Research Methodology

Lecture No :24

Recap Lecture

In the last lecture we discussed about:•Frequencies•Bar charts and pie charts•Histogram •Stem and leaf display •Pareto diagram•Box plot•SPSS cross tabulation

Lecture Objectives

Getting the feel for the data•Measure of central tendency•Measure of Dispersion•Relationship Between Variables•χ² Test

Lecture Objectives Cont.

Testing the goodness of data

Reliability•Cronbach’s alpha•Split half

Validity •Factorial•Criterion •Convergent•Discriminant

Measure of Central Tendency

There are three measures of central tendency

1.The mean

2.The median

3.The mode

Measure of Central Tendency Cont.

The mean•The mean or the average, is a measure of central tendency that offers a general picture of the data.•The mean or average of a set of, say, ten observations, is the sum of ten individual observations divided by ten (the total no of observations).•(54+50+35+67+50)/5=51.2

Measure of Central Tendency Cont.

The median•The median is the central item in a group of observations when they are arrayed in either an ascending or a descending order.•35,50,50,54,67------50

Measure of Central Tendency Cont.

The mode•In some cases, a set of observations does not lend itself to meaningful representation through either the mean or the median, but can be signified by the most frequently occurring phenomenon.•54,50,35,67,50-----50

Measure of Dispersion

• Dispersion is the variability that exist in a set of observations.

• Two sets of data might have the same mean, but the dispersion could be different.

54 3450 5050 50

35 35

67 87

mean 51.2 51.2

sdv 11.43241 21.46392

Measure of Dispersion Cont.

The three measures of dispersions connected with the mean are

1.The range

2.The variance

3.The standard deviation

Measure of Dispersion Cont.

The range•Range refers to the extreme values in a set of observations. •54,50,35,67,50•(35,67)

Measure of Dispersion Cont.

The variance•The variance is calculated by subtracting the mean from each of the observations in the data set, taking a square of this difference, and dividing the total of these by the number of observations.

Measure of Dispersion Cont.

The standard deviation•Another measure of dispersion for interval and ratio scaled data, offers an index of the spread of a distribution or the variability in the data.•It is a very commonly used, measure of dispersion, and is simply square root of the variance.

Relationship Between Variables

• Parametric tests from testing relationship between variables such as Person Correlation using interval and ratio scales

• Nonparametric tests are available to assess the relationship between variables measured on a nominal or an ordinal scale.

• Spearman’s rank correlation and Kendall’s rank correlation are used to examine relationships between interval and/or ratio variables.

Pearson Correlation

Rank Correlations

• To test the strength and direction of association that exists between two variables

• The variables are using ordinal scale• E.g Students’ score in two different exams

i.e. English and Math• Correlations (SPSS)

» Bi vitiate » Spearman

– Check for value of r and P

Relationship Between Nominal Variables: χ² Test

• Sometimes we want to know if there is a relationship between two nominal variables or whether they are independent of each other.

• The χ² test compares the expected frequencies (based on the probability) and the observed frequency.

Testing Goodness of Data

Goodness of data can be tested by two measures•Reliability•Validity

Reliability

• The reliability of a measure is established by testing for both consistency and stability.

• Consistency indicates how well the items measured a concept having together as a set.

Reliability Cont.

• Cronbach’s alpha is a reliability coefficient that indicates how well the items in a set are positively correlated to one another.

• Cronbach’s alpha is computed in terms of the average intercorrelations among the items measuring the concept.

• The closer Cronbach’s alpha is to one, the higher the internal consistency reliability.

Reliability Cont.

• Another measure of consistency reliability used in specific situations is the split half reliability coefficient.

• Split half reliability is obtained to test for consistency when more than one scale, dimensions, or factor is assessed.

Validity

• Factorial validity can be established by submitting the data for factor analysis.

• Factor analysis reveals whether the dimensions are indeed tapped by the items in the measure, as theorized.

Validity Cont.

• Criterion related validity can be established by testing for the power of the measure to differentiate individuals who are known to be different.

Validity Cont.

• Convergent validity can be established when there is high degree of correlation between two different sources responding to the same measure.

• Example: Both supervisors and subordinates respond similarly to a perceived reward system measure administered to them.

Validity Cont.

• Discriminant validity can be established when two distinctly different concepts are not correlated to each other .

• Example: Courage and honesty, leadership and motivation, attitudes and behaviors.

SPSS

• Cronbach Alpha (Reliability)• Factor Analysis (Validity)

Recap

• Goodness of data is measured by reliability and validity.

• Three measures of central tendency: mean, median and mode.

• Dispersion is the variability.• Three measures of dispersion are: range,

variance and standard deviation.• Correlation• SPSS Cronbach Alpha (Reliability) Factor

Analysis (Validity)