Dr. Nancy Pfenning

September 2013

After starting MINITAB, you'll see a **Session window** above
and a **worksheet **below. The Session window displays
non-graphical output such as tables of statistics and character
graphs. A worksheet is where we enter, name, view, and edit data. At
any point, the session or worksheet window (whichever is currently
active) may be printed by clicking on the print icon (third from left
at top of screen) and clicking on **OK**. If multiple worksheets are
in use, you may acess other worksheets from the Window menu, upper right.

The menu bar across the top contains the main menus: File, Edit, Data, Calc, Stat, Graph, Editor, Tools, Window, and Help. Beneath the menu bar is the Toolbar which provides shortcuts for several important actions.

In the instructions that follow, text to be typed will be underlined. Menu instructions will be set in boldface type with the entries separated by pointers.

Each data set is stored in a **column**, designated by a
"C" followed by a number. For example, C1 stands for Column
1. The column designations are displayed along the top of the
worksheet. The numbers at the left of the worksheet represent
positions within a column and are referred to as **rows**. Each
rectangle occurring at the intersection of a column and a row is
called a **cell**. It can hold one observation.

The **active cell** has the worksheet cursor inside it and a
dark rectangle around it. To enter or change an observation in a
cell, we first make the cell active and then type the value.

Directly below each column label in the worksheet is a cell optionally used for naming the column. To name the column, we click on this cell and type the desired name.

**Example A**: Suppose we want to store heights, in inches, of
female recitation members [64, 65, 61, 70, 65, 66, ...] into column C1
and name the column "FHts". Just click in the name cell for this
column, type __FHts__, and press the "Enter" key. Then
type __64__, Enter, __65__, Enter, __61__, Enter, and so
on. Note that a height of ``5 foot 7" would be entered as 67, and
``6 foot 1" would be 73.

**Example B**: To store male heights, name column C2
"MHts" and enter those data values in this column.

**Note:** After viewing each graph, close it by clicking the red X in the upper right corner; answer no (don't save).

**Example C:** For sample size N, number of non-responses N*, mean,
SE Mean,
standard deviation, minimum, Q1, median, Q3, and maximum of female height
data,

- Choose
**Stat>Basic Statistics>Display Descriptive Statistics**... - Specify FHts in the
**Variables**text box (instead of typing it directly, you may double-click on FHts in the box on the left). - Click
**OK**.

For histogram(**D**), stemplot(**E**), and boxplot(**F**)
of female height data,

**Example D:**

- Choose
**Graph>Histogram**... - Double-click on the
**Simple**histogram (upper left). - Specify FHts in the
**Graph variables**text box. - Click
**OK**.

**Example E**:

- Choose
**Graph>Stem-and-Leaf**... - Specify FHts in the
**Graph variables**text box. - Click
**OK**.

**Example F:**

- Choose
**Graph>Boxplot**... - Double-click on the
**Simple**boxplot, under**One Y**(upper left). - Specify FHts in the
**Graph variables**text box. - Click
**OK**.

To produce side-by-side boxplots of male and female heights,

- Choose
**Graph>Boxplot**... - Double-click on the
**Simple**boxplot under**Multiple Y's**(lower left). - Specify FHts and MHts in the
**Graph variables**text box. - Click
**OK**.

**Example G**: To combine and sort female and male recitation members'
heights,

- Choose
**Data>Stack>Columns**. - Specify FHTS and MHTS with a space between them as columns to be stacked.
Click the
**Column of current worksheet**button and type HTS in this box (Click**OK**). - Choose
**Data>Sort**. - Specify HTS in the
**sort columnn(s)**text box, HTS in the**By column**box, and SORTEDHTS in the**Store sorted data in:**box, either in**New worksheet**or**Original column**or**Column of current worksheet**. - Click
**OK**.

The remaining examples work with existing data that are to be downloaded
into MINITAB. Data for dozens of variables about hundreds of students
can be accessed on Dr.
Pfenning's website http://www.pitt.edu/~nancyp/stat-0200/index.html
where the file name is highlighted.
To download into MINITAB, type ctrl A to highlight and ctrl C to copy. Start up
MINITAB [or if it's already running, choose **File>New>Minitab Worksheet**]
, type ctrl V to paste it. If it asks about delimiters, click OK.
** Important:** When you paste the data, have the cursor on the blank shaded cell under C1 but above Row 1. This puts the column names where they belong, so they will not be treated as data values.

