# Research Methods

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Research Methods ­STA630
VU
Lesson 32
THE PARTS OF THE TABLE
1.
Give each table a number.
2.
Give each table a title, which names variables and provides background information
3.
Label the row and columns variables and give name to each of the variable categories.
4.
Include the totals of the columns and rows.  These are called marginals.They equal the
univariate frequency distribution for the variable.
5. Each number or place that corresponds to the intersection of a category for each variable is a
cell of a table.
6. The numbers with the labeled variable categories and the totals are called the body of the table.
7. If there is missing information, report the number of missing cases near the table to account for
all original cases.
Researchers convert raw count tables into percentages to see bi-variate relationship. There are three
ways to percentage a table: by row, by column, and for the total. The first two are often used and show
relationship.
Is it best to percentage by row or column? Either could be appropriate. A researcher's hypothesis may
imply looking at row percentages or the column percentages. Here, the hypothesis is that age affects
attitude, so column percentages are most helpful. Whenever one factor in a cross-tabulation can be
considered the cause of the other, percentage will be most illuminating if they are computed in the
direction of the causal factor.
Reading a percentage Table: Once we understand how table is made, reading it and figuring out what
it says are much easier. To read a table, first look at the title, the variable labels, and any background
information. Next, look at the direction in which percentages have been computed ­ in rows or
columns.
Researchers read percentaged tables to make comparisons. Comparisons are made in the opposite
direction from that in which percentages are computed. A rule of thumb is to compare across rows if the
table is percentaged down (i.e. by column) and to compare up and down in columns if the table is
percentaged across (i.e. by row).
It takes practice to see a relationship in a perentaged table. If there is no relationship in a table, the cell
percentages look approximately equal across rows or columns. A linear relationship looks like larger
percentages in the diagonal cells. If there is curvilinear relationship, the largest percentages form a
pattern across cells. For example, the largest cells might be the upper right, the bottom middle, and the
upper left. It is easiest to see a relationship in a moderate-sized table (9 to 16 cells) where most cells
have some cases (at least five cases are recommended) and the relationship is strong and precise.
Linear relationship
· Table 4: Age by attitude towards women
.
empowerment
.
Age (in years)
.
Level of
under 40
40 ­60
61 +
Total
attitude
F.
%
F.
%
F
%
F
%
Hi Favorable
600
60
300
30
200
20
1100
37
Med. Favorable 300
30
500
50
250
25
1050
28
Lo Favorable
100
10
200
20
500
50
850
28
Total
1000
100
1000 100
1000
100
3000
100
·
Larger percentages in the diagonal cells
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Research Methods ­STA630
VU
Linear
Linear
Negative relationship
Positive relationship
Y
Y
X
X
Curvilinear
A simple way to see strong relationships is to circle the largest percentage in each row (in row
percentaged tables) or columns (for column-percentaged tables) and see if a line appears.
A simple way to see strong relationship is to
circle the largest percentage in applicable
row or column and see if a line appears
· Table 4: Age by attitude towards women
.
empowerment
.
Age (in years)
.
Level of
under 40
40 ­60
61 +
Total
attitude
F.
%
F.
%
F
%
F
%
60
Hi Favorable
600
60
300
30
200
20
1100
37
50
Med. Favorable 300
30
500
250
25
1050
35
50
Lo Favorable
100
10
200
20
500
850
28
Total
1000
100
1000 100
1000
100
3000
100
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Research Methods ­STA630
VU
The circle-the-largest-cell rule works ­ with one important caveat. The categories in the percentages
table must be ordinal or interval. The lowest variable categories begin at the bottom left. If the
categories in a table are not ordered the same way, the rule does not work.
Statistical Control
Showing an association or relationship between two variables is not sufficient to say that an independent
variable causes a dependent variable. In addition to temporal order and association, a researcher must
eliminate alternative explanations ­ explanations that can make the hypothetical relationship spurious.
Experimental researchers do this by choosing a research design that physically controls potential
alternative explanations for results (i.e. that threaten internal validity).
In non-experimental research, a researcher controls for alternative explanations with statistics. He or
she measures possible alternative explanations with control variables, and then examines the control
variables with multivariate tables and statistics that help him or her to decide whether a bivariate
relationship is spurious. They also show the relative size of the effect of multiple independent variables
on dependent variable.
A researcher controls for alternative explanation in multivariate (more than two variables) analysis by
introducing a third (sometimes fourth, or fifth) variable. For example, a bivariate table shows that
young people show more favorable attitude towards women empowerment.  But the relationship
between age and attitude towards women empowerment may be spurious because men and women may
have different attitudes. To test whether the relationship is actually due to gender, a researcher must
control for gender; in other words, effects of gender are statistically removed. Once this is done, a
researcher can see whether the bivariate relationship between age and attitude towards women
empowerment remains.
