Dr. Nancy Pfenning

May 2014

After starting MINITAB, you'll see a **Session window** above
and a **worksheet **below. The Session window displays
both graphs and non-graphical output such as tables of statistics and character
graphs. A worksheet is where we enter, name, view, and edit data.
The ** Navigator** bar at the left enables you to access any of the summaries or graphs produced during your session. You can highlight a specific item and
right-click to Delete or Export as PDF or HTML.

The menu bar across the top contains the main menus: File, Edit, Data, Graph, Statistics, View, Window, and Help. Beneath each item in the menu bar is a drop-down list of 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. Variable names begin with a capital letter.

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
blue 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.

Whenever a variable name is to be entered in a text box, instead of typing it directly, you may double-click on its name in the box on the left.

**Example A**: Suppose we want to store heights, in inches, of
female class 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:** It is possible to opt out of unwanted summaries by choosing Statistics from the middle of the upper box under Descriptive Statistics, and unchecking them.

**Example C:** For sample size N, number of non-responses N*, Mean,
SE Mean,
StDev, Minimum, Q1, Median, Q3, and Maximum of female height
data,

- Choose
**Statistics>Summary Statistics>Descriptive Statistics**... - Specify FHts in the
**Variable**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**... - Click on the
**Simple**histogram (on the left). - Specify FHts in the
**Variables**text box. - Click
**OK**.

**Example E**:

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

**Example F:**

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

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

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

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

- Choose
**Data>Stack Columns...**. - Specify FHTS and MHTS with a space between them as columns to be stacked.
- Click
**OK**, resulting in a new column called Stack. - Choose
**Data>Sort**. - Specify Stack in the
**Columnns to sort:**text box, and also Stack in the**Columns to sort by:**box. Do not select**Store the sorted data in the original columns**. - Click
**OK**, resulting in a new column called Sorted Stack; consider renaming this Sorted_Hts.

In Example G, you can also opt to "Store the sorted data in the original columns." Unlike its predecessors, Minitab for the Mac doesn't give the user additional options for where the stacked data should be stored, such as into a new worksheet, or into a new column specified with a new column name. To store in a new worksheet, simply cut the column, open a new worksheet, and paste it in. The column can be given a more meaningful name by accessing and changing it directly in the worksheet.

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** to open up a new
worksheet]
, type ctrl V to paste it.
** 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
**Statistics>Summary Statistics>Descriptive Statistics**... - Specify Height in the
**Variable**text box. - Specify Gender in the
**Group variable**text box. - Choose
**Display**and check**Boxplot**. - 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**Unstack using the values in:** - Click
**OK**. - Obtain desired descriptive statistics and displays for Earned_1 to
Earned_4. [Boxplots would be
**Simple**under**Multiple Y Variables**as in the second part of Example F.]

Observation: in Example H, the new columns are automatically called Earned_1 through Earned_Other and are stored in additional columns at the end of the same worksheet. Unlike its predecessors, Minitab for the Mac doesn't give users the option of storing the data in a new worksheet.

- Choose
**Graph>Boxplot...** - Click on the
**With Groups**, under**Single Y Variable**(upper right). - Specify Height in the
**Variable**text box and Gender in the**Group variable**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
**Data>Sample from Columns**. - Specify Height in the
**Take a sample from the following columns:**box and type__10__for the**Number of rows of each sample**box. - For most purposes, keep the default
**Sample without replacement**option. - Click
**OK**. (Minitab stores the data in a new column called Sample From Height.)

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).

**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
**Data>Generate Patterned Data>Numeric...** - Keep the default
**Equally spaced numbers.** - For the
**First number**type__1__. - For the
**Second number**type__100__, keeping the default of 1 as the**Size of each step**. - Click
**OK**and the numbers will be stored in a new column called Numeric Pattern. - Choose
**Data>Sample From Columns...** - Specify Numeric Pattern in the
**Take a sample from the following columns:**box. - Type
__5__in the small text box after**Number of rows in each sample:** - Leave default
**Method:**as**Sample without replacement**. - Click
**OK**and the random sample of 5 numbers is stored in a new column called Sample From Numeric Pattern.

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.

I see you took my suggestion to replace ** One-Sample Hypothesis Tests** with
** 1-Sample Inference** but maybe my other suggestion
** 1-Sample Tests or Intervals** is better? Same goes for
** 2-Sample Tests or Intervals**.

Minor observation: why is it capital Z-test and lower-case t-test?

**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
**Statistics>1-Sample Inference>Z...** - Keep the default
**Sample data in a column**and specify VerbalSAT in the**Sample**box. - Type
__100__in the**Known standard deviation**text box. - Select the
**Options**button from the top to change from the default 95% level. - In the
**Confidence level**box type__90__. - Make sure
**Alternative hypothesis**is at the default**Mean not equal hypothesized value**. - 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
**Statistics>1-Sample Inference>t...** - Specify VerbalSAT in the
**Samples**box. - Select the
**Options**button from the top. - Click in the
**Confidence level**text box and type__99__. - Make sure
**Alternative**is at the default**Mean not equal hypothesized value**. - 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
**Statistics>1-Sample Inference>Z...** - Specify VerbalSAT in the
**Sample**box. - Click in the
**Known 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 from the top. - Under
**Alternative**select**Mean greater than hypothesized value**. - Click
**OK**.

