Monday, 2 December 2013

Determination of sample size


Determination of sample size is a difficult task.
Particularly in social research, where we consider
a set of variables, it becomes really difficult to ascertain
the size of sample. However, it is possible to determine
the size of sample by using a representative sampling
procedure.
Based on the assumptions of probability sampling
it is possible to select a sampling procedure which
will be representative. This helps researchers to
estimate the extent to which the sample statistics
are likely to differ from population parameters. This
means, if probability sampling method is used, it
is possible to ascertain the size of the sample that
will be needed if we want to have a given degree of
certainty that their sample results do not differ
by more than a specified value from those of the
population parameters.
There are a number of sampling techniques which
decrease the likelihood of misleading generalisations
based on sample statistics. These techniques assure
the inclusion of diverse elements of the population
in the sample by controlling the proportions of the
various types of elements. Alternatively, statistical
procedures are used in the analysis of the data.
Krejcie and Morgan (1970) have given a table in
which no calculations are needed to determine the
size of the sample.


Table is reproduced here for
your reference.
N        S           N          S            N                S
10      10         220        140          1200          291
15     14          230        144         1300           297
20      19          240         148        1400         302
25      24         250          152       1500          306
30      28       260          155        1600            310
35      32        270         159         1700            313
40       36       280        162         1800             317
45      40       290        165          1900              320
50       44      300        169         2000               322
55        48     320        175            2200                327
60        52     340         181          2400              331
65         56     360         186          2600              335
70        59     380          191        2800               338
75       63       400          196      3000              341
80       66     420           201         3500             346
85       70      440          205         4000               351
90       73       460           210         4500              354
95       76       480            214       5000               357
100       80     500            217          6000               361
110      76       550           226        7000              364
120      92        600            234         8000               367
130      97        650            242           9000              368
140     103       700              248         10000            370
150    108        750              254           15000             375
160    113         800             260           20000            377
170     118       850              265          30000          380
180     123       900             269           40000          380
190    127         950           274           50000          381
200    132        1000           278           75000           382
210    136        1100           285         1000000         384

Note –  N is population size, S is sample of size
For example if you want to know the sample size
required to be representative of the opinions of 300
social work students, refer table at N=300. The sample
size representative of the social work students in
this case will be 169. The table given above is applicable
to any defined population.