Calculating Paired Comparison Pairs
The question asks for the total number of pairs formed when comparing twelve attitude items using the paired comparison method. This is a problem of combinations, specifically finding the number of ways to choose 2 items from a set of 12.
Paired Comparison Formula
The number of pairs (or combinations) from a set of n items is calculated using the combination formula:
$ \text{Number of pairs} = \binom{n}{2} = \frac{n(n-1)}{2} $
Applying the Formula
In this study, there are 12 attitude items, so n = 12.
- Substitute n = 12 into the formula:
$ \text{Number of pairs} = \frac{12(12-1)}{2} $
- Simplify the expression:
$ \text{Number of pairs} = \frac{12 \times 11}{2} $
- Calculate the result:
$ \text{Number of pairs} = \frac{132}{2} = 66 $
Conclusion
Therefore, the total number of pairs in a study scaling twelve attitude items by the method of paired comparison is 66.
Important Questions from Statistics
- Match the LIST-I with LIST-II
LIST-I LIST-II A. Sampling error I. Values that describe the characteristics of a population B. Parameters II. The standard deviation of the sampling distribution C. Sampling fraction III. Variation among sample statistics due to change D. Standard error IV. Proportion of the population contained in a sample
Choose the correct answer from the options given below: Given below are two statements one is labelled as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A): Additive model considers the total of various components resulting in the given
values of the over all time series and it is stated as:
$Y=T+C+S+I$
Reason (R): Multiplicative model assumes that the various components interact in a
multiplicative manner to produce the given values of the over all time series and
can be stated as $Y=T \times C \times S \times I$
In the light of the above statements, choose the most appropriate answer from the options given
below:
Match List - I with List - II.
List - I List - II A. Sample proportion P = x/n I. $\frac{\sigma}{\sqrt{n}}$ B. Sample variance $S_1^2 = \frac{1}{n-1} \sum_{i=1}^{n}(xi-x̄)^2$ II. $\sigma^2 \sqrt{\frac{2}{n}}$ C. Sample variance $S^2 = \frac{1}{n} \sum_{i=1}^{n}(xi-x̄)^2$ III. $\sigma^2 \sqrt{\frac{2}{(n-1)}}$ D. Sample mean $\bar{x} = \frac{1}{n} \sum_{i=1}^{n}xi$ IV. $\sqrt{\frac{\pi(1-\pi)}{n}}$
Choose the correct answer from the options given below :- The measurement or determinations of length, height, weight, volume, area, pressure etc. comes under:
- Which of the following options explain what a 'mean' assumes ?
(i) an interval level of measurement
(ii) a nominal level of measurement
(iii) an ordinal level of measurement
(iv) a ratio level of measurement
