Minitab Modul

Module 1: Presentation of data Minitab Laboratory Work Sheet Part I Question 1 The residues (parts per million) of a drug in tissue from a random sample of 40 people, 20 days after oral administration of the drug, were as follows: 1.63 1.52 1.43 1.71

1.40 1.87 1.41 1.32

1.64 1.83 1.51 1.29

1.30 1.97 1.15 1.82

1.49 1.62 1.61 1.99

1.58 1.21 1.10 1.43

1.03 1.01 1.03 1.53

1.06 1.14 1.84 1.56

1.33 1.58 1.61 1.48

1.20 1.76 1.54 1.58

Obtain a histogram and interpret the data using a box plot. Obtain the sample mean and standard deviation, also the median and IQR. Compare the histogram and box plot. Which summary statistics are the most appropriate here? Find a suitable confidence interval for the population mean residue. (Note: See Guidelines on next page.) It is desired to estimate the mean residue in these circumstances to within ±0.05 parts per million with 95% confidence. How large a sample would you judge to be necessary in order to achieve this?

Question 2 The following data represent the prepatency times in days observed in 50 people who contracted an infectious disease from the times of their known first contacts with the infection: 12 12 12 13 14 11 13 14 12 12 13 13 15 14 14 14 12 12 15 12 14 12 14 11 14 14 15 12 11 14 12 14 12 13 15 14 13 13 13 14 12 12 13 12 14 13 14 12 13 12 Obtain the sample mean and the sample standard deviation, and estimate the population median and IQR. Using a box plot and histogram, comment on whether you think the data are skew or symmetrical. Choose the most suitable sample estimators of the population location and spread.

Question 3 In a nerve system the speed in metres per second at which impulses travelled in 48 axons of approximately the same diameter were as follows: 62 70 69 63

64 70 68 68

61 62 73 65

69 60 78 67

60 61 62 77

62 75 71 73

71 70 75 65

78 77 73 66

73 76 59 69

64 73 58 71

69 73 66 65

76 72 69 62

Using suitable plots and sample statistics, contrast these results with the following speeds for impulses observed in 40 axons all of a larger diameter: 68 79 78 70

68 64 73 70

73 74 69 71

67 72 65 67

70 69 69 68

74 79 68 61

68 82 71 66

70 76 71 65

66 64 70 68

69 70 63 71

Prepare a brief statement which communicates your findings to colleagues who haven’t seen the data.

Question 4 The creatinine levels (g/24h) in people suffering from extensive skin lesions and being treated with an anti-inflammatory steroid compound were monitored: 1.34 1.42 1.45 1.33 1.35 1.26 1.34 1.40 1.39 1.32 1.24 1.32 1.29 1.35 1.19 1.34 1.41 1.31 1.44 1.31 1.28 1.39 1.22 1.41 1.40 1.47 1.36 1.40 1.36 1.38 Prepare a brief report describing the characteristics of the data.

Guidelines Once you have selected the Minitab application, you can carry out analyses as required. The following guidelines for Question 1 should help you to get started. Go to the Worksheet window and click in the box corresponding to row 1 and column C1. Type the first data value (1.63) in this box and hit return. Type in the second data value (1.40) — it should appear in row 2 of column C1. Similarly, type the other values into the first column of the worksheet. Name C1 by typing ‘residue’ in the box below C1 and above the data values. To create a histogram of ‘residue’, click Graph, then Histogram. Click on residue, then select, OK. The plot should look something like this:

A box plot is obtained from the sequence Graph, Boxplot, residue, select, OK. The graph should look like this:

The mean, standard deviation and median are obtained by clicking Stat, Basic Statistics, Display Descriptive Statistics, residue, select, OK.

Descriptive Statistics

Variable residue

N 40

Mean 1.4778

Median 1.5150

Tr Mean 1.4753

Variable residue

Min 1.0100

Max 1.9900

Q1 1.2925

Q3 1.6275

StDev 0.2657

SE Mean 0.0420

In the output above “Tr mean” is the trimmed mean. It is the mean of the middle 90% of values. It is rarely used or quoted in practice and can be ignored in this course. Summary statistics can also be obtained using Calc, Column Statistics then click on the statistic of interest and select residue, then click OK. Note however that you can only select one statistic at a time. A t-interval is calculated using Stat, Basic Statistics, 1-sample t. (You could also try a z-interval; you need to supply a value for sigma). Your output should look something like this: Confidence Intervals Variable residue

N 40

Mean 1.4778

StDev 0.2657

SE Mean 0.0420

(

95.0 % CI 1.3928, 1.5627)

Details of how to choose a sample size for a mean are given in the notes for module 1 on pages 11–12. To perform the calculations, you can either use your own handheld calculator or use Minitab. Within Minitab, the simplest approach is to enable the prompt line in the Session window (Editor, Enable Commands) and type commands. For the sample size calculation in question 1, s = 0.2657 (from the Descriptive Statistics) and a = 0.05. The following commands could be typed into Minitab at the “MTB >” prompt: let k1 = (1.96**2) * (0.2657**2) / (0.05**2) print k1 Note that Minitab uses K1, K2, etc to store constants. The output from the above commands appears as, Data Display K1

108.481

suggesting that the residue would need to be measured in 109 individuals to enable estimation of the sample mean to within ±0.05 parts per million with 95% confidence. To print and/or save your Minitab workings and plots, see the handout ‘Reference Guide to Minitab and Computing’. Complete the remaining questions in a similar way. Choose File, Exit to exit Minitab.

Module 1: Presentation of data Minitab Laboratory Work Sheet Part II Question 5 See question 2 in part I. Let p be the proportion of such people in whom the prepatency time is 14 days or more. What is the sample proportion pˆ? Use this to calculate a 95% confidence interval for p. If it is required to estimate p to within ±0.1, how large a sample would you recommend be taken (a) if 95% confidence in the accuracy is required, (b) if 99% confidence in the accuracy is required?

Guidelines Firstly, we need to determine the number of people with prepatency times greater than or equal to 14 days. One way to achieve this is to sort the data (Manip, Sort and sorting by the column of times and placing the sorted data into a new column. You need to Sort by the column of times), then note the number of times satisfying the criteria and convert that to a proportion (you should find that p = 0.38). To calculate a confidence interval for a proportion, go to Stat, Basic Statistics, 1 Proportion. Check the Summarized data box and enter 50 and 19 for the number of trials and successes respectively. Sample size calculations can be performed using the prompt line in the Session window as in Part I, for example let k1 = (1.96**2) * 0.38 * (1-0.38) / (0.1**2) prin k1 suggesting that the prepatency times would need to be measured in 91 people to enable estimation of the sample proportion, p = 0.38, to within ±0.1 with 95% confidence.