Presentation ARM Week10

7/31/2019 Presentation ARM Week10

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Week-10

COURSE

ONAdvanced

RESEARCH METHODOLOGY

(MSBA/MBA, FACULTY OF MANAGEMENT SCIENCES)

PROFESSOR

Dr.Alyas Qadeer Tahir

E-Mail: [email protected]
mailto:[email protected]:[email protected]


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2

Types of

Data

Qualitative(categorical/Attributes)

1*Data that refers only toname classification (done

using numbers)

2* Can be placed intodistinct categories

according to somecharacteristic or attribute.

Quantitative(Ratio/Scale/Numerical)

1*Data that representcounts or measurements

(can be count or measure)

2*Are numerical in natureand can be ordered or

ranked.

Nominal Data (cant be rank)Gender, race, citizenship. etc

Ordinal Data (can be rank)Feeling (dislike like),

color (dark bright) , etc.

Discrete VariablesAssume values that can be

counted and finiteEx : no of something

Continuous variablesCan assume all values

between any two specificvalues & it obtained by

measuringEx: weight, age, salary, height,

temperature, etc.

Use code

numbers (1,

2,)

Variable Types:


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Exploring Relationship

(Finding out the strength of relationshipbetween variables)

Partial Correlation

Multiple Regression

Correlation (Pearson/Spearman)

Logistic Regression Factor Analysis


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Partial CorrelationExample of Research Question:

Is there a relationship between the level of satisfaction of

employees and the amount of production of a industry?

OR

Is a industry with higher level of satisfaction of itsemployees experience more production?

OR

Is a industry with lower level of satisfaction of its employees

experience less production?


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Conti. Partial Correlation

What you need:

Two variables, both continuous, or one continuous and theother dichotomous (e.g, sex M/F).

What it does:

This clarifies the relationship between two continuous

variables, in terms of both the strength of the relationship

and the direction.

Major Assumptions:

1. Normality2. Linearity


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Multiple RegressionExample of Research Question:

How well do the two measures of variables (level of

satisfaction and salary) predict the amount of production of

a industry?

ORHow much variance in a factory production measure can

be explained by the measures on the level of employees

satisfaction and their salaries.?

OR

Which is the best predictor of a factory production: the

employees level of satisfaction or their salaries?


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Conti. Partial Correlation

What you need:

One continuous dependent variable (factory production) Two or more continuous variables (satisfaction score

and salaries). You can also use dichotomousindependent variables (e.g, sex, M/F).

What it does:This tells us how much of the variance in you dependent

variable can be explained by our independent variables.

Major Assumptions:

1. Normality

2. Linearity


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Exploring Differences between

Groups(Whether statistically significant difference exists among a numberof groups)

Non-Parametric Test

Chi-square for independenceParametric Tests

T-tests

ANOVAMANOVA

ANCOVA


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Chi-square for independence(comparing groups)Research Questions:

Are males more likely to drop out of therapy than females?

Is the proportion of permanent staff that recommends theorganization as a good place to work significantly differentfrom the proportion of casual staff that recommend?

This test is used to explore relationship between twocategorical variables. Each of these variable can have againtwo or more categories. This test compares the observedfrequencies or population of cases that occur in each of thecategories, with the values that would be expected if there wasno association between the two variables being measured. It isbased on cross-tabulation, with cases classified according tothe categories in each of variable. (e.g. male/female;dropout/clear etc.)


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For Chi-Square test for independence

From our file: staffsurvey3Ed.savWe need: Two categorical variables;

Employees status (permanent/casual)

Recommendation (no/yes)

Assumptions: The lowest expected frequency in

80% cells should be more than 5.


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T-TestsIndependent-sample t-test: used to compare the mean

scores of two different groups of peoples or conditions.

Paired-sample t-test: used to compare the means scoresfor the same group of people on two different occasions.

Research Question: Is there a significant difference in the

mean total scores for permanent and casual staff.

We need: Two variables

One categorical, independent variable (per./cas)

One continuous, dependent variable (total satis. score)


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ANOVA(One-way Analysis of Variance)In T-Tests, we compare mean scores of two different groups. For comparing

mean scores of more than two groups, we use ANOVA.

ANOVA involves one independent variable (called as a factor), which has anumber of different levels. These levels correspond to the different groupsor conditions.

