Minitab

One-Way

1. Enter the data for the different groups into separate columns.

2. Under Stat, choose ANOVA, then One-way.

3. In the dropdown select Response data are in a separate column for each factor level.

4. Click the mouse in the box labeled Responses. Highlight the appropriate columns in the box on the left. Click Select.

   

5. Press Options. Change Confidence level if desired.

   

6. Press OK and OK.

   One-way ANOVA: C1, C2, C3

   Method

   Null hypothesis	All means are equal
   Alternative hypothesis	Not all means are equal
   Significance level	α = 0.05
   Equal variances were assumed for the analysis.

   Factor Information

   Factor	Levels	Values
   Factor	3	C1, C2, C3

   Analysis of Variance

   Source	DF	Adj SS	Adj MS	F-Value	P-Value
   Factor	2	6.500	3.250	0.93	0.430
   Error	9	31.500	3.500
   Total	11	38.000

   Model Summary

   S	R-sq	R-sq(adj)	R-sq(pred)
   1.87083	17.11%	0.00%	0.00%

   Means

   Factor	N	Mean	StDev	95% CI
   C1	4	12.250	1.708	(10.134, 14.366)
   C2	4	14.00	2.16	(11.88, 16.12)
   C3	4	12.750	1.708	(10.634, 14.866)
   Pooled StDev = 1.87083

Fisher's LSD

1. Enter the category labels in Column C1. Enter the corresponding data value in Column C2.

   

2. Choose Stat, ANOVA, and One-Way.

3. Enter the data for the Response and the categories for the Factor. Select Options and enter the desired Confidence level. Press OK.

   

4. Click on Comparisons and check the box for Fisher and for Tests. Press OK. Press OK again.

   

5. Observe the results of Fisher's LSD test.

   

Tukey's HSD

1. Enter the category labels in Column C1. Enter the corresponding data value in Column C2.

   

2. Choose Stat, ANOVA, and One-Way.

3. Enter the data for the Response and the categories for the Factor. Select Options and enter the desired Confidence level. Press OK.

   

4. Click on Comparisons and check the box for Tukey and for Tests. Press OK. Press OK again.

   

5. Observe the results of Tukey's HSD test.

   

Two-Way

1. Enter all the data into C1, one column at a time. Enter the row numbers into C2 and the column numbers into C3. Label the columns as is fitting.

2. Under Stat, choose ANOVA, then General Linear Model, then Fit General Linear Model….

   

3. Use select to input C1 as Responses and C2, C3 as Factors. Select OK.

   

Binomial Probability Distribution

1. Set up the worksheet in C1 and C2 as shown below.

   

2. Press Calc, Probability Distributions, and Binomial.

3. Designate Probability. (Alternatively, Cumulative Probability)

4. Complete the dialog box with Number of trials – "12", Event probability – "0.1", Input column – "x", and Optional storage – "p(x)".

   

5. Press OK and read output in C2.

   

Critical Value

1. Enter the area to the left of the desired critical value in the first row of column C1. If the area we are given is to the right of the critical value, we must first determine the area to the left by calculating (1-area to the right).

   

2. Go to Calc, Probability Distributions, Chi-Square.

   

3. Choose Inverse cumulative probability and enter the number for Degrees of freedom. Select C1 as the input column.

   

4. Click OK and the critical value will appear in the Session window.

   

Left Tailed Probability (cdf)

1. Enter the Chi-Square value in the first row of column C1.

   

2. Go to Calc, Probability Distributions, Chi-Square.

   

3. Select Cumulative probability and enter the number for Degrees of freedom. Select C1 as the input column.

   

4. Click OK and the probability will appear in the Session window.

   

Test for Association

1. Input the data in the Worksheet.

   

2. Choose Stat, Tables, and Chi-Square Test for Association.

3. Select Summarized data in a two-way table from the dropdown.

4. Under Columns containing the table, input column "C2 Yes" and column "C3 No". Press OK.

   

   Chi-Square Test for Association: Worksheet rows, Worksheet columns

   Rows: Worksheet rows Columns: Worksheet columns

   	Yes	No	All
   1	208 288.8	193 112.2	417
   2	387 300.3	30 116.7	417
   3	476 481.8	193 187.2	669
   All	1071	416	1487

   Cell Counts
   CellCount
   CellExpected count

   Chi-Square Test

   	Chi-Square	DF	P-Value
   Pearson	170.467	2	0.000
   Likelihood Ratio	187.856	2	0.000

   Note: The first row (labeled ‘Pearson’) under Chi-Square Test in the output corresponds to the methods used in the texts.

