CHAPTER 7 DESCRIPTIVE ANALYSIS

CHAPTER 7 DESCRIPTIVE ANALYSIS

7.0 Chapter Overview

This chapter presents a descriptive analysis of the data obtained through data collection instruments. The data were analyzed descriptively in terms of measures of central tendency and measures of variability. A measure of central tendency includes the mean, median and mode. A measure of variability includes standard deviation, skewness and kurtosis. Descriptive analysis of data is necessary as it helps to determine the normality of the distribution. The nature of the statistical technique to be applied for inferential analysis of the data depends on the characteristics of the data.

7.1 Introduction

Research consists of systematic observation and description of the characteristics or properties of objects or events for the purpose of discovering relationships between variables. The ultimate purpose is to develop generalizations that may be used to explain phenomena and to predict future occurrences. To conduct research, principles must be established so that the observation and description have a commonly understood meaning. Measurement is the most precise and universally accepted process of description, assigning quantitative values to the properties of objects and events.(Best, 1981). Planning and care in research design and data collection provides a substantial guarantee of quality in research but the ultimate test lies in the analysis (Best J. W., 1981). Data in the real world often comes with a large quantum and in a variety of formats that any meaningful interpretation of data cannot be achieved straightway. In order to achieve the objectives of the study, analysis of the data collected forms an important and integral part. Analysis means categorizing, classifying and summarizing data to obtain answers to the research questions. Classification also helps to reduce the vast data into intelligible and interpretable forms (Youngman, 1979).

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In order to do statistical analysis, two types of data are recognized these are 1. Parametric data: Data of this type are measured data, and parametric statistical tests assume that the data are normally or nearly normally distributed. Parametric tests are applied to both interval and ratio scaled data. 2. Non Parametric data: data of this type are either counted or ranked non parametric tests, sometimes known as distribution free tests, do not rest upon the more stringent assumption of normally distributed populations

Two types of statistical application are used for generalization. These are descriptive statistical analysis and inferential statistical analysis. The present chapter discusses the descriptive data analysis used by the researcher for her study.

7.2 Descriptive Data Analysis

Descriptive analysis of data limits generalization to a particular group of individuals observed. No conclusions extend beyond this group and any similarity to those outside the group cannot be assumed. The data describe one group and that group only. Much simple action research involves descriptive analysis and provides valuable information about the nature of the particular group of individuals (Best & Kahn, 2003). The descriptive analysis of data provides the following:

The first estimates and summaries, arranged in tables and graphs, to meet the objectives.

Information about the variability or uncertainty in the data Indications of unexpected patterns and observations that need to be

considered when doing formal analysis

Descriptive analysis is used to describe the basic features of the data in the study. They provide simple summaries about the sample and the measures. Together with simple graphical analysis, they form the basic virtual of any quantitative analysis of data. With descriptive analysis, one simply describes what is or what the data shows. Description of data is needed to determine the normality of the distribution, description of the data is necessary as the nature of the techniques to be applied for inferential analysis of the data depends on the characteristics of the data

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7.3 Procedure of Descriptive Analysis

Once the data are grouped, different statistical measures are used to analyze data and draw conclusions. For the present study, the following statistical measures of descriptive analysis were used to compute further statistical testing.

1. Measures of Central tendency. 2. Measures of Variability. 3. Measures of Divergence from Normality. 4. Measures of Probability. Graphical methods have been adopted for translating numerical facts into more concrete and understandable form.

7.3.1 Measures of central tendency The central tendency of a distribution is an estimate of the "center" of a distribution value. There are three major types of measures of central tendency

Mean The Mean or average is probably the most commonly used methods of describing a central tendency. The mean represents the center of gravity of distribution. Each score in a distribution contributes to the determination of mean. It is also known as arithmetic average. Mean is the average of all values in a distribution (Krishnaswamy & Ranganathan, 2006). To compute the mean, all the values are added and divided by the total number of values. It is the ratio of summation of all scores to the total numbers of scores. Using mean one can compare different groups. It also helps in computing further statistics. Since this method involves handling of large numbers and entails tedious calculations, the researcher used data analysis tools available in a simple Microsoft? office suite, Excel 2007 to calculate the mean. The mode of function is Formulas/More functions/Statistical/ Average. The mean is calculated as: AVERAGE (number1, number2...) Where, Average= mean (number1, number2...) = range of scores

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Mean can also be calculated using the formula:x =

Where, x = sample mean fx = sum of scores in a distribution

N = number of items

Median The median is the positional average that divides a distribution into two equal parts so that one half of items falls above it and the other half below it. In other words, the midpoint of a distribution of values is called the median. It is the point, below and above which 50% of the population lies. The Median is the score found in the exact middle of the set of values. One way to compute the median is to list all scores in numerical order, and then locate the scores in the center of the sample. If there is an even number of numbers in the set, then the median calculates the average of the two numbers in the middle.

Median =

Where, l = lower limit of median class. N = number of scores in a series. fm = frequency of median class c = length of class interval F= no, of cases below the median. The researcher used data analysis tools available in the simple Microsoft? office suite, Excel 2007 to calculate the median. The mode of function is Formulas/More functions/Statistical/ Median.

Mode The mode is the most frequently occurring value in the set of scores. The mode is indirectly calculated mean and median. It is a quick and appropriate measure of central tendency.

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The mode can be calculated as the largest frequency in the distribution, using the following formula:

Mode = 3 (median) ? 2 (mean) The researcher used data analysis tools available in the simple Microsoft? office suite, Excel 2007 to calculate the mode. The mode of function is Formulas/More functions/Statistical/ Mode.

