Statistics2x2'x2'yates 'x'2

In Statistics Yates's correction for continuity (or Yates's chi-square test) is used in certain situations when testing for independence in a contingency table, let us understand it with illustration.

1. Statistics in Psychology
presentation

2. Presentation topic
2x2’x2’ yates ‘x’2
( with illustration)
Presented by: Mangal Kardile

3. Yates's correction for continuity
•Theory by Frank Yates (1902-1994) was one of
the pioneers of 20th century Statistics
•In Statistics Yates's correction for continuity (or
Yates's chi-square test) is used in certain
situations when testing for independence in a
contingency table.
•In some cases, Yates's correction may adjust
too far, and so its current use is limited.

4. Yates's correction for continuity
Yates's chi-square test - used in certain
situations when testing for independence in a
contingency table
Right-handed Left-handed Totals
Males
Females
43 9
44 4
52
48
Total 87 13 100

5. Chi square – a Goodness of Fit
•Karl Pearson- used x
2
distribution for
devising a test

•To determine how well experimentally
obtained results fit in the results expected
theoretically on some hypothesis.

6. Hypothesis of Normal distribution
•Expected results or frequencies are determined
on the basis of the Normal distribution curve
•E.g. Classification of group of 200 individuals
as very good, good, average, poor, very poor
•The observed frequencies are –
Very good
55
Good
45
Average
35
Poor
35
Very poor
30

7. Normal distribution curve
•Normal distribution of adjustment scores
into five categories

8. Chi square testing
fo- observed frequency
Computation of x
2
Contingency table
fe- expected frequency
•
fo fe fo – fe ( fo - fe )
2
( fo – fe )
2
/ fe
14 19.4 -5.4 29.16 1.50
66 62.5 3.5 12.25 0.19
10 8 2.0 4.00 0.50
27 21.6 5.4 29.16 1.35
66 69.5 -3.5 12.25 0.18
7 9 -2.0 4.00 0.44
Total 190 190 x
2
= 4.16

9. Using Yates's correction
•When problem arising particularly in a 2x2 table
with 1 degree of freedom
•The procedure is to subtract 0.5 from the
absolute value of the difference between
observed and expected frequency
•So each (fo) which is larger than it’s (fe) is
decreased by 0.5 and each (fo) which is
smaller than it’s (fe) is increased by 0.5

10. Yates's correction for small data
•The effect of Yates's correction is to prevent
overestimation of statistical significance for small data.
•This formula is chiefly used when at least one cell of the
table has an expected count smaller than 5.
•Unfortunately, Yates's correction may tend to
overcorrect. This can result in an overly conservative
result that fails to reject the null hypothesis when it
should.
•So it is suggested that Yates's correction is unnecessary
even with quite low sample sizes,such as

11. Pearson’s chi squared statistics
•The following is Yates's corrected version of Pearson’s chi-sqared statistics
•where:
•Oi = an observed frequency
•Ei = an expected (theoretical) frequency, asserted by the null hypothesis
•N = number of distinct events
ORA a b NA
B c d NB
NS NF N
S F

12. Summary
•The chi square test is used as a test of significance,
when we have data that are given or can be expressed
in frequencies / categories.
•It does not require the assumption of a normal
distribution like z and t or other parametric tests.
•Sum of the expected frequencies must always be equal
to the sum of the observed frequencies in a x
2
test.
•It is a completely distribution free and non-parametric
test.

13. Thank you