Brian E. Smith
McGill University
Montreal, Quebec, Canada
Email: smithb@management.mcgill.ca
MINITAB - Release 12
MINITAB is well established as a statistical package that combines ease-of-use with powerful computational algorithms. MINITAB has been adopted as the statistical software of choice in many colleges and universities because of its user-friendliness, and the ability to teach statistics using MINITAB, without having to spend a great deal of time instructing students in the use of the software. The graphic user interface is intuitive and a brief introduction is sufficient to get students started.
MINITAB, Release 12, has added several new features, which further enhance its usefulness as a teaching tool. In this introduction to Release 12 the focus is on those new features which are likely to be of interest to instructors and students in an introductory college course in statistics.
New in Release 12
General
Data and File Management
Basic Statistics
Analysis of Variance
Statistical Process Control
Reliability and Survival Analysis
Designed Experiments
Sample Size and Power
Graphics
DYNAMIC WORKSHEET SIZE
A new feature of MINITAB 12 is the ability to dynamically allocate worksheet size so that less memory is used when working with smaller worksheets. To see the options for memory allocation use Edit è Preferences è General to obtain the dialog boxes shown below:
The default is 100,000 cells, but may be smaller if you do not have enough available memory. In the second box above the worksheet size is changed to 50,000 cells.
DATA SET DESCRIPTIONS
MINITAB includes a useful collection of data sets. A helpful new feature is data set descriptions for each data set. Click on HELP and then type data set descriptions:
Scrolling down in the second screen above reveals the names of the more than 200 data sets in alphabetical order. For example, the data set SALARY is described below:
PROJECTS
A MINITAB project includes all of your work &emdash; multiple worksheets, text output from commands, graphs etc.
When you open a worksheet the following dialog box appears:
You can add as many worksheets as you wish to a project. Thus, if you want to add the data sets "acid" and "bears" to the same project you can open both worksheets and position them side by side on the screen:
DATA SUBSETTING
Create a new worksheet by selecting a subset of the data in an existing worksheet. For example, to create a worksheet consisting of a subset of the BEARS data set which includes rows satisfying the condition "ID < 100 and AGE > 50" select Manip è Subset Worksheet and click on Condition to complete the following box:
The result is the following worksheet:
The worksheet may also be split into two or more new worksheets by using the Manip è Split Worksheet command. For example if we wish to split the BEAR worksheet into two new worksheets by sex we would complete the following dialog box:
The result is the creation of two new worksheets (while retaining the original) as follows:
STORING DESCRIPTIVE STATISTICS
You can store descriptive statistics for each column, or for subsets within a column.
Choose Stat è Basic Statistics è Store Descriptive Statistics and select the variables for which you wish to store basic statistics. In the screen below we have selected the variables Age and Length.
Next click on Statistics and select the statistics you wish to store.
Click on OK to return to the previous dialog box and then click on OK again. The result is shown in the session window below:
Note that the mean, median and N (sample size) statistics are stored in the first available empty columns (in this case C13-C18) and that MINITAB automatically names the columns Mean1, Mean2, Median1, Median2, N1, and N2.
The stored constants can be displayed in the session window by using Manip è Display Data
Click on OK to obtain the result:
MTB > Print 'Mean1'-'N2'.
Data Display
Row Mean1 Mean2 Median1 Median2 N1 N2
1 43.4337 61.2825 32 61 83 143
PAIRED T-TEST AND T-INTERVAL
MINITAB 12 supports matched sample (paired) t-tests. Consider the worksheet EXAM.MTW located in the Student1 directory.
To test the hypothesis that the scores in Exam1 and Exam2 are the same at the 5% level of significance, choose Stat è Basic Statistics è Paired t… and select Exam1 and Exam2 as First sample and Second sample, respectively.
Next select the Options as shown below:
Click on OK to obtain the following results in the session window:
Paired T for Exam 1 - Exam 2
N Mean StDev SE Mean
Exam 1 8 82.50 13.31 4.71
Exam 2 8 84.62 7.82 2.76
Difference 8 -2.12 10.79 3.81
95% CI for mean difference: (-11.15, 6.90)
T-Test of mean difference = 0 (vs not = 0): T-Value = -0.56 P-Value = 0.595
We see that the 95% confidence interval for the mean difference is given by &emdash;11.15 £ m d £ 6.90 and the p-value for the two-sided test of hypothesis is 0.595. We conclude that there is no significant difference in mean test scores for the two examinations, based on the sample of 8 subjects.
ESTIMATION AND TESTS FOR 1 AND 2 PROPORTION PROBLEMS
The commands Stat è Basic Statistics è 1 Proportion invoke the following dialog box. The file BEARS.MTW is used for the illustration and column C4 (Sex) is selected. This column contains only 1s and 2s, where 1 = male and 2 = Female.
Click on OK to obtain the following results in the session window:
Test and Confidence Interval for One Proportion
Test of p = 0.5 vs p not = 0.5
Success = 2
Exact
Variable X N Sample p 95.0 % CI P-Value
Sex 44 143 0.307692 (0.233280, 0.390269) 0.000
MINITAB automatically defines Success as the higher number, so that in this case Success = 2 (Female). We see that there are 44 female bears in the sample of 143 bears, for a sample proportion of 0.307692. The confidence interval indicates that we are 95% confident that the proportion of female bears lies between 23.33% and 39.03%. The p-value shows us that the population proportion of female bears is significantly different from 0.5 (50%).
