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TABULATION OF DATA

In document Business Research Methods (Page 194-200)

Type II error - An error caused by failing to reject a null hypothesis that is not true

TABULATION OF DATA

STRUCTURE

· Table

· Relations frequency table

· Cross tabulation and stub-and-banner tables

· Guideline for cross tabulation INTRODUCTION

To get meaningful information from the data it is arranged in the tabular form.

Frequency tables, histograms are simple form of tables.

Frequency Tables

Frequency table or frequency distribution is a better way to arrange data. It helps in compressing data. Though some information is lost, compressed data show a pattern clearly. For constructing a frequency table, the data are divided into groups of similar values (class) and then record the number of observations that fall in each group.

Table 1: Frequency table on age-wise classification of respondents

The data of collection days are presented in the following table as a frequency table. The number of classed can be increased by reducing the size of the class. The choice of class intervals is mostly guided by practical consideration rather than by rules. Class intervals are made in such a way that measurements are uniformly distributed over the class and the interval is not very large. Otherwise, the mid value will either overestimate or

underestimate the measurement.

Relative frequency tables

Frequency is total number of data points that fall within that class. Frequency of each value can also be expressed as a fraction or percentage of the total number of

observations. Frequencies expressed in percentage terms are known as relative frequencies. A relative frequency distribution is presented in the table below.

Table 2: Relative frequency table on occupation-wise classification of respondents

It may be observed that the sum of all relative frequencies is 1.00 or 100% because frequency of each class has been expressed as a percentage of the total data.

Cumulative frequency tables

Frequency or one-way tables represent the simplest method for analyzing categorical data. They are often used as one of the exploratory procedures to review how different categories of values are distributed in the sample.

For example, in a survey of spectator interest in different sports, we could summarize the respondents' interest in watching football in a frequency table as follows:

Table 3: Cumulative frequency table on Statistics about football watchers

The table above shows the number, proportion, and cumulative proportion of

respondents who characterized their interest in watching football as either (1) Always interested, (2) Usually interested, (3) Sometimes interested, or (4) Never interested.

Applications

In practically every research project, a first "look" at the data usually includes frequency tables. For example, in survey research, frequency tables can show the number of males and females who participated in the survey, the number of respondents from particular ethnic and racial backgrounds, and so on. Responses on some labeled attitude

measurement scales (e.g., interest in watching football) can also be nicely summarized via the frequency table. In medical research, one may tabulate the number of patients displaying specific symptoms; in industrial research one may tabulate the frequency of different causes leading to catastrophic failure of products during stress tests (e.g., which parts are actually responsible for the complete malfunction of television sets under extreme temperatures?). Customarily, if a data set includes any categorical data, then one of the first steps in the data analysis is to compute a frequency table for those categorical variables.

Cross Tabulation and Stub-and-Banner Tables

Managers and researchers frequently are interested in gaining a better understanding of the differences that exist between two or more subgroups. Whenever they try to identify characteristics common to one subgroup but not common to other subgroups, (i.e. they

are trying to explain differences between the subgroups). Cross tables are used to explain the difference between the subgroups.

Cross tabulation is a combination of two (or more) frequency tables arranged such that each cell in the resulting table represents a unique combination of specific values of cross tabulated variables. Thus, cross tabulation allows us to examine frequencies of observations that belong to specific categories on more than one variable.

By examining these frequencies, we can identify relations between cross tabulated variables. Only categorical variables or variables with a relatively small number of different meaningful values should be cross tabulated. Note that in the cases where we do want to include a continuous variable in a cross tabulation (e.g., income), we can first recode it into a particular number of distinct ranges (e.g. low, medium, high).

Guidelines for Cross Tabulation

The most commonly used method of data analysis is cross tabulation. The following guidelines will helpful to design proper cross tabulation,

1. The data should be in categorical form

Cross tabulation is applicable to data 1 which both the dependent and the independent variables appear in categorical form. There are two types of categorical data.

One type (assume type A) consists of variables that can be measured only in classes or categories. Like marital status, gender, occupation variables can be measured in categories not quantifiable (i.e. no measurable number).

Another type (say type B) variables, which can be measured in numbers, such as age, income. For this type the different categories are associated with quantifiable numbers that show a progression from smaller values to larger values.

Cross tabulation is used on both types of categorical variables. However when

construction across tabulation is done using type B categorical variables, researchers find it helpful to use several special steps to make such cross tabulations more effective analysis tools.

