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
Methods of presentation of data are:
Consider 35 i.i.d. observations X1, X2, ...., X15 and Y1, Y2, ..., Y20. Let R be the Wilcoxon's rank sum statistic based on the ranks of the X' s in the combined sample. Then the expected value of R is
Let I, J > 5. Consider two-way ANOVA, where the observations satisfy the linear model
yij = α + βi + γj + εij, 1 ≤ i ≤ I, 1 ≤ j ≤ J
E(εij) = 0, Var(εij) = σ2, \(\sum_{i=1}^{!} β_i=\sum_{j=1}^j γ_j=0 .\)
In this set - up
Let X1,X2,...,Xn be a random sample from exponential distribution with mean θ. Which of the following is NOT a sufficient statistic for θ?
A newly developed algorithm for random number generation needs to be tested. The first step is to check whether the sequence of numbers generated can be considered a random sample from the uniform distribution on the interval (0, 1). Which of the following is an appropriate nonparametric test?