Proportion

1. Choose Stat, select Basic Statistics and then choose 1 Proportion.

2. Select Summarized data from the dropdown and enter Number of events and Number of trials.

   

3. Click the Options button. Enter the Confidence level and select Normal approximation from the second dropdown.

   

4. Press OK and press OK again.

   

t-Interval

1. Select Stat, then Basic Statistics, and 1-Sample t.

2. In the dropdown menu select Summarized data and input the sample size, mean, and standard deviation. (Or if you have the raw data, enter the data into into C1 and select One or more samples, each in a column from the dropdown menu and then select C1.)

   

3. Select Options and choose your confidence level. For a confidence interval select a Mean ≠ hypothesized mean as the alternative hypothesis from the dropdown menu.

   

   

4. Click OK on the Options window and OK on the main dialog window and the confidence interval is displayed in the Session window.

Two Sample t-Interval (Independent Samples)

1. Select Stat, then Basic Statistics, and 2-Sample t.

2. In the dropdown menu select Summarized data and input the sample size, sample mean, and sample standard deviation. (If you have the raw data, enter the data for the first sample into C1 and for the second sample into C2 and select Each sample is in its own column. Then select C1 for Sample 1 and C2 for Sample 2.)

   

3. Select Options and choose your Confidence level. For a confidence interval select Difference ≠ Hypothesized difference as the alternative hypothesis from the dropdown menu. If you assume the sample variances are equal, check the box Assume equal variances. Press OK. (Note the box was not checked for the results that follow.)

   

4. Press OK. The confidence interval is produced in the Session window.

   

Two Sample Proportions z-Interval

1. Go to Stat > Basic Statistics > 2 Proportions.

2. Choose Summarized data and enter x₁ for Number of events for the Sample 1, and n₁ for Number of trials. Then enter x₂ for Number of events for the Sample 2 and n₂ for Number of trials.

   

3. Choose Options and enter the desired Confidence level.

   

4. Click OK on the Options and main dialog window and the confidence interval is displayed in the Session window.

Minimum Sample Size

1. Under the Stat menu, select Power and Sample Size, and then select Sample Size for Estimation

2. Select the Parameter and then enter an estimate of the specified parameter for Planning Value.

   1. You can use information from a previous study, subject-matter knowledge, design specifications, etc. to determine this Planning Value

3. In the second dropdown, choose Estimate sample sizes and provide your desired Margins of error for confidence itervals.

4. Click Options… and input the appropriate confidence level.

5. Click OK and OK.

Standard Deviation

1. Under the Stat menu, select Basic Statistics, and then select 1 Variance...

2. Select Sample Standard Deviation in the dropdown menu. Then, fill in the boxes labeled Sample size and Sample standard deviation.

3. Click on the button labeled Options... In the pop-up window that appears, specify the confidence level and Standard deviation ≠ hypothesized standard deviation for the Alternative hypothesis.

4. Click OK on the Options window andOK on the main dialog window and the confidence interval is displayed in the Session window.

Variance

1. Under the Stat menu, select Basic Statistics, and then select 1 Variance...

2. Select Sample Variance in the dropdown menu. Then, fill in the boxes labeled Sample size and Sample variance.

   

3. Click on the button labeled Options... In the pop-up window that appears, specify the confidence level and Standard deviation ≠ hypothesized standard deviation for the ≠ Alternative hypothesis.

   

4. Click OK on the Options window and OK on the main dialog window and the confidence interval is displayed in the Session window.

   

z-Interval

1. Select Stat, then Basic Statistics, and 1-Sample Z.

2. In the dropdown menu select Summarized data and input the sample size, sample mean, and known standard deviation. (If you have the raw data enter the data into C1 and select One or more samples, each in a column from the dropdown menu and then select C1.)

   

3. Click Options and enter the desired Confidence level. For a confidence interval select a Mean ≠ alternative mean as the Alternative hypothesis from the dropdown menu. Press OK.