Inference concerning two population proportions may be performed by selecting the sequence Stat è Basic Statistics è 2 Proportions. In the resulting dialog box below we have chosen to perform a test of hypothesis for the difference between population proportions for summarized data, where the first population has a sample of size 200 with 110 successes and the second population is represented by a sample of size 100 with 40 successes.
The results are as follows:
Test and Confidence Interval for Two Proportions
Sample X N Sample p
1 110 200 0.550000
2 40 100 0.400000
Estimate for p(1) - p(2): 0.15
95% CI for p(1) - p(2): (0.0317913, 0.268209)
Test for p(1)-p(2)=0 (vs not = 0): Z = 2.49 P-Value = 0.013
We see that the test is significant with a p-value of 0.013.
P-VALUES FOR CORRELATION
Select Stat è Basic Statistics è Correlation to obtain the following dialog box.
In this dialog box the BEARS.mtw worksheet is active and the variables Age, Length (the height of the bear), Chest.G (chest girth) and Weight have been selected. In order to display the correlation matrix for these four variables, click on OK to display the following results. Note that the p-values are shown directly beneath the correlation coefficients. In this example all of the p-vlaues are equal to 0.000, indicating that all of the correlation coefficients are significant.
MTB > Correlation 'Age' 'Length' 'Chest.G' 'Weight'.
Correlations (Pearson)
Age Length Chest.G
Length 0.691
0.000
Chest.G 0.734 0.889
0.000 0.000
Weight 0.774 0.875 0.966
0.000 0.000 0.000
Cell Contents: Correlation
P-Value
SAMPLE SIZE AND POWER CALCULATIONS
The commands Stat è Power and Sample Size
allow you to calculate power and sample size for the following procedures:
1-Sample Z
1-Sample t
2-Sample t
1 Proportion
2 Proportions
One-Way ANOVA
2-Level Factorial Design
Plackett-Burman Design
Example&endash;Determining sample size for a 1-sample Z-test
A machine is supposed to fill containers with 32 oz of soda. The quality control department requires that the volume cannot vary more than 0.25 oz per container. The filling machine tolerances are set so that the process standard deviation s is 1. How many samples must be taken to estimate the mean container volume at a confidence level of 95% (a = .05) for power values of 0.5, 0.7, and 0.9?
Solution
Choose Stat è Power and Sample Size è 1-Sample Z and you will see the dialog box below.
Observe that there are three different calculations that can be performed:
In the dialog box, the choice Calculate sample size for each power value is selected, and the power values of 0.5, 0.7, and 0.9 are entered in the Power values box. The value of Sigma is set at 1.0 (the default value).
Click on OK to obtain the following results:
Power and Sample Size
1-Sample Z Test
Testing mean = null (versus not = null)
Calculating power for mean = null + 0.25
Alpha = 0.05 Sigma = 1
Sample Target Actual
Size Power Power
62 0.5000 0.5034
99 0.7000 0.7011
169 0.9000 0.9015
Note that MINITAB displays the sample size required to obtain the requested power values. Because the target power values would result in non-integer sample sizes, MINITAB displays the power (Actual Power) of the test to detect differences in volume greater than 0.5 oz using the next integer value for sample size. For example, if you take a sample of size 99 containers, the power for the test will be .7011.
Example&endash; Determining sample size for tests of proportions
In an educational research project you want to test the hypothesis that the proportion of high-school teachers who express job satisfaction has increased by at least 10% since the latest educational reforms took effect. Previous studies have shown 60% job satisfaction. Thus the test of hypothesis is Ho: p = 0.6 vs H1: p > 0.6. Assume a 5% level of significance.
Solution
Choose Stat è Power and Sample Size è 1-Propotion.
Next select the Options subdialog box and select an upper tail test:
Clicking on OK in both boxes we get the following results:
Power and Sample Size
Test for One Proportion
Testing proportion = 0.6 (versus > 0.6)
Calculating power for proportion = 0.7
Alpha = 0.05 Difference = 0.1
Sample
Size Power
100 0.6641
200 0.9079
400 0.9954
We conclude that if you select a random sample of 100 high-school teachers, you will have a probability of 66.41% of detecting a 10% increase in the proportion of teachers who express job satisfaction. Similarly sample sizes of 200 and 400 will result in probabilities of 90.79 and 99.59%, respectively, of detecting a 10% increase.
Power and Sample Size for One-way ANOVA
The following dialog box shows how to compute the power for an analysis of variance with 3 treatments (number of levels) each represented by a sample of size 12. In this analysis all sample sizes must be equal. The sample means are shown to be 127, 122, and 118, respectively. The population standard deviation estimate is taken to be s = 5.
The results are displayed below:
Power and Sample Size
One-way ANOVA
Sigma = 5 Alpha = 0.05 Number of Levels = 3
Corrected Sum of Squares of Means = 40.6667
Means = 127, 122, 118
Sample
Size Power
12 0.9729
HIGH RESOLUTION DOT PLOT
Select Graph è Dotplot to obtain the dialog box. The worksheet Acid.mtw is open and the variable Acid1 is selected.
Clicking on OK results in the following high-resolution
dotplot:
CONCLUSION
This ends our presentation of MINITAB 12. We have emphasized several of the features which are new to this release and which further enhance MINITAB as an excellent choice for teaching statistics.