1. If certain variable is believed to be influenced by some other variable, the former can be considered to be a dependent variable and the later is called as independent

variable.

2. Cross tabulate an important dependent variable with one or more 'explaining' independent variables.

Researchers typically cross tabulate a dependent variable of importance to the objectives of the research project (such as heavy user versus light user or positive attitude versus negative attitude) with one or more independent variables that the researchers believe

can help explain the variation observed in the dependent variable. Any two variables can be used in a cross tabulation so long as they both are in categorical form, and they both appear to be logically related to one another as dependent and independent variables consistent with the purpose and objectives of the research project.

3. Show percentage in a cross tabulation

In a cross tabulation researchers typically show the percentage as well as the actual count s of the number of responses falling into the different cells of the table. The

percentages more effectively reveal the relative sizes of the actual counts associated with the different cells and make it easier for researchers to visualize the patterns of

differences that exist in the data.

Constructing and Interpreting a Cross Tabulation

After drawing the cross table the interpretations has to be drawn from the table. It should convey the meaning and findings from the table. In management research interpretations has more value. From the interpretations and findings managers take decisions.

2x2 Tables

The simplest form of cross tabulation is the 2 by 2 table where two variables are

"crossed," and each variable has only two distinct values. For example, suppose we conduct a simple study in which males and females are asked to choose one of two different brands of soda pop (brand A and brand B); the data file can be arranged like this:

The resulting cross tabulation could look as follows.

Each cell represents a unique combination of values of the two cross tabulated variables (row variable Gender and column variable Soda), and the numbers in each cell tell us how many observations fall into each combination of values. In general, this table shows us that more females than males chose the soda pop brand A, and that more males than females chose soda B. Thus, gender and preference for a particular brand of soda may be related (later we will see how this relationship can be measured).

Marginal Frequencies

The values in the margins of the table are simply one-way (frequency) tables for all values in the table. They are important in that they help us to evaluate the arrangement of frequencies in individual columns or rows. For example, the frequencies of 40% and 60% of males and females (respectively) who chose soda A (see the first column of the above table), would not indicate any relationship between Gender and Soda if the

marginal frequencies for Gender were also 40% and 60%; in that case they would simply reflect the different proportions of males and females in the study. Thus, the differences between the distributions of frequencies in individual rows (or columns) and in the respective margins inform us about the relationship between the cross tabulated variables.

Column, Row, and total Percentages. The example in the previous paragraph

demonstrates that in order to evaluate relationships between cross tabulated variables we need to compare the proportions of marginal and individual column or row

frequencies. Such comparisons are easiest to perform when the frequencies are presented as percentages.

Evaluating the Cross Table

Researchers find it useful to answer the following three questions when evaluating cross tabulation that appears to explain differences in a dependent variable.

1. Does the cross tabulation show a valid or a spurious relationship?

2. How many independent variables should be used in the cross tabulation?

3. Are the differences seen in the cross tabulation statistically significant, or could they have occurred by chance due to sampling variation?

Each of this is discussed below.

Does the cross tabulation show a valid explanation?

If it is logical to believe that changes in the independent variables can cause changes in the dependent variables, then the explanation revealed by the cross tabulation is

thought to be a valid one.

Does the cross tabulation show a valid or a spurious relationship?

An explanation is thought to be a spurious one if the implied relationship between the dependent and independent variables does not seem to be logical.

Example: family size, income seem appear to be logically related to the household consumption of certain basic food products. However it may not be logical to relate the number of automobiles owned with the brand of toothpaste preferred, or to relate the type of family pet with the occupation of the head of the family. If the independent variable does not logically have an effect or influence on the dependent variable, the relationship that a cross tabulation seems to show may not be a valid cause and effect relationship, and therefore may be a spurious relationship.

How many independent variables should be used?

When cross tabulating an independent variable that seems logically related to the dependent variable, what should researchers do if the results do not reveal a clear-cut relationship?

Two possible courses of actions are available.

1. Try another cross tabulation, but this time using one of the other independent variable hypothesized to be important when the study was designed.

2. A preferred course of action is to introduce each additional independent variable simultaneously with rather than as an alternative to the first independent variable tried in the cross tabulation. By doing so it is possible to study the interrelationship between the dependent variable and two or more independent variables.

SUMMARY

The data can be summarized in the form of table. Cross table given the meaning full information from the raw data. The way of constructing cross tables and interpreting and evaluating is very important.

KEY WORDS

· Class

· Frequency

In document Business Research Methods (Page 194-200)