# Identifying Parametric and Nonparametric Data

Label each of the following situations "P" if it is an example of parametric data or "NP" if it is an example of nonparametric data.

1. A manufacturer produces a batch of memory chips (RAM) and measures the mean-time-between-failures (MTBF). The manufacturer then changes a manufacturing process and produces another batch and again measures the MTBF. Did the change to the process improve the MTBF?

2. From a written survey where the respondents were asked to rate an individual on a scale of 1 to 5, one group rated an individual a 3.7, another group rated the individual a 4.3. Is the difference statistically significant?

3. A catering company is buying equipment in order to set up their own store. They have a choice of two ovens that they can purchase for the store. The used oven is $100 less than the new oven, but its heating calibration is off by 20 degrees. Which one is a better buy for them?

4. Jim Smith owns three real estate offices in Anytown. He has decided to open one more office, but he cannot decide between Hometown or Uptown as the town where he wants to locate. He will be comparing the mean number of homes sold per real estate agent, and the mean commission percentage earned by agents in the two towns to make his decision.

5. A study to determine if job absenteeism is distributed evenly over the week.

6. Mel's Diner has been surveying their customers for the past couple of years about their dining experience in the restaurant. The survey uses a scale of one to five, five being best to indicate customer satisfaction. Mel's customer satisfaction averaged 2.5 last year, but this year it is 2.9. Is this difference statistically significant?

7. Sally's Beauty Salon just opened for business. Sally assigns the stylists customers on a rotation basis so that everyone is kept busy all day. One month after she opened the salon, Sally's customer count for each stylist was

(a) 20 customers;

(b) 30 customers;

(c) 15 customers; and

(d) 25 customers.

Has Sally been fair in how she allocates customers to each of the stylists?

8. A comparison of salaries between male and female employees in the

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#### Solution Preview

Hi,

Lets look at the three rules that make data parametric:

In statistical terms a parameter is a statistic calculated from a set of data, e.g. a mean or a standard deviation are both parameters. In order to calculate parameters, and to use them in statistical analysis three assumptions must be tested against the data. The data is considered as parametric if these three assumptions are valid:

1. Can it be assumed that the data has been obtained from a population which is considered "normal" in the statistical sense. In other words if a sufficiently large sample of data was obtained from the population is it likely that it would be normally distributed. This may be known from similar research, but if not, and provided the sample is reasonably large, it may be possible to estimate from the sample whether this assumption is reasonable.

2. The populations from which the samples are drawn should have equal variances. This can be determined by inspection of the data, looking at the spread or standard deviation of the data. The F - test can also be used to test the hypothesis that the samples have been drawn from populations with the equal variance.

3. The data should be measured, at the very least, on an interval scale. Even this is not always easy to determine, but a useful "rule of thumb" is to compare two scores, (say) a 5 and a 10, and to ask yourself if a score of 10 means that there is exactly twice as much of that particular attribute compared with a score of ...

#### Solution Summary

This posting looks at eight different situations and assesses if the data is parametric (P) or non-parametric (NP) in nature. It first presents the three rules in determining the nature of the data, and then gives an explanation for each of the eight situations.