In ANOVA, we compare the variance (variability) in scores between thedifferent groups with the variability within each of the groups.

For ANOVA, we calculate F ratio (variance between the groups divided byvariance within the groups).

A large F ratio indicates that there is more variability between the groups thanthere is within groups. A significant F test indicates that we can reject thehypothesis, which states that the population means are equal. It does not,however tells us which of the groups differ. For this , we conduct Post-hoc

analysis.

There are two types of One-way of ANOVA.1.Betweengroups ANOVA (independent group design).2.Repeated-measures ANOVA (within-subject design).


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ONE-WAY ANOVAResearch Question: Is there a significant difference

in total scores of employees having service of oneyear or more, 3 to 5 years and 6 years or more?

We need: Two variables

One categorical (factor), independent variable withthree or more distinct categories or a continuousvariable with three groups

One continuous, dependent variable (totalsatis.score), Assumption: Normality


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TWO-WAY ANOVAIn 2-Way ANOVA between groups, we explore two-way

between groups analysis of variance. There are twoindependent variables and there are different peoples ineach of the groups

This techniques allowed us to look at the individual and

joint effect of two independent variables on onedependent variable.

The advantage of using a two-way design is that we cantest the main effect for each independent variable and

also explore the possibility of an interaction effect. Aninteraction effect occurs when the effect of oneindependent variable on the dependent variabledepends on the level of a second independent variable.


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Two-WAY ANOVAResearch Question:

What is the impact of service groups and service status on staffsatisfaction? Does service status moderate the relationship betweenservice group and staff satisfaction?

ORConduct a two-way ANOVA with post-hoc tests (if appropriate) tocompare staff satisfaction scores (totsatis) across each of the lengthof service categories (servicegp3) for permanent versus casual staff

(employeestatus).

We need: Three variables Two categorical independent variable; servicegp3and

employeestatus

One continuous, dependent variable (totalsatisscore)Assumption:

The variance should be homogeneous (Apply Levenes Test).


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MULTIVARIATE ANALYSIS OFVARIANCE(MANOVA)

MANVOA is an extension of ANOVA for use when we have more thanone dependent variable. MANOVA compares the groups that tellswhether the mean differences between the groups on thecombination of dependent variables are likely to have occurred bychance. There is way to conduct ANOVAs separately for eachdependent variable but in such case there is chance of occurringType 1 error. Therefore, it is not recommended.

MANOVA can be used in one-way, two-way and higher-order factorialdesigns (with multiple independent variables) and when using

ANCOVA.What MANOVA does: Compares two or more groups in terms of their

means on a group of dependent variables. Tests the null hypothesisthat the population means on a set of dependent variables do notvary across different levels of a factor or grouping variable.


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For MANOVA ExampleWe use data File: survey3ED.savIn this example, the difference between males and females

on a number of measures of wellbeing is explored.These include a measure of negative mood (-ive Affectscale), positive mood (+ive affect scale) and perceivedstress (total Perceived Stress scale).

Research Question: Are males better adjusted than

females in terms of their positive and negative moodstates and levels of perceived stress?Do males and females differ in terms of overallwellbeing?

We need: One-way MANOVA

One categorical independent variable (e.g, sex) and Two or more continuous, dependent variable (-ive affect,

+ive affect, perceived stress).


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Assumptions: MANOVA has following assumptions.

1.Sample size (Minimum dependent variables 3, more cells arepreferred)

2.Normality (a sample size of 20 in each cell should ensurenormality)

3.Outliers (data points or scores that are different from the

reminder of the scores, we need to check this)

4.Linearity (presence of a straight-line relationship betweeneach pair of dependent variables)

5.Homogenearity of regression

6.Multicollinearity and singularity7.Homogeneity of variance-covariance matrices


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ANALYSIS OF COVARIANCE

(ANCOVA)ANCOVA is an extension of ANOVA. This allows to explore differencesbetween groups while statistically controlling for an additional variable. Thisadditional variable is called covariate. This variable we may suspectinfluencing scores on the dependent variable. ANCOVA can be used as partof one-way, two-way and multivariate ANOA techniques.