   

4. Press OK.

   

Combination

1. Go to Calc > Calculator.

2. Type C1 in the box after "Store result in variable:".

3. Select Combinations under the All functions drop down box and click Select.

4. Then input a number to replace "number of items" and a number to replace "number to choose" in the expression. For example, input 15 to replace "number of items" and 13 to replace "number to choose" in order to calculate ₁₅C₁₃.

5. Click OK. The result will be displayed in row 1 of column C1.

   

Factorial

1. Go to Calc > Calculator.

2. Type C1 in the box after "Store result in variable:".

3. Select Factorial under the All functions drop down box and click Select.

4. Then input a number to replace "number of items" in the expression. For example, input 10 to calculate 10!

5. Click OK. The result will be displayed in row 1 of column C1.

   

Permutation

1. Go to Calc > Calculator.

2. Type C1 in the box after "Store result in variable:".

3. Select Permutations under the All functions drop down box and click Select.

4. Then input a number to replace "number of items" and a number to replace "number to choose" in the expression. For example, input 18 to replace "number of items" and 7 to replace "number to choose" in order to calculate ₁₈P₇.

5. Click OK. The result will be displayed in row 1 of column C1.

   

One Variable

1. Enter the data into column C1.

2. Under Stat, choose Basic Statistics, then Display Descriptive Statistics.

3. In the dialog box, input "C1" under Variables.

   

4. Click Statistics to select which statistics to include. Select OK.

5. Observe the Output Screen for the summary statistics.

   

F Critical Value

1. Enter the area to the left of the F critical value into cell C1,1.

2. Choose Calc, Probability Distributions, and Inverse Distribution Function.

3. Change Distribution to F. Change Form of input to 'A column of values'. Enter C1 for Values in. Enter the desired numerator and denominator degrees of freedom. For Output select the radio button next to 'Display a table of inverse cumulative probabilities.' Press OK.

   

4. Observe the results.

   

F-Probability (cdf)

1. Enter the F critical value into cell C1,1.

2. Choose Calc, Probability Distributions, and F.

3. Select the radio button next to Cumulative probability. Enter the desired numerator and denominator degrees of freedom. Select the radio button next to Input column and enter C1. Press OK.



Note: You can also select Input constant and enter the F critical value there.



4. Observe the results.

Bar Charts

1. Enter the category labels in C1 and the corresponding data counts in C2. The axis labels can be entered in the column header.

   

2. Select Graph, Bar Chart.

3. From the Bars represent: dropdown, select Values from a table and ensure Simple is selected for One column of values. Press OK.

   

4. Select C2 for Graph variables and C1 for Categorical variable.

   

5. To add a title, select Labels and enter the title under Title.

   

6. Press OK and OK.

   

Boxplot

1. Enter the data for each box plot in a separate column. The column header can be used to display the label for each box plot.

   

2. Select Graph, Boxplot.

3. Select One Y, Simple for a single data column or select Multiple Y's, Simple for side-by-side boxplots for several data columns. Press OK.

   

4. Select the appropriate column(s) for Graph variables.

   

5. To add a title to the box plot, click Labels and enter the title under Title.

   

6. Click OK and OK.

   

Dot Plot

1. Enter the data into column C1.

   

2. Select Graph, Dotplot.

3. Select One Y, Simple and click OK.

   

4. Select C1 for Graph variables.

   

5. To add a title, click Labels and enter the title under Title.

   

6. Click OK and OK.

   

Histogram

1. Enter the data in the column, C1.

2. Select GRAPH, Histogram.

3. Select Simple. Press OK.

   

4. Select C1 for Graph variables.

   

5. To add a title, choose Labels and enter the title under Title.

   

6. Press OK and OK to generate the graph.

7. To edit the axis labels, double-click on the text along the axis. Double-click on the text again in the Edit Graph pop-up window. Type the text of the axis label in the Text: window.

   

8. There are two options for how the classes are displayed along the horizontal axis. For either, double-click on one of the numbers on the x-horizontal axis. Double click on a horizontal axis number in the Edit Graph pop-up window. Select the Binning tab on the Edit Scale menu.