** Example H** Suppose all heights are entered in a single column
Height, and genders (male or female) are entered in the column Gender. To compare heights
of students in the two gender groups,

- Choose
**Stat>Basic Statistics>Display Descriptive Statistics**... - Specify Height in the
**Variables**text box. - Specify Gender in the
**By variables**text box. - Choose
**Graphs**and check**Boxplot of data**. - Click
**OK**. - Click
**OK**.

Now suppose all earnings are entered in a single column Earned, and Year contains values 1, 2, 3, 4, and Other. To compare earnings of students in Years 1 to 4 only (if for some reason the Others are to be omitted),

- Choose
**Data>Unstack columns**. - Specify Earned for
**Unstack the data in**and Year for**Using subscripts in**. By default, the unstacked columns Earned_1 to Earned_Other will be stored**In a new worksheet**, but you can also request**After last column in use**. - Click
**OK**. - Obtain desired descriptive statistics and displays for Earned_1 to
Earned_4. [Boxplots would be
**Simple**under**Multiple Y's**as in the second part of Example F.]

- Choose
**Graph>Boxplot**. - Double-click on the
**With groups, One Y**(upper right). - Specify Height in the
**Graph variables**text box and Gender in the**Categorical variables for grouping**text box. - Click
**OK**.

**Example J** We can use MINITAB to take a random sample of, say,
10 heights from those in a data column.

- Choose
**Calc>Random Data>Sample From Columns**. - Type
__10__in the box to specify how many rows, and after "from column(s)" enter__Height__. - After "Store samples in:" type the name of a new column, such as
__SampledHts__. Do not check the "sample with replacement" box. - Click
**OK**.

Note: for independent samples (such as for two-sample t or ANOVA),
perform the above steps twice. To sample pairs of values (such as for
paired t or regression), two columns ** of equal length **
can be specified (eg. MOMAGE and DADAGE)
and then two empty columns must be specified for storage.

**Example K**: We can also use MINITAB to randomly select 5 from 100
names in a hard-copy list. Assume the names are listed alphabetically, where
the first name corresponds to the number 1 and the last corresponds to the
number 100.

- Choose
**Calc>Make Patterned Data>Simple Set of Numbers...** - Type
__NUMBERS__in the**Store Patterned Data**text box. - Click in the
**From first value**text box and type__1__. - Click in the
**To last value**text box and type__100__. - Click
**OK**. - Choose
**Calc>Random Data>Sample From Columns...** - Type
__5__in the small text box after**Number of rows to sample**. - Click in the
**From columns**text box and specify NUMBERS. - Click in the
**Store samples in**text box and type SampledNumbers. - Click
**OK**.

Note: Confidence intervals are automatically provided in the output for a hypothesis test, but it will not be the standard confidence interval unless the two-sided alternative has been selected.

**Example L: ** Assume Verbal SAT scores of surveyed students
to be a random sample taken from scores of all Pitt
students, whose mean score is unknown [actually, it is about 625] and
standard deviation is assumed to be 100. Use sample scores to obtain a 90%
confidence interval for population mean score.

- Choose
**Stat>Basic Statistics>1-Sample Z...** - Specify VerbalSAT in the
**One or more samples, each in a column**box. - Click in the
**Known standard deviation**text box and type__100__. - Select the
**Options**button. - Click in the
**Confidence level**text box and type__90__. - Make sure
**Alternative**is at the default**Mean not equal hypothesized mean**. - Click
**OK**. - Click
**OK**.

**Example M**: Assume Verbal SAT scores of surveyed students
members to be a random sample taken from scores of all Pitt students,
whose mean **and** standard deviation are unknown. Use
sample scores to obtain a 99% confidence interval for population mean
score.

- Choose
**Stat>Basic Statistics>1-Sample t...**. - Specify VerbalSAT in the
**One or more samples, each in a column**box. - Select the
**Options**button. - Click in the
**Confidence level**text box and type__99__. - Make sure
**Alternative**is at the default**Mean not equal hypothesized mean**. - Click
**OK**. - Click
**OK**.

