

Hypothesis

df Error df Sig.

Partial Eta

Squared

Noncent.

Parameter

Observed

Powerb

Intercept Pillai's Trace .987 10841.625a 3.000 428.000 .000 .987 32524.875 1.000

Wilks'

Lambda

.013 10841.625a 3.000 428.000 .000 .987 32524.875 1.000

Hotelling's

Trace

75.993 10841.625a 3.000 428.000 .000 .987 32524.875 1.000

Roy's Largest

Root

75.993 10841.625a 3.000 428.000 .000 .987 32524.875 1.000

sex Pillai's Trace .024 3.569a 3.000 428.000 .014 .024 10.707 .788

Wilks'

Lambda

.976 3.569a 3.000 428.000 .014 .024 10.707 .788

Hotelling's

Trace

.025 3.569a 3.000 428.000 .014 .024 10.707 .788

Roy's Largest

Root

.025 3.569a 3.000 428.000 .014 .024 10.707 .788

a. Exact statistic


c. Design: Intercept + sex

The Multivariate Tests table is where we find the actual result of the one-way MANOVA.

You need to look at the second Effect, labelled "Sex", and the Wilks' Lambda row

(highlighted in red). To determine whether the one-way MANOVA was statistically significant

you need to look at the "Sig." column. We can see from the table that we have a "Sig."

value of .014, which means P < 0.0166. Therefore, we can conclude that this sex gender

impact was significantly dependent on which prior behaviours they had attended (P <

0.05/3= 0.01666).


F df1 df2 Sig.

Total positive affect 1.065 1 430 .303

Total negative affect 1.251 1 430 .264

Total perceived stress 2.074 1 430 .151

Tests the null hypothesis that the error variance of the dependent variable is equal

across groups.

a. Design: Intercept + sex

Levene's Test of Equality of Error Variances Table, as shown

We can see from the table above that all dependent variables have homogeneity of

variances (P > .05)

Tests of Between-Subjects Effects

Source Dependent

Variable Type III Sum

of Squares df

Mean

Square F Sig.

Partial

Eta

Squared

Noncent.

Parameter

Observed

Powerb

Corrected

Model

Total

positive

affect

.440a 1 .440 .008 .927 .000 .008 .051

Total

negative

affect

172.348c 1 172.348 3.456 .064 .008 3.456 .458

Total

perceived

stress

281.099d 1 281.099 8.342 .004 .019 8.342 .822

Intercept Total

positive

affect

478633.634 1 478633.634 9108.270 .000 .955 9108.270 1.000

Total

negative

affect

158121.903 1 158121.903 3170.979 .000 .881 3170.979 1.000

Total

perceived

stress

299040.358 1 299040.358 8874.752 .000 .954 8874.752 1.000

sex Total

positive

affect

.440 1 .440 .008 .927 .000 .008 .051

Total

negative

affect

172.348 1 172.348 3.456 .064 .008 3.456 .458

Total

perceived

stress

281.099 1 281.099 8.342 .004 .019 8.342 .822

Error Total

positive

affect

22596.218 430 52.549

Total

negative

affect

21442.088 430 49.865

Total

perceived

stress

14489.121 430 33.696

Total Total

positive

affect

512110.000 432

Total

negative

affect

184870.000 432

Total

perceived

stress

323305.000 432

Corrected

Total

Total

positive

affect

22596.657 431

Total

negative

affect

21614.435 431

Total

perceived

stress

14770.220 431

a. R Squared = .000 (Adjusted R Squared = -.002)


c. R Squared = .008 (Adjusted R Squared = .006)

d. R Squared = .019 (Adjusted R Squared = .017)

Documents

QTIA Report 2012 IQRA UNIVERSITY