   Option 1: Choose Midpoint for the Interval Type, select Midpoint/Cutpoint positions under Interval Definition. Enter the midpoints of each class

   

   Option 2: Choose Cutpoint for the Interval Type, select Midpoint/Cutpoint positions under Interval Definition. Enter the upper class boundaries of each class

   
   

Line Graph

1. Enter the category labels in C1 and the corresponding data in C2. The axis labels can be entered in the header column. (Category labels are not required.)

   

2. Select Graph, Time Series Plot.

3. Select Simple and click OK.

   

4. Select C2 for Series.

   
5. Select Time/Scale and select Stamp for Time Scale. Select C1 for Stamp columns. Press OK.
   

6. To add a title, click Labels and enter the title under Title.

   

7. Click OK and OK.

   

Normal Probability Plot

1. Input your data in C1.

2. Select Graph, Probability Plot.

3. With Single selected press OK.

4. Input "C1" into Graph variables.

5. Press OK.

   

Pareto Chart

1. Enter the category labels in C1 and the corresponding data counts in C2. The axis labels can be entered in the column header.

   

2. Select Graph, Bar Chart.

3. From the Bars represent: dropdown, select Values from a table and ensure Simple is selected for One column of values. Press OK.

   

4. Select C2 for Graph variables and C1 for Categorical variable.

   

5. Select Chart Options and select Decreasing Y under Order Main X Groups By.

   

6. To add a title, select Labels and enter the title under Title.

   

7. Press OK and OK.

   

Pie Chart

1. Enter the category labels in C1 and the corresponding data counts in C2.

   

2. Select Graph, Pie Chart

3. Select Chart values from a table and select C1 for Categorical variables and C2 for Summary variables.

   

4. To add a title, click Labels and enter the title under Title.

   

5. To display the percentages each slice represents on the graph, click Slice Labels and choose Percent.

   

6. Click OK and OK.

   

Scatterplot

1. Enter the data with the independent(explanatory) variable in C1 and the corresponding dependent(response) variable in C2. Add column headers if desired.

   

2. Select Graph, Scatterplot.

3. Select Simple. Press OK.

   

4. Select C2 for Y variables and C1 for X variables.

   

5. To add a title to the scatterplot, click Labels and enter the title under Title.

   

6. Press OK and OK.

   

Stem-and-Leaf Plot

1. Enter the data in C1.

   

2. Select Graph, Stem-and-Leaf

3. Select C1 for Graph variables and enter Increment: value of the stems.

   

4. Press OK and OK.

   Note: The middle column is the stem with the rightmost column displaying the leaves. The first (leftmost) column contains cumulative counts. The count for the row that contains the median value is enclosed in parentheses. The count for a row above the median shows the total count for that row and all the rows above it. The value for a row below the median shows the total count for that row and all the rows below it.

   

Time Series Plot

1. Enter the data with time periods in C1 and corresponding data in C2.

   

2. Select Graph, Time Series Plot.

3. Select Simple. Press OK.

   

4. Select C2 for Series.

   

5. Click Time/Scale and then choose Stamp. Select C1 for Stamp columns. Press OK.

   

6. To add a title, choose click Labels and enter the title under Title.

   

7. Press OK and OK.

   

z-Test

1. Enter the sample data into column C1.

2. Choose Stat, Basic Statistics, and 1-Sample Z. Select Options to set the appropriate Alternative hypothesis and press OK.

3. Enter "C1" for Variables, and enter the Known standard deviation, if applicable. Check the box for Perform hypothesis test and enter the Hypothesized mean. Press OK.

   

4. Observe the session window for the results.

   

One Proportion z-Test

1. Select Stat, Basic Statistics, 1 Proportion.

2. From the dropdown choose Summarized data.

3. Enter the Number of events and the Number of trials. Check Perform hypothesis test and enter a Hypothesized proportion.

   

4. Click Options. Enter a Confidence level, select an Alternative hypothesis, and choose Normal approximation for the Method.

   

5. Press OK and OK.

   Test and CI for One Proportions

   Method

   p: event proportion

   Normal approximation method is used for this analysis.