**Example N**: Test the null hypothesis that Verbal SAT scores of
surveyed students are a random sample taken from a
population with mean 600 against the alternative that the mean is
greater than 600. Assume population standard deviation to be
100. [If population standard deviation were **not** assumed to be
known, a **1-Sample t** test would be used, and **Standard deviation
** would not
be specified.]

- Choose
**Stat>Basic Statistics>1-Sample Z...** - Specify VerbalSAT in the
**One or more samples, each in a column**box. - Click in the
**Standard deviation**text box and type__100__. - Check the
**Perform hypothesis test**box and enter__600__in the**hypothesized mean**box. - Select the
**Options**button. - Under
**Alternative**select**Mean greater than hypothesized mean**. - Click
**OK**. - Click
**OK**.

**Example O**: Do students' dads tend to be older than their moms?
Test the null hypothesis that the mean of differences: (ages of dads minus
ages of moms) for the larger population is zero vs. the
alternative that the mean of differences is positive.

- Choose
**Stat>Basic Statistics>Paired t...** - Under
**Each sample is in a column**click in the**Sample 1**text box and specify DadAge. - Click in the
**Sample 2**text box and specify MomAge. - Click in the
**Options**button. - Make sure the
**Hypothesized Difference**text box says__0.0__. - Click the arrow button at the right of the
**Alternative**drop-down list box and select**Difference greater than hypothesized difference**. - Click
**OK**. - Click
**OK**.

**Example P**: Use MINITAB to verify that female heights are
significantly less than male heights. Procedure may or may not be pooled.

- Choose
**Stat>Basic Statistics>2-Sample t...** - Select
**Both samples are in one column**and enter Height for Samples and Gender for Sample IDs... - Click in the
**Options**button. - Verify that the hypothesized difference is 0.0.
- Click the arrow button at the right of the
**Alternative**drop-down list box and select**Difference less than hypothesized difference**(MINITAB considers the difference Females minus Males, with Females first because F comes before M in the alphabet). - If sample standard deviations are close and you have reason to assume
equal population variances, you may select the
**Assume equal variances**check box, which carries out a pooled procedure. Otherwise, unselect it. - Click
**OK**. - Click on
**Graphs**and select**Boxplot**. - Click
**OK**. - Click
**OK**.

Alternatively, the data may occur in two columns of height values, one for each sex.

- Select the
**Each sample is in its own column**option button if that is the case. - Click in the
**Sample 1**text box and specify FHeights. - Click in the
**Sample 2**text box and specify MHeights. - Proceed as above.

**Example Q**: Use MINITAB to examine the relationship between
ages of students fathers and ages of their mothers; after
verifying the linearity of the scatterplot, find the correlation
**r** and the regression equation; produce a fitted line plot. Produce a
histogram of residuals and a plot of residuals vs. the explanatory variable
(MomAge). Obtain a confidence interval for
the mean age of all fathers when mothers are 40, and a prediction
interval for an individual father when the mother is 40 years old.

- Choose
**Graph>Scatterplot**and double-click on**Simple**. - Specify DadAge in the
**Y variables**text box next to the**1**. - Specify MomAge in the
**X variables**text box next to the**1**. - Click
**OK**. - Choose
**Stat>Basic Statistics>Correlation...** - Specify MomAge and DadAge in the
**Variables**text box. - Click
**OK.** - Choose
**Graph>Scatterplot**and double-click on**With regression**. - Specify DadAge in the
**Y variables**text box next to the**1**. - Specify MomAge in the
**X variables**text box next to the**1**. - Click
**OK.** - Choose
**Stat>Regression>Regression>Fit Regression Model**. - Specify DadAge in the
**Responses**text box. - Click in the
**Continuous Predictors**text box and specify MomAge. - Click on the
**Graphs...**box. - Check the
**Histogram of residuals**box. - In the
**Residuals versus the variables**box, specify MomAge. - Click
**OK.** - Click
**OK.** - Choose
**Stat>Regression>Regression>Predict**. - Verify DadAge appears in the
**Response**text box. - Verify MomAge appears below.
- Type
__40__in first line of MomAge box. - Click
**OK.**

**Example R: **Use MINITAB to see if there is a significant
difference in mean earnings of freshmen, sophomores, juniors, and
seniors in the class. Include side-by-side boxplots to display the data.

