Research Methodology

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 • The mean • The median • 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.

Measure of Dispersion Cont. The three measures of dispersions connected with the mean are • The range • The variance • 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)

Research Methodology