Variables, Z Scores, Population and Output
Respond to the following short answer questions from Chapter Three in the Morgan, Leech, Gloeckner, & Barrett textbook:
If you have categorical, ordered data (such as low income, middle income, high income) what type of measurement would you have? Why?
D2.3.2. (a) Compare and contrast nominal, dichotomous, ordinal, and normal variables. (b) In social science research, why isn’t it important to distinguish between interval and ratio variables?
D2.3.3. What percent of the area under the standard normal curve is within one standard deviation of (above or below) the mean? What does this tell you about scores that are more than one standard deviation away from the mean?
D2.3.4. (a) How do z scores relate to the normal curve? (b) How would you interpret a z score of –3.0? (c) What percentage of scores is between a z of –2 and a z of +2? Why is this important?
D2.3.5. Why should you not use a frequency polygon if you have nominal data? What would be better to use to display nominal data?
Variables, Z Scores, Population and Output
A z-score (also called a standard score) gives you an idea of how far from the mean a data point is. But more technically it is a measure of how many standard deviations below or above the population mean a raw score is. A z-score tells you where the score lies on a normal distribution curve. A z-score of zero tells you the values is exactly average while a score of +3 tells you that the value is much higher than average. The z-score is positive if the value lies above the mean, and negative if it lies below the mean.