You are trying to develop a reliable test on fear to see why some people freak out in haunted houses while others aren't fazed at all. You've developed a test of 20 items in length (e.g. “I hate when things jump out at me”, “Loud, sudden noises don't bother me at all”). Individuals respond to each item by indicating the extent to which each statement describes them, on a scale from 1 (does not describe me at all) to 5 (describes me extremely well). The total scores (what a person can get on the test) range from 20 to 100. A low score means that they are aren't scared in haunted houses while a high score means they find them to be terrifying!

 a) You decide to assess the internal consistency of the test by administering the test to a sample of people waiting in line for a haunted house and dividing the test into two halves, producing two scores for each person. The correlation between the two halves is 0.73. Using the Spearman-Brown formula, calculate a reliability coefficient, correcting for the fact that the two tests are half the length of the original. How reliable does the test seem to be now? Why do we need to make this kind of correction?

 b) You administer your scale to 135 people, and get a scale mean of 77, with a standard deviation of 4.5. Using the internal consistency reliability that you calculated in question a, calculate the standard error of measurement for your scale. 

c) Suppose someone gets a score of 83 on your scale. What would the 95% confidence interval for that score be? What does this mean? 

d) Say you wanted to increase the reliability of your test to .85. How many items would you need to add to do this? Do you think you should add the extra items? Why or why not? What are some things to consider when making this type of decision?