RESEARCH METHOD COHEN ok

MULTIDIMENSIONAL DATA: SOME WORDS ON NOTATION 581
Box 25.16
Reliability coefficients for peer descriptions
Liked peers
Disliked peers
Dimension Younger Older Younger Older
subjects subjects subjects subjects
Descriptiveness 0.83 0.91 0.80 0.84
Personal 0.76 0.80 0.84 0.77
involvement
Depth 0.65 0.71 0.65 0.75
Evaluative
consistency
0.69 0.92 0.76 0.69
Box 25.19
Expected frequencies in sex, voting preference and
social class
Middle class
Working class
Conservative Labour Conservative Labour
Men 55.4 61.7 77.0 85.9
Women 53.4 59.5 74.3 82.8
Source:adaptedfromWhiteley1983
Chapter 25
Source:PeeversandSecord1973
Box 25.17
Sex, voting preference and social class: a three-way
classification table
Middle class
Working class
Conservative Labour Conservative Labour
Men 80 30 40 130
Women 100 20 40 110
Source:adaptedfromWhiteley1983
Box 25.18
Sex, voting preference and social class: a three-way
notational classification
Middle class
Working class
Conservative Labour Conservative Labour
Men n 111 n 121 n 112 n 122
Women n 211 n 221 n 212 n 222
working class we assume that these variables are
statistically independent (that is to say, there is no
relationship between them) and simply apply the
multiplication rule of probability theory:
p 222 =(p 2++ )(p +2+ )(p ++2 )
=(0.49)(0.53)(0.58) = 0.15
This can be expressed in terms of the expected
frequency in cell n 222 as:
N(p 2++ )(p +2+ )(p ++2 ) = 550 (0.49)(0.53)(0.58)
= 82.8
Similarly, the expected fre quency in cell n 112 is:
and
and
N(p 1++ )(p +1+ )(p ++2 )where :
p 1++ = n 1++
n +++
= 280
550 = 0.51
p +1+ = n +1+
n +++
= 260
550 = 0.47
p ++2 = n ++2
n +++
= 320
550 = 0.58
Thus N(p 1++ )(p +1+ )(p ++2 )
= 550 (0.51)(0.47)(0.58) = 77.0
Box 25.19 gives the expected frequencies for the
data shown in Box 25.17.
With the observed frequencies and the expected
frequencies to hand, chi-square is calculated in the
usual way:
χ 2 = ∑ (O − E) 2
= 159.41
E
Whiteley (1983) observes that degrees of freedom
in a three-way contingency table is more complex
than in a 2 × 2classification.Essentially,however,
degrees of freedom refer to the freedom with which
the researcher is able to assign values to the cells,
given fixed marginal totals. This can be computed