Introduction

Scales

Likert Scales

Bogardus
Social
Distance
Scales

Guttman
Scales

Indices

Additional Considerations

Typologies

Measurement
Error

Aids

Table 7.1. Frequency distribution of total scores for 125 respondents

After these groups are identified, means or medians are calculated for the responses for each item for each group. The mean (or what is commonly known as the average) is the sum of scores divided by the number of scores added. The median is the middle score in any set of numbers; half of the numbers or scores are above the median score, half are below it. Calculation of the mean and median are described in detail in Chapter 17.

For our item analysis, let's use the mean for responses to the 7 items for highest and lowest scoring groups. Illustrative mean scores for each item for the two groups are shown in Table 7.2

Next, we compare the means (or it could be medians) between the low and high groups for each item.   A larger difference between the means indicates that the responses to that item differentiate between the low and high scorers. Little or no difference indicates that the items failed to discriminate between the two groups. Using these guidelines we would select items having the largest differences between the means for low and high scoring groups.

In our example, item 5, shows little difference between the two means. Respondents having low or high composite scores gave about the same response to this item. Also, the difference for item 4 is a lot smaller than differences for other items. Since neither would add much to the total scores, both are eliminated.

Table 7.2. Means for the lowest 25% and highest 25%

Larger mean differences are found for the remaining items. Deciding on what is "small" or "large" rests on judgment, unless you want to do a statistical test for the significance of the difference between the means. (This test is explained in Chapter 19). Statistical tests, however, are not necessary and require a considerable amount of tedious calculating. Judgment, based on the sizes of differences between sets of means, generally is sufficient. In making decisions, remember that the means are based on small numbers.   In our example the raw data for calculating the means ranged from 0 to 4. Thus, the difference of 1.22 for item 2, the smallest difference we accepted, may seem small, but it is quite large when considered in terms of the 0 to 4 range. The mean of 0.95 for the low scoring group was just under the score for disagree, which was scored as 1, while the mean for the high scoring group of 3.17 was just over the score of agree, which was scored as 3. Item 2, therefore, would be considered a strong item.