- First unstack earnings according to year (see Example H).
- Choose
**Stat>ANOVA>Oneway**. - Choose
**Response data are in a separate column for each factor level**. - Specify Earned_1, Earned_2, Earned_3, Earned_4 in the
**Responses**text box. - Click on the
**Graphs...**box - Check the box for
**Boxplot of data**. - Click
**OK.** - Click
**OK**.

You may also compare mean responses of stacked data as it appears in
the original worksheet by specifying
Earned in the Response box and Year as the Factor variable, using
**Stat>ANOVA>One Way**
and **Response data are in one column for all factor levels**. In this case, the ``Other" students
cannot be omitted.

**Example S:** Use MINITAB to do inference about the population
proportion of males/females. [The following only works for categorical
variables like Gender that have just 2 possibilities.]

- Choose
**Graph>Pie Chart**and enter Gender as the**Categorical variables**. - Click
**OK**. - Choose
**Stat>Basic Statistics>1Proportion...** - Choose
**One or more samples, each in a column**. - Specify Gender in the box below.
- Check
**Perform hypothesis test**. - Type
__0.5__in the Hypothesized proportion box. - Click on
**Options**to specify a one-sided alternative or to opt for Method to be a normal approximation. - Click
**OK**.

**Example T: ** Use MINITAB to do inference about the population
proportion preferring a certain color. These steps may be followed if the
variable of interest has more than 2 possibilities.

- Choose
**Graph>Pie Chart**and enter FavoriteColor as the**Categorical variables**. - Click
**OK**. - Choose
**Stat>Tables>Tally Individual Variables**. - Specify FavoriteColor in the
**Variables**box. - Check
**Counts**for**Display**box. - Click
**OK**. - Note the count in the color of interest (events) and the total count N (trials).
- Choose
**Stat>Basic Statistics>1Proportion**. - Choose
**Summarized data**. - Specify the numbers of events and trials.
- Check
**Perform hypothesis test**and type__0.125__as the hypothesized proportion - Click on
**Options**and specify a one-sided alternative if you suspected more or fewer than 1/8 would prefer that color. Under**Method**check "Normal approximation" to make your results consistent with our calculations by hand. - Click
**OK**. - Click
**OK**.

**Example U: ** Use MINITAB to check for a relationship between
gender and year at Pitt.

- Choose
**Stat>Tables>Cross Tabulation and Chi-Square**. - Choose
**Raw data (categorical variables)**. - Decide which should be the explanatory variable; in this case, it would
be Gender. Specify Gender for
**Rows**and Year for**Columns** - For data analysis, check
**Counts**and**Row percents**under**Display**. The row percents are conditional percentages for respective values of the explanatory variable. - For statistical inference, check the
**Chi-Square test**under the**Chi-Square**box. - Click
**OK**. - Click
**OK**. - Choose
**Graph>Bar Chart...** - Double-click on
**Cluster**. - Enter Gender and Year as the
**Categorical variables**(Gender first because it is the explanatory variable, graphed horizontally). - Click
**Chart Options**. - Select
**Show Y as Percent**and**Within Categories at level 1**to get side-by-side charts of percentages within each gender group. - Click
**OK**. - Click
**OK**.

If a two-way table has been created to summarize the data (as in the **Cross Tabulation** option) you may enter the counts directly into r rows (where r is the number of possibiities for the explanatory variable) and c columns (where c
is the number of possibilities for the response variable) in a Minitab
worksheet. For instance, for the first (Female) row enter 32 for the 1st
(Year) column, 196 for the 2nd column, 71 for the 3rd, 25 for the 4th, and 7 for Other. For the second (Male) row enter 13, 114, 62, 28, 11, respectively,
for the five columns 1st through Other.
Then
choose **Stat>Tables>Chi-Square Test for Association** and
** Summarized data in a two-way table**. Then type the five column names 1st through Other in the box ** Columns containing the table** and Click OK.