Introduction To Tabulation © Copyright 1990 John F Hall The notes below are intended to refer to data analysis rather than statistics as such; they especially refer to the analysis of data from sample surveys. Wherever possible examples are drawn from real surveys conducted by students and/or staff at the Polytechnic of North London. Bear in mind that there is a difference of approach which may at first seem strange to students in sociology and related subjects. Most surveys are conducted by personal interview with respondents, and most analysis is of a descriptive kind, taking the people themselves as units of analysis. Another, and more rigorous approach, is what we call explanatory, in which we attempt to explain rather than describe, and in which we look at variables rather than people. Both approaches are dealt with here. The basic idea Social research involves many weird and wonderful methods over which debate, often bitter, rages continuously. However, at some stage even the most virulently anti-positivist and anti-empiricist will need to be able to name, sort and count things, or to read, understand or even act on, reports based on things which have been named, sorted and counted. Perhaps the easiest way of explaining one of the most basic skills in statistics is to try to make sense of raw data through a process of naming, sorting and counting. For instance, take the following data relating to 20 sixth form students. Information is provided on their sex and on their intentions towards higher education. Student Sex H.E.?
1 Male Yes
2 Male No
3 Female Yes
4 Female No
5 Female No
6 Male No
7 Female No
8 Male No
9 Female No
10 Female Yes
11 Male Yes
12 Male No
13 Male Yes
14 Female No
15 Male Yes
16 Male No
17 Female No
18 Female No
19 Male No
20 Male No It is not easy to tell from these data how many males and females there are, let alone make any meaningful statement about the relationship between sex and plans for higher education. What can we do to make them easier to understand? The first thing we need to do is to sort them into some kind of order. We can do this by arranging all the males in one group and the females in another, or we can do it by sorting all those with H.E. plans into one group and the rest into another. Thus by sex:
Female Yes
Female No
Female No
Female No
Female No
Female No
Female Yes
Female No
Female No Total Females = 9 Male Yes
Male No
Male Yes
Male No
Male Yes
Male No
Male Yes
Male No
Male No
Male No
Male No Total Males = 11 ...and by college plans:
Male No
Female No
Male No
Female No
Male No
Female No
Male No
Female No
Male No
Male No
Female No
Female No
Male No
Female No Total with no college plans = 14 Male Yes
Male Yes
Female Yes
Male Yes
Female Yes
Male Yes Total with college plans = 6
If we want to look at both distributions together we can sort on both variables to yield: By sex and college plans:
Female No
Female No
Female No
Female No
Female No
Female No
Female No Total females with no college plans = 7 Female Yes
Female Yes Total females with college plans = 2 Male No
Male No
Male No
Male No
Male No
Male No
Male No Total males with no college plans = 7 Male Yes
Male Yes
Male Yes
Male Yes Total males with college plans = 4 These data can be summarised by tabulating one variable at a time in frequency distributions. Sex:
Female 9 45%
Male 11 55%
-----------
Total 20 100% College:
No 14 70%
Yes 6 30%
-----------
Total 20 100% If we want to summarise data from both variables at the same time we need to construct a contingency table. We do this by constructing a blank table with the same number of rows as there are categories in one of the variables, and the same number of columns as there are categories in the other. Let us take "Sex" as the column variable and "College plans" as the row variable. In this case both variables have only two categories, and so the table will have 2 rows and 2 columns, and therefore 4 cells. Sex Male Female
-----------------------------
I I I
No I I I
I I I
College -----------------------------
I I I
Yes I I I
I I I
----------------------------- These four cells form the body of the table into which we can now enter the counts from the list sorted on both variables at once. At the same time we enter outside the table the row-totals and column-totals from the original frequency distributions for each variable and the grand total for the number of cases in the whole table. Thus: Sex
(Raw data)
Male Female Row Total
-----------------------------
I I I
No I 7 I 7 I 14
I I I
College -----------------------------
I I I
Yes I 4 I 2 I 6
I I I
----------------------------- Column total 11 9 20
This is at least a little easier to interpret than the original sorted lists, but it is still difficult to answer a question as to whether males are more likely to want to go college than are females, or vice versa. To answer this question we need to ask not, "How many?", but, "What proportion?" of each sex have college plans. One further operation is now necessary - to standardise the data by converting the raw counts for each sex into percentages - to enable direct comparison between sexes. Sex
(% data)
Male Female Row Total
-----------------------------
I I I
No I 63.6 I 77.8 I 70.0
College -----------------------------
I I I
Yes I 36.4 I 22.2 I 30.0
-----------------------------
Column total 100.0 100.0 100.0
(Base for %) (11) (9) (20)
From this table we can now state that female sixth-formers are less likely to have plans for Higher Education.
|
