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Home arrow Analysing Survey Data arrow Introduction To Tabulation
Introduction To Tabulation PDF Print E-mail
Written by John F Hall   
08 Mar 2006

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.

 

Last Updated ( 30 Dec 2008 )
 
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