USES of ANCOVA: ANCOVA can be used when we have a two differentinterventions pre-test/post or post-test/delayed post-design. That is forcomparing the impact of two different interventions taking before and aftermeasures for each group. The scores on the pre-test are treated as acovariate to control for pre-existing differences between the groups. Thismakes ANCOVA very useful in situations when we have very small sample

size and only small or medium effect size.ANCOVA is also handy when we are unable to randomly assign oursubjects to the different groups but instead have had to use existing groups(classes of students etc.)


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Assumptions:

ANCOVA has following assumptions.

(In addition to the one used for one-way ANOVA)

1. Influence of treatment on covariatemeasurement

2. Reliability of covariates

3. Correlations among covariates

4. Linear relationship between dependent

variable and covariate5. Homogeneity of regression slopes


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ONE-WAY ANCOVAFile Name: experim3ED

In this example, we will explore the impact of themath.skills class (Group 1) and the confidence buildingclass (Group 2) on students scores on the Fear ofStatistic Test, while controlling for the scores on this test

administered before the program (Pre-test, covariate).

Research Question:

Is there difference in the Fear of Statistics Test scoresfor the math.skills (group 1) and the confidence buildinggroup (group 2), while controlling for their pre-test scoreson this test?


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We Need: Three Variables (Note: Here we are going for Time2) One categorical independent variable with two or more levels

(group 1/ group 2); One continuous dependent variable (score on the Statistics Test

at Time 2 i.e post-test);

One or more continuous covariates (scores on the Fear statisticsTest at Time 1).

What it does: ANCOVA will tell us if the mean Fear statistics Testscores at Time 2 (post-test) for the two groups are significantlydifferent after initial pre-test scores are controlled for.

Assumptions: All normal one-way ANOVA assumptions apply in

ANCOVA. Additional ANCOVA assumptions are as under:1. The covariate is measured prior to the interventions or

experimental manipulation;

2. The covariate is measured without error (or as reliably as possible);


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3. The covariates are not strongly correlated with one another;

4. There is a linear relationship between the dependent variable andthe covariate for all groups (linearity);

5. The relationship between the covariate and dependent variable isthe same for each of the groups (homogeneity of regressionslopes).

Testing Assumptions: (Only additional one)

Assumption 1: measurement of the covariateYes, covariate (pre-test) is measured before the experiment.

Assumption 2: Reliability of the covariate

Yes, the reliability Cronbach alpha in this case is .78.

Assumption 3: Correlation among the covariates

Here, we have only one covariate, therefore need not to do.Assumption 4: To check the assumption of a linear relationship

between the dependent variable and the covariates for all ourgroups, we proceed as:


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Two-WAY ANCOVA

IntroductionIn one-way ANCOVA, we were interesting todetermine that which intervention (maths skills or

confidence building) was more effective in reducing

students fear of statistics. We found no significant

difference between the groups.

Now, suppose that in reading further in the literature

on the topic, we found some research thatsuggested that there might be a difference in how

males and females respond to different

interventions.


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Cont from two-way ANCOVA

Therefore, in literature you will see this additional

variable (e.g, sex) described as moderator. That is,it moderates or influences the effect of the other

independent variable. Often, these moderator

variables are individual difference variables,

characteristics of individuals that influence the way

in which they respond to an experimental

manipulation or treatment condition.

Important: If you obtain a non-significant result foryour one-way ANCOVA, then you need to consider

for a moderator variable and go for

a 2-way ANCOVA.


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Two-WAY ANCOVAFile Name: experim3EDResearch Question:

Does gender influence the effectiveness of two programsdesigned to reduce participants fear of statistics? OR

Is there a difference in post-intervention Fear of StatisticsTest scores between males and females in theirresponse to a math.skills program and a confidencebuilding program.

We Need: Four variables:

1. Two categorical independent variables with two or more levels (sex:

M/F, group: math.skills/confidence building).2. One continuous dependent variable (score on the Statistics Test at

Time 2 i.e post-test);3. One or more continuous covariates (scores on the Fear statistics

Test at Time 1).


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What it does:

ANCOVA will control for scores on our covariate (s) and thenperform a normal two-way ANOVA. This will tell us if there is :

a significant main effect for our first independent variable (group).

a main effect for our second independent variable (sex);

a significant interaction between the two.

Assumptions:

All normal two-way ANOVA assumptions apply (normality,homogeneity of variance). These should be checked first.

Additional ANCOVA assumptions:

Same as discussed under one-way ANCOVA. These should bechecked first.

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Presentation ARM Week10