   Descriptive Statistics

   N	Event	Sample p	90% Lower Bound for p
   180	133	0.738889	0.696932

   Test

   Null hypothesis	H0: p = 0.7139
   Alternative hypothesis	H1: p > 0.7139

   Z-Value	P-Value
   0.74	0.229

t-Test

Using Data

1. Enter the sample data into column C1.

   

2. Choose Stat, Basic Statistics, and 1-Sample t.

3. From the dropdown menu choose One or more samples, each in a column. Click in the empty window below the dropdown. Select "C1" for the variable. Check the box for Perform hypothesis test and enter the value of the Hypothesized mean.

   

4. Select Options to set the appropriate Confidence level and Alternative hypothesis. Press OK.

   

5. Press OK.

   

Using Summary Statistics

1. Choose Stat, Basic Statistics, and 1-Sample t.

2. From the dropdown choose Summarized data. Enter the Sample size, Sample mean, and the Standard deviation. Check Perform hypothesis test and enter a value for the Hypothesized mean.

   

3. Select Options to set the appropriate Confidence level and Alternative hypothesis. Press OK.

   

4. Press OK.

   

Two Proportion z-Test

Method: Summary Statistics

1. Select Stat, Basic Statistics, 2 Proportions

2. From the dropdown choose Summarized data.

3. Enter the Number of events and the Number of trials for each sample.

   

4. Choose Options to adjust the Confidence level, Hypothesized difference, Alternative hypothesis, and Test Method.

   

5. Press OK and OK.

   Test and CI for Two Proportions

   Method

   p1: proportion where Sample 1 = Event

   p2: proportion where Sample 2 = Event

   Difference: p1 - p2

   Descriptive Statistics

   Sample	N	Event	Sample p
   Sample 1	72	10	0.138889
   Sample 2	72	8	0.111111

   Estimation for Difference

   Difference	90% Lower Bound for Difference
   0.0277778	-0.042799
   CI based on normal approximation

   Test

   Null hypothesis	H0: p1 − p2 = 0
   Alternative hypothesis	H1: p1 - p2 > 0

   Method	Z-Value	P-Value
   Normal approximation	0.50	0.307
   Fisher's exact		0.401
   The test based on the normal approximation uses the pooled estimate of the proportion (0.125).

Two Sample t-Test (Independent Samples)

Using Data:

1. Enter the data for the first sample into column C1 and the second sample into column C2.



2. Choose Stat, Basic Statistics, and 2-Sample t.

3. From the dropdown choose Each sample is in its own column. Select "C1" for Sample 1: and "C2" for Sample 2:



4. Select Options to set the appropriate Confidence Level:, Hypothesized Difference, and Alternative hypothesis. Check box if we Assume equal variances. Press OK.




5. Press OK.

Using Summary Statistics:

1. Choose Stat, Basic Statistics, and 2-Sample t.

2. From the dropdown choose Summarized data. Enter the Sample size, Sample mean, and the Standard deviation for each sample.



3. Select Options to set the appropriate Confidence Level:, Hypothesized Difference, and Alternative hypothesis. Check box if we Assume equal variances. Press OK.



4. Press OK.

Two Sample t-Test (Dependent Samples, Paired Difference)

Method: Raw Data

1. Enter the data for the first sample into C1 and the second sample into C2.

   

2. Select Stat, Basic Statistics, Paired t

3. From the dropdown choose Each sample is in a column.

4. Click the mouse in the box labeled Sample 1. Highlight the appropriate column in the box on the left. Press Select. Click the mouse in the box labeled Sample 2, highlight the appropriate column in the box on the left, and press Select.

   Note that Minitab calculates the paired differences by subtracting the values for the second sample from the values for the first sample, which is the opposite of what we do when we calculate them by hand or using a TI-83/84 Plus calculator.

   

5. Choose Options to adjust the Confidence level, Hypothesized difference, and Alternative hypothesis.

   

6. Press OK and OK.

   Paired T-Test and CI: Cindy, Roommate

   Descriptive Statistics

   Sample	N	Mean	StDev	SE Mean
   Cindy	15	26.67	4.81	1.24
   Roommate	15	27.33	5.69	1.47

   Estimation for Paired Difference

   Mean	StDev	SE Mean	95% CI for μ_difference
   -0.667	2.059	0.532	(-1.807, 0.473)
   µ_difference: mean of (Cindy - Roommate)

   Test

   Null hypothesis	H0: μ_difference = 0
   Alternative hypothesis	H1: μ_difference ≠ 0

   T-Value	P-Value
   -1.25	0.230

Two Sample F-Test

1. Select Stat, Basic Statistics, 2 Variances.

2. From the dropdown choose Sample variances.

3. Enter the Sample size and the Variance for each sample.

   

4. Press Options. For the Ratio dropdown choose (sample 1 variance) / (sample 2 variance). Enter a Confidence level, Hypothesized ratio (default is 1), and Alternative hypothesis.

