For a 2x2 Contingency Table:
·Rates, Risk
Ratio, Odds, Odds Ratio, Log Odds
·Phi Coefficient of
Association
·Chi-Square Test of Association
·Fisher Exact
Probability Test
For two groups of subjects, each sorted according to the absence or presence
of some particular characteristic or condition, this page will calculate
standard measures for Rates, Risk Ratio, Odds, Odds Ratio, and
Log Odds. It will also
calculate the Phi
coefficient of association;T
perform a chi-square
test of association, if the sample size is not too small; andT
perform the Fisher
exact probability test, if the sample size is not too large. [Although the Fisher test is traditionally used with
relatively small samples, the programming for this page will handle fairly
large samples, up to about n=1000, depending on how the
frequencies are arrayed within the four cells.]T
For intermediate
values of n, the chi-square and Fisher tests will both be performed.
To proceed, enter the values of X0Y1,
X1Y1, etc., into the designated cells. When all four cell
values have been entered, click the «Calculate» button. To perform a new
analysis with a new set of data, click the «Reset» button.
The logic and computational details of the Chi-Square and Fisher tests are
described in Chapter 8 and Subchapter 8a, respectively, of Concepts
and Applications.
Data EntryT
|
| Condition
|
|
| Expected Cell
Frequencies
per
Null Hypothesis
|
|
| absent
| present
| Totals
|
|
Group 1
|
|
|
| Rate
| Risk
Ratio
| Odds
| Odds
Ratio
| Log
Odds
|
Group 1
|
|
Rate = proportion in
group with condition present
Risk
Ratio = Rate[1]/Rate[2]
Odds[1] = present[1]/absent[1]
Odds[2] =
present[2]/absent[2]
Odds Ratio = Odds[1]/Odds[2]
Log Odds = natural
logarithm of Odds Ratio
|
| Chi-Square
|
| Chi-square is calculated only if all
expected cell frequencies
are equal
to or greater than 5. The Yates value
is corrected for
continuity; the Pearson
value is not. Both probability estimates
are
non-directional.
|
Phi
| Yates
| Pearson
|
|
|
Fisher Exact Probability Test:T