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 1.40 1.64 1.30 1.49 1.58 1.03 1.06 1.33 1.201.52 1.87 1.83 1.97 1.62 1.21 1.01 1.14 1.58 1.761.43 1.41 1.51 1.15 1.61 1.10 1.03 1.84 1.61 1.541.71 1.32 1.29 1.82 1.99 1.43 1.53 1.56 1.48 1.58

Obtain a histogram and interpret the data using a box plot. Obtain the sample meanand standard deviation, also the median and IQR. Compare the histogram and box plot.Which summary statistics are the most appropriate here? Find a suitable confidenceinterval 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 partsper million with 95% confidence. How large a sample would you judge to be necessaryin order to achieve this?

Question 2

The following data represent the prepatency times in days observed in 50 people whocontracted an infectious disease from the times of their known first contacts with theinfection:

12 12 12 13 14 11 13 14 12 1213 13 15 14 14 14 12 12 15 1214 12 14 11 14 14 15 12 11 1412 14 12 13 15 14 13 13 13 1412 12 13 12 14 13 14 12 13 12

Obtain the sample mean and the sample standard deviation, and estimate the populationmedian and IQR. Using a box plot and histogram, comment on whether you thinkthe data are skew or symmetrical. Choose the most suitable sample estimators of thepopulation location and spread.

Question 3

In a nerve system the speed in metres per second at which impulses travelled in 48 axonsof approximately the same diameter were as follows:

62 64 61 69 60 62 71 78 73 64 69 7670 70 62 60 61 75 70 77 76 73 73 7269 68 73 78 62 71 75 73 59 58 66 6963 68 65 67 77 73 65 66 69 71 65 62

Using suitable plots and sample statistics, contrast these results with the following speedsfor impulses observed in 40 axons all of a larger diameter:

68 68 73 67 70 74 68 70 66 6979 64 74 72 69 79 82 76 64 7078 73 69 65 69 68 71 71 70 6370 70 71 67 68 61 66 65 68 71

Prepare a brief statement which communicates your findings to colleagues who haven’tseen the data.

Question 4

The creatinine levels (g/24h) in people suffering from extensive skin lesions and beingtreated 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 1.321.24 1.32 1.29 1.35 1.19 1.34 1.41 1.31 1.44 1.311.28 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 columnC1. Type the first data value (1.63) in this box and hit return. Type in the second datavalue (1.40) — it should appear in row 2 of column C1. Similarly, type the other valuesinto 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 Statis-tics, Display Descriptive Statistics, residue, select, OK.

Descriptive Statistics

Variable N Mean Median Tr Mean StDev SE Mean

residue 40 1.4778 1.5150 1.4753 0.2657 0.0420

Variable Min Max Q1 Q3

residue 1.0100 1.9900 1.2925 1.6275

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 onthe statistic of interest and select residue, then click OK. Note however that you canonly select one statistic at a time.

A t-interval is calculated using Stat, Basic Statistics, 1-sample t. (You could also trya z-interval; you need to supply a value for sigma). Your output should look somethinglike this:

Confidence Intervals

Variable N Mean StDev SE Mean 95.0 % CI

residue 40 1.4778 0.2657 0.0420 ( 1.3928, 1.5627)

Details of how to choose a sample size for a mean are given in the notes for module1 on pages 11–12. To perform the calculations, you can either use your own handheldcalculator 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 enableestimation 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 Guideto 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 p̂? 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 recommendbe 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 thanor equal to 14 days. One way to achieve this is to sort the data (Manip, Sort andsorting by the column of times and placing the sorted data into a new column. You needto Sort by the column of times), then note the number of times satisfying the criteriaand 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 numberof trials and successes respectively.

Sample size calculations can be performed using the prompt line in the Session windowas 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 enableestimation of the sample proportion, p = 0.38, to within ±0.1 with 95% confidence.