   

5. Press OK and OK.

   Test and CI for Two Variances

   Method

   σ12: variance of Sample 1

   σ22: variance of Sample 2

   Ratio: σ12/σ22

   F method was used. This method is accurate for normal data only.

   Descriptive Statistics

   Sample	N	StDev	Variance	90% Lower Bound for σ2
   Sample 1	20	0.079	0.006	0.004
   Sample 2	23	0.066	0.004	0.003

   Ratio of Variances

   Estimated Ratio	90% Lower Bound for Ratio using F
   1.44186	0.816

   Test

   Null hypothesis	H2:  σ12 / σ₂2 = 1
   Alternative hypothesis	H1:  σ12 / σ₂2 > 1
   Significance level	α = 0.1

   Method	Test Statistic	DF1	DF2	P-Value
   F	1.44	19	22	0.204

The Kruskal-Wallis Test

1. Enter the category labels in Column C2. Enter the corresponding data value in Column C1.

   

2. Choose Stat, Nonparametrics, and Kruskal-Wallis.

3. Enter the data for the Response and the categories for the Factor. Press OK.

   

4. Observe the results of the Kruskal-Wallis Test.

   

Runs Test for Randomness

1. Enter the data into column C1.

   

2. Choose Stat, Nonparametrics, and Runs Test.

3. Select C1 as the variables. Press OK.

   

4. Observe the outcome of the runs test.

   

Sign Test

1. Enter the category labels in Column C1. Enter the corresponding data value in Column C2.

   

2. Choose View, and then Command Line/History. In the Command Line box enter Let C3=C1-C2. Press Run. The differences are now calculated in column C3.

3. Choose Stat, Nonparametrics and 1-Sample Sign.

4. Enter C3 for Variables and select the radio button next to Test median. Choose the appropriate Alternative from the drop down and press OK.

   

5. Observe the results of the test.

   

Spearman Rank Correlation Test

1. Enter data in different columns.

   

2. Choose Stat, Basic Statistics, and Correlation.

3. Enter the desired columns for the two associated variables in the Variables box. Select Options and select Spearman correlation from the Method drop down menu and input the desired Confidence level. Press OK. Press OK again.

   

4. Observe the results.

   

Wilcoxon Rank-Sum Test

1. Input the data into Columns C1 and C2.

2. Choose Stat, Nonparametrics, and Mann-Whitney. Enter C1 as the First Sample and C2 as the Second Sample. Enter the desired confidence level and Alternative hypothesis. Press OK.

   

3. Observe the result of the Wilcoxon rank-sum test (also known as the Mann-Whitney test).

   

Wilcoxon Signed-Rank Test

1. Enter the data into Column C1 and Column C2.

2. Choose View, and then Command Line/History.

3. In the Command Line box, enter LET C3=C1-C2. Press Run. The differences are now calculated in column C3.

   

4. Choose Stat, Nonparametrics and 1-Sample Wilcoxon.

5. Enter C3 for variables and select the radio button next to Test median. Choose the appropriate Alternative from the drop down and press OK.

   

6. Observe the output screen for the Wilcoxon signed-rank test.

   

Inverse Normal

1. To find a z- or x-value for a given probability in Minitab, enter the probability in the first column and row.

2. Go to Calc > Probability Distributions > Normal.

3. When the Normal Distribution menu appears, select Inverse cumulative probability and enter the Mean and Standard deviation.

4. Select C1 as the Input column. Click OK, and the probability will appear in the Session window.

Note: The probability is the area under the normal distribution curve to the left of the z-score or x-value calculated by Minitab.

Normal Probability (cdf)

1. Enter the given x- or z-value in the first column and row.

2. Go to Calc > Probability Distributions > Normal.

3. When the Normal Distribution menu appears, make sure Cumulative probability is selected and enter the Mean and Standard deviation.

4. Select C1 as the Input column. Once you are finished, click OK, and the probability will appear in the Session window.