Observation: Unlike its predecessors, for paired and two-sample tests, Minitab for the Mac no longer provides the option of comparing the mean of differences, or the difference between means, to any number other than zero. This might be OK for most of us, although it is conceivable that we might want to make other comparisons, such as if dads average more than 2 years older than moms, or if male students' mean weight is over 25 pounds more than female students.

**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
**Statistics>2-Sample Inference>Paired t...** - Keeping the default
**Each sample is in a column**, specify DadAge in the**Sample 1**text box. - Specify MomAge in the
**Sample 2**text box. - Click in the
**Options**button at the top. - Click the arrow button at the right of the
**Alternative hypothesis**drop-down list box and select**Mean difference greater than 0**. - 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
**Statistics>2-Sample Inference>t...** - Keep the default
**Both samples are in one column**and enter Height for Samples and Gender for Sample IDs... - Click in the
**Options**button at the top. - Click the arrow button at the right of the
**Alternative hypothesis**drop-down list box and select**Difference less than 0.**(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 on
**Display**and select**Boxplot**. - 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. - In the
**Sample 1**text box, specify FHeights. - In the
**Sample 2**text box, 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
plot of residuals vs. the explanatory variable
(MomAge). Produce a scatterplot showing bands for confidence intervals and
prediction intervals.
Obtain a confidence interval for
the mean height 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 click on**Simple**. - Specify DadAge in the
**Y variable**text box. - Specify MomAge in the
**X variable**text box. - Click
**OK**. - Choose
**Statistics>Regression>Correlation...** - Specify MomAge and DadAge in the
**Variables**text box. - Click
**OK.** - Choose
**Graph>Scatterplot**and click on**With regression**. - Specify DadAge in the
**Y variable**text box. - Specify MomAge in the
**X variable**text box. - Click
**OK.** - Choose
**Statistics>Regression>Simple Regression**. - Specify DadAge in the
**Response (Y):**text box. - Specify MomAge in the
**Predictor (X):**text box. - Click on the
**Graphs**box at the top. - Check the
**Residuals versus variables:**box and specify MomAge. - Click
**OK.** - Choose
**Statistics>Regression>Simple Regression...** - Specify DadAge in the
**Response (Y):**box. - Specify MomAge in the
**Predictor (X):**box. - Choose the
**Options**button and click in both**Display 95% confidence interval**and**Display 95% prediction interval**. - 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
**Statistics>ANOVA>One-Way**. - Choose
**Responses 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**. (Note that the**Confidence interval plot**is provided by default. - 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
**Statistics>ANOVA>One Way**
and **Responses 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 variable**. - Keep the default
**Counts of unique values in a categorical variable**. - Click
**OK**. - Choose
**Statistics>1-Sample Inference>Proportion...** - Keep default
**Sample data in a column**. - Specify Gender in the
**Sample**box. - Choose female in the drop-down
**Event**box below. - Check
**Perform hypothesis test**. - Type
__0.5__in the**Hypothesized proportion**box. - Click on
**Options**at the top to specify a one-sided alternative or to use another confidence level besides 95% 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
**Statistics>Summary Statistics>Tally...**. - Specify FavoriteColor in the
**Variable**box. - Check
**Counts**under**Statistics**. - Click
**OK**. - Note the Count in the FavoriteColor of interest (this counts the Events) and the total count N (this counts the Trials).
- Choose
**Statistics>1-Sample Inference>Proportion**. - Choose
**Summarized data**from the drop-down menu at the top. - Specify the
**Number of events**and**Number of trials**as reported by Minitab in the earlier step. - Check
**Perform hypothesis test**and type__0.125__as the hypothesized proportion - Click on
**Options**at the top and specify a one-sided alternative if you suspected more or fewer than 1/8 would prefer that color. Under**Method**check "Normal approximation" if you want your results to be consistent with calculations by hand. - Click
**OK**.

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

- Choose
**Statistics>Tables>Cross Tabulation and Chi-Square**. - Keep the default
**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**. - Choose
**Display**from the top. For simple data analysis, check**Percent of row total**under**Percents to display in each cell.**The row percents are conditional percentages for respective values of the explanatory variable. - For statistical inference, under
**Display**check the**Chi-Square test for association**box. - Click
**OK**. - Choose
**Graph>Bar Chart...** - Click on
**Clustered**. - Enter Gender and Year as the
**Categorical variables**(Gender first because it is the explanatory variable, graphed horizontally). - 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 **Statistics>Tables>Cross Tabulation and Chi-Square**
and select
** Summarized data in a two-way table** from the drop-down menu. Then enter
the five column names 1st through Other in the box ** Columns containing the table**. Request **Chi-square test for Association** under the **Display**
menu and Click OK.