Q5 Knowledge Base

Research Methods -- CRJU 3002 – Quiz 5

Survey Research (95% Confidence Interval)

 The percentages of scores between each Z-score are not equal.. The percentages between each Z-score represent the likelihood of a person’s score falling in that range in the population. In other words, this is how the normal curve is used to compute the posterior probabilities on metric variables.

The 95% Confidence Interval

      This problem is used when you want to know what scores are least likely to be randomly drawn from the population. If a score is unlikely to be randomly drawn, and turns up any way, there are only two possible explanations:  It happened by chance (unlikely), or there is a good reason (which lends support to the “theory” being tested).

      We want to know the two scores between which 95% of all the scores in the population could be randomly drawn. We do this to isolate the 5% of scores that are unlikely to be randomly drawn.

      This is how it works:  In every population, there is a score above the mean that includes 47.5% of the distribution, and a score below the mean that includes 47.5% of the distribution. We call it the “95% confidence interval” around the mean. 

      This problem is similar to a “find the percentage between two scores” problem, one score falls 47.5% below the mean, and the other falls 47.5% above the mean.

        What we are doing is finding a score when given a percentage. The percentage is always 47.5%.  When you include 47.5% below the mean and 47.5% above the mean, you end up with the middle 95% of the distribution. So we realize that the Z-scores for this percentage (47.5%) are always going to be -1.96 and +1.96.