7.3.2. Measures of variability The measures of central tendency indicate the central value of the distribution. However, the central value alone is not sufficient to fully describe the distribution. (Kaul, 2007). In addition to the measures of centrality, we require a measure of the spread of the actual scores. The extent of such spread may vary from one distribution to another. The extent of such variability is measured by the measures of variability. Variability describes the way the classes are distributed and how they are changing in relation to a variety. For example, Range and Standard Deviation. The technique employed in the present study is Standard Deviation. The range is simply the highest value minus the lowest value. The standard deviation is more accurate and detail measure of dispersion.

Standard Deviation The standard deviation shows the relation that set of scores has with the mean of the sample. Standard deviation is expressed as the positive square root of the sum of the squared deviations from the mean divided by the number of scores minus one. It is the average difference between observed values and the mean. The standard deviation is used when expressing dispersion in the same unit as the original measurement. It is designated as () The standard deviation can be calculated using the following formula:

= ifx2-c2 N

Where, = Standard Deviation (S.D.) i = length of class interval = sum of x2= squares of the deviations of scores from the assumed mean

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f = frequency of class interval c2 = square of correction N = total number of scores

The researcher used data analysis tools available in the simple Microsoft? office suite, Excel 2007 to calculate the S.D. The mode of function is Formulas/More functions/Statistical/ STDEV.

7.3.3. Measure of Divergence from Normality An important aspect of the "description" of a variable is the shape of its distribution, which tells the frequency of values from different range of variables. A researcher is interested in how well the distribution can be approximated from the normal distribution. Simple description statistic can provide some information relevant to this issue. The two measures used to determine the shape of distributions are skewness and kurtosis. Skewness: Many times it is seen that the mean, median and mode of the distribution don't fall at the same place, i.e. the scores may extend much farther in one direction than the other. Such a distribution is called a skewed distribution. Positively skewed distribution: The distribution is positively skewed when most of the scores pile up at the low end (or left) of the distribution and spreads out more gradually towards the high end of it. In a positively skewed distribution, the mean falls on the right side of the median. Negatively skewed distribution: The distribution is negatively skewed if the scores are concentrated towards the upper value and it is positively skewed if they cluster towards lower value. The mean of the distribution is higher than the median in positive skewness whereas the median value is greater than the mean in negative skewness.

Skewness = Mean - Mode SD

For the present study skewness was calculated using Microsoft Excel 2007.The mode of function is Formulas/More functions/Statistical/ SKEW.

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Kurtosis The term "Kurtosis "refers to "peakedness " or the flatness of a frequency distribution as compared with the normal. A frequency distribution more peaked than the normal is said to be Leptokurtic and a frequency distribution flatter than the normal is called Platykurtic. A normal curve is also termed as Mesokurtic. Positive kurtosis indicates a relatively peaked distribution leptokurtic and negative kurtosis indicates a relatively flat distribution, which is platykurtic. The researcher used data analysis tools available in the simple Microsoft? office suite, Excel 2007 to calculate the Kurtosis. The mode of function is Formulas/More functions/Statistical/ KURT.

7.3.4 Measures of Probability (fiduciary limits) In order to estimate the population mean or the probable variability, it is necessary to set up limits for a given degree of confidence which will embrace the mean or the standard deviation since limits define the confidence interval.

Estimation of Population parameters :-( Fiduciary Limits) The limits of the confidence intervals of parameters are called fiduciary limits. They are calculated for both mean and standard deviation at 0.95 and 0.99 levels of confidence. The formula used for calculating standard error of mean and fiduciary limits is:-

S.EM. = N

At 0.95 level; mean +S. EM ? 1.96 At 0.99 level; mean +S. EM ? 2.58 The formula used for calculating standard error of S.D.:-

S.ED = 0 .71 N

At 0.95 level; S.D.+ S. ED ? 1.96 At 0.99 level; S.D.+ S. ED ? 2.58 Where,

S. EM = standard error of mean S. ED = standard error of standard deviation = standard deviation

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N= total number of scores M= Mean

7.4 Graphical Representation

Aid in analyzing numerical data may often be obtained from a graphic or pictorial treatment of the frequency distribution. The advertisements have long used graphic methods because these devices catch the eye and hold the attention when the most careful array of statistical evidence fails to attract notice for this and other reasons the research worker also utilizes the attention- getting power of visual presentation; and at the same time, seeks to translate numerical facts often abstract and difficult to interpret, into more concrete and understandable form. In the present study, the researcher used graphical representation in the form of line diagrams and pie-charts.

7.5 Descriptive Statistical Analysis of data

The data were obtained for the variables involved in the study from Bachelor of Education students of different B Ed colleges. The study was conducted in two phases; hence this chapter deals with the description of the variables in the two phases of the study. Phase I: This section deals with the description of the following variables:

1. Information Literacy Skills of students from Arts Faculty 2. Information Literacy Skills of students from Science Faculty 3. Information Literacy Skills of students from Commerce Faculty 4. Information Literacy Skills of students with Graduate degree 5. Information Literacy Skills of students with Post Graduate degree Phase II: This section deals with the description of the following variables: 1. Information Literacy Skills pre-test scores of control group 2. Information Literacy Skills post-test scores of control group 3. Information Literacy skills pre-test scores of experimental group 4. Information Literacy skills post-test scores of experimental group

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