Note: Minitab only calculates the area under the normal distribution curve to the left of the given z-score or x-value.

Test for Normality

1. Enter the category labels in Column C1. Enter the corresponding data value in Column C2.

   

2. Choose Stat, Basic Statistics, and Normality Test.

3. Enter the data for the variable. Select the desired Test for Normality. Press Ok.

4. Observe the results of the Test for Normality.

   

Poisson Probability Distribution

1. Set up the worksheet with "x" as the label for the first column, C1 and "p(x)" as the label for C2. In C1 starting with row 1, enter whole numbers for the value of the discrete random variable.

   

2. Press Calc, Probability Distributions, and Poisson.

3. Designate Probability for the pdf. (Alternatively, Cumulative Probability for the cdf.)

4. Complete the dialog box by inputting "5" for the Mean, selecting "x" for the Input column and selecting "p(x)" for Optional storage.

   

5. Press OK and the Poisson probabilities are displayed in column C2.

   

Confidence Intervals for Slope and y-Intercept

1. Enter your X and Y data into two columns, C1 and C2.

2. Press Stat, Regression, and Regression, then Fit Regression Model.

3. Enter the Response variable and the Predictor variable (continuous).

   

4. Click Results and then choose Display of results: Expanded tables. Click OK and OK.

   

5. Note in the following example that the confidence intervals for the slope (Constant) and y-intercept (Age) are displayed in the output under the Coefficients heading.

   

Linear Regression Fitted Line Plot with Confidence Interval

1. Enter your data in the worksheet.

2. Under the Stat menu select Regression, and Fitted Line Plot.

3. Select the Response (Y) and Predictor (X), make sure the Type of Regression Model is Linear. Click Options and under Display Options check Display confidence interval. Click OK and OK.

   

   

   

Linear Regression Fitted Line Plot with Prediction Interval

1. Enter your data in the worksheet.

2. Under the Stat menu select Regression, and Fitted Line Plot.

3. Select the Response (Y) and Predictor (X), make sure the Type of Regression Model is Linear. Click Options and under Display Options check Display prediction interval. Click OK and OK.

   

   

   

Multiple Regression

1. Enter the data in columns with the variable names at the top of each column.

2. Under Stat, choose Regression, then Regression, and Fit Regression Model….

3. In the dialog box, use Select to input the Reponse variable and the Predictor variables. Select OK.

   

   

Regression Prediction Intervals

1. Enter the data in columns with the variable names at the top of each column.

2. First run Regression (see Linear Regression or Multiple Regression).

3. Under Stat, choose Regression, then Regression, and Predict

4. Enter the individual value(s) you wish to predict for. Use Options… to select the Confidence Level. Select OK and OK.

   

   

Simple Linear Regression

1. Enter your X and Y data into two columns, C1 and C2.

   

2. Press Stat, Regression, and Fitted Line Plot. Enter the Response variable and the Predictor variable, and press OK.

3. Observe the least squares coefficients, ${\mathsf{R}}^2$, and standard error, as well as the regression plot.

   

4. Press Stat, Regression, and Regression, then Fit Regression Model for additional output. Enter the Response variable and the Predictor variable (continuous), and press OK.

   

Simple Exponential Smoothing

1. Enter the data of the table into the Minitab worksheet. Make sure the cell for the period you are trying to forecast is blank (the * sign is not blank). To remove the * sign, right click on the cell and select Clear Cells.

   

2. Choose Stat, Time Series, and Single Exp Smoothing.

3. Enter C2 in the Variable box. Under Weight to Use in Smoothing, select the radio button next to Use and enter the desired alpha level. Check the box for Generate forecasts and enter the Number of forecasts (using a value of 1 will give the first forecast). Click on Options and enter 1 for K. Press OK. Click on Storage and check the box for Forecasts. Press OK. Click on Results and check the box for Summary table and results table. Press OK. Press OK again.

   

4. Observe the results.

   

Simple Moving Average

1. Enter the data into the Minitab worksheet.

   

2. Choose Stat, Time Series, and Moving Average.

3. Enter C2 in the Variable box, and n, the number of periods, in the MA length box. Click on Storage and check the box for Moving Averages. Press OK. Press OK again.

   

4. Observe the results.