How to Solve One-Way ANOVA Assignments Using Minitab

• Dependent variable: Relief time (in minutes)
• Independent variable (Factor): Type of drug (Control, T15, T40, T50)

The goal is to determine whether there is a significant difference in mean relief time among the four treatments.

Data Entry in Minitab

Minitab requires two columns for one-way ANOVA:

• One column for the dependent variable (relieftime)
• One column for the independent variable (drugs)

Here’s how the data might look:

relieftime drugs
12 Control
20 T15
17 T40
14 T50
… …

Entering this structure into Minitab ensures proper analysis later.

Checking ANOVA Assumptions with Graphs

Graphical exploration is a crucial step in any statistical assignment involving ANOVA. Minitab offers intuitive ways to check for normality and equal variance using visual tools.

Using Boxplots to Compare Groups

Boxplots are used to visualize the distribution of the relief time for each treatment group. To create boxplots in Minitab:

1. Go to Graph ➤ Boxplot ➤ With Groups
2. Set relieftime as the graph variable
3. Set drugs as the categorical grouping variable
4. Click OK

This allows us to quickly compare medians and identify outliers. If the boxplots are symmetric and similarly spread, the normality and equal variance assumptions are likely met.

Visualizing Data with Stem-and-Leaf Plots

Stem-and-leaf plots allow you to see the shape of the data distribution for each group:

1. Navigate to Graph ➤ Stem-and-Leaf
2. Set relieftime as the graph variable
3. Set drugs as the By variable to view individual group plots
4. Click OK

If needed, leave out the By variable to view a combined plot. This step helps confirm that the data distribution is not heavily skewed or multimodal.

Verifying Normality and Equal Variance

Before running the ANOVA test, it is essential to check whether the data meet the assumptions. Minitab provides tools to verify both normality and variance homogeneity.

Creating Normal Probability Plots

To test the assumption of normality:

1. Go to Graph ➤ Probability Plot
2. Set relieftime as the graph variable
3. Use the Multiple Graphs option ➤ Choose By Variable ➤ Move drugs into the panel
4. Click OK

This generates individual normal probability plots for each group. If the points fall along a straight line, the data are approximately normally distributed.

Testing Homogeneity of Variances

One-way ANOVA assumes that group variances are equal. Minitab helps you test this with:

1. Stat ➤ ANOVA ➤ Test for Equal Variances
2. Select relieftime as the response and drugs as the factor
3. Click OK

Minitab outputs the p-value of the test. If p > 0.05, the assumption of equal variances holds, and you can proceed with the ANOVA.

Performing One-Way ANOVA in Minitab

Once the assumptions are verified, running the ANOVA is straightforward. This section details how to execute the test and interpret the results.

Running the Analysis

To perform the ANOVA:

1. Go to Stat ➤ ANOVA ➤ One-Way
2. Set relieftime as the Response variable
3. Set drugs as the Factor
4. Click OK

Minitab will produce the ANOVA output, including the F-value and the p-value.

Interpreting ANOVA Output

The null hypothesis (H₀) assumes that all group means are equal:

H₀: μ₁ = μ₂ = μ₃ = μ₄

The alternative hypothesis (H₁) states that at least one mean is different. If the p-value is less than 0.05, we reject H₀.

In the given example, the observed F-value is 12.72, and the p-value is 0.000—this is strong evidence against the null hypothesis. It suggests that at least one treatment has a significantly different mean relief time.

Understanding Post Hoc Tests and Contrasts

After finding a significant result in ANOVA, students often need to go further to identify which groups differ. Minitab provides tools like Tukey's test and contrast analysis for this purpose.

Performing Tukey's Post Hoc Test

To examine specific group differences:

1. Return to Stat ➤ ANOVA ➤ One-Way
2. Click Comparisons
3. Choose Tukey’s Family Error Rate
4. Click OK

Minitab provides a table showing group means and statistically significant differences using alphabetical lettering. Groups with different letters are significantly different from each other.

Conducting Contrasts for Specific Comparisons

Contrasts are pre-planned comparisons between specific group combinations. In this case, we consider:

1. Control vs. All compounds
2. Low concentration (T15) vs. High concentration (T40 & T50)
3. T40 vs. T50

These contrasts help you isolate the effects of specific treatments. The steps to perform contrasts:

1. Prepare coefficients that sum to zero
   e.g., Control vs. All: (3, -1, -1, -1)
2. Enter the coefficients in a new column in Minitab
3. Press Ctrl+L to open the Command Line Editor
4. Type: %contrast C; Groups Y X.
   C = column of contrast coefficients
   Y = response variable column
   X = factor column
5. Press Enter

Minitab will output the estimated contrast, standard error, t-value, and confidence interval. A two-sided p-value is used for interpreting significance (multiply one-sided p-value by 2).

Conclusion

Solving one-way ANOVA assignments using Minitab involves more than just running the test. A complete analysis includes data preparation, assumption checking, test execution, and post hoc exploration. From visual tools like boxplots and probability plots to tests like ANOVA and Tukey's post hoc, Minitab provides everything needed to complete such assignments accurately.

By following each step and interpreting the output correctly, students can confidently solve complex statistical problems and report findings clearly. Whether the goal is academic success or better statistical understanding, using Minitab effectively transforms how one-way ANOVA assignments are approached. If you're aiming to solve your statistics assignment efficiently, mastering these techniques in Minitab is a valuable step forward.