A researcher controls for a third variable by seeing whether the bivariate relationship persists within
categories of the control variable. For example controls for gender, and the relationship between age
and attitude persists. This means that both male and females show negative association between age
and attitude toward women empowerment. In other words, the control variable has no effect. When
this is so, the bivariate relationship is not spurious.
If the bivariate relationship weakens or disappears after the control variable is considered, it means that
the age is not real factor that makes the difference in attitude towards women empowerment, rather it is
the gender of the respondents.
Statistical control is a key idea in advanced statistical techniques. A measure of association like the
correlation co-efficient only suggests a relationship. Until a researcher considers control variables, the
bivariate relationship could be spurious. Researchers are cautious in interpreting bivariate relationships
until they have considered control variables.
After they introduce control variables, researchers talk about the net effect of an independent variable ­
the effect of independent variable "net of," or in spite of, the control variable. There are two ways to
introduce control variables: trivariate percentaged tables and multiple regression analysis.
Constructing Trivariate Tables
In order to meet all the conditions needed for causality, researchers want to "control for" or see whether
an alternative explanation explains away a causal relationship. If an alternative explanation explains a
relationship, then bivariate relationship is spurious. Alternative explanations are operationalize as a
third variable, which are called control variables because they control for alternative explanation.
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Research Methods ­STA630
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One way to take such third variables into consideration and see whether they influence the bivariate
relationship is to statistically introduce control variables using trivariate or three variable tables.
Trivariate tables differ slightly from bivariate tables; they consist of multiple bivariate tables.
A trivariate table has a bivariate table of the independent and dependent variable for each category of
the control variable. These new tables are called partials. The number of partials depends on the
number of categories in control variable. Partial tables look like bivariate tables, but they use a subset
of the cases. Only cases with a specific value on the control variable are in the partial. Thus it is
possible to break apart a bivariate table to form partials, or combine the partials to restore the initial
bivariate table.
Trivariate tables have three limitations. First, they are difficult to interpret if a control variable has more
that four categories. Second, control variables can be at any level of measurement, but interval or ratio
control variables must be grouped (i.e. converted to an ordinal level), and how cases are grouped can
affect the interpretation of effects. Finally, the total number of cases is a limiting factor because the
cases are divided among cells in partials. The number of cells in the partials equals the number of cells
in the bivariate relationship multiplied by the number of categories in the control variables. For example
if the control variable has three categories, and a bivariate table has 12 cells, the partials have 3 X 12 =
36 cells. An average of five cases per cell is recommended, so the researcher will need 5 X 36 = 180
cases at minimum.
Like a bivariate table construction, a trivariate table begins with a compound frequency distribution
(CFD), but it is a three-way instead of two-way CFD. An example of a trivariate table with "gender" as
control variable for the bivariate table is shown here:
Partial table for males
.
.
·
.
Age (in years)
.
·
Level of
.
Under 40
40--60
61+
Total
.
·
Attitude
F
%
F
%
F.
%
F.
%.
·
High
300
60
200
33
30
6  530
33
·
Medium
140
28
270
45
120
24  530
33
·
Low
60
12
130
22
350
70  540
34
·
Total
500
100
600
100
500 100 1600
100
Partial table for females
.
.
·
.
Age (in years)
.
·
Level of
.Under 40
40--60
61+
Total
.
·
Attitude
F
%
F
%
F.
%
F.
%.
·
High
350
70
200
50
20
4
570
41
·
Medium
150
30
150
38
220
44
520
37
·
Low
-
-
50
12
260
52
310
22
·
Total
500
100
400
100
500
100
1400
100
The replication pattern is the easiest to understand. It is when the partials replicate or reproduce the
same relationship that existed in the bivariate table before considering the control variable. It means
that the control variable has no effect.
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Research Methods ­STA630
VU
The specification pattern is the next easiest pattern. It occurs when one partial replicate the initial
bivariate relationship but other partials do not. For example, we find a strong (negative) bivariate
relationship between age of the respondents and attitude towards women empowerment. We control for
gender and discover the relationship holds only for males (i.e. the strong negative relationship was in the
partial for males, but not for females). This is specification because a researcher can specify the
category of the control variable in which the initial relationship persists.
The interpretation pattern describes the situation in which the control variable intervenes between the
original independent variable and the dependent variables.
The suppressor variable pattern occurs when the bivariate tables suggest independence but relationship
appears in one or both of the partials. For example, the age of the respondents and their attitudes
towards women empowerment are independent in a bivariate table. Once the control variable "gender"
is introduced, the relationship between the two variables appears in the partial tables. The control
variable is suppressor variable because it suppressed the true relationship; the true relationship appears
in partials.
Multiple Regression Analysis
Multiple regression controls for many alternative explanations of variables simultaneously (it is rarely
possible to use more than one control variable using percentaged tables). Multiple regression is a
technique whose calculation you may have learnt in the course on statistics.
Note
In the preceding discussion you have been exposed to the descriptive analysis of the data. Certainly
there are statistical tests which can be applied to test the hypothesis, which you may have learnt in your
course on statistics.
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