How to Tackle One-Way ANOVA Assignments Using SPSS

• Control (existing medication)
• T15 (15% active ingredients)
• T40 (40% active ingredients)
• T50 (50% active ingredients)

A sample of 20 patients is randomly divided into four groups, each receiving one treatment. The time until pain relief (in minutes) is recorded.

Data Entry in SPSS

In SPSS, create two variables:

• relieftime (dependent variable: time in minutes until pain relief)
• drug (independent variable: treatment group)

Data for each patient under each treatment is entered into SPSS accordingly.

Conducting Graphical Analysis

Graphical analysis is essential for visually assessing the data before performing statistical tests. It helps identify any patterns, outliers, or deviations from assumptions such as normality and equal variance. SPSS provides several plotting tools, including boxplots and stem-and-leaf plots, which can be easily generated through the Explore function. Visual inspection of these plots not only aids in understanding the dataset but also plays a crucial role in ensuring that the statistical assumptions required for ANOVA are satisfied. A careful graphical analysis can prevent misinterpretations and support more accurate conclusions.

Checking Normality

Before running One-Way ANOVA, it is essential to check the assumption of normality. In SPSS:

• Go to Analyze > Descriptive Statistics > Explore
• Set "relieftime" as the dependent variable
• Set "drug" as the factor
• Click on "Plots" and ensure stem-and-leaf plots, boxplots, and normal plots are selected

Review the outputs to ensure no significant departures from normality.

Checking Homogeneity of Variance

The assumption of equal variances across groups is tested:

• Within the ANOVA window, select "Options" and check the box for Homogeneity of variance test
• Run the analysis and look at the Levene's Test results
• If the significance value (p-value) is greater than 0.05, the assumption holds

In the example, the p-value was 0.197, indicating homogeneity.

Running One-Way ANOVA in SPSS

Running the One-Way ANOVA is the core analytical step where statistical calculations are performed to determine if there are any significant differences among group means. SPSS simplifies this process through its intuitive interface. By specifying the correct variables and using the Compare Means function, users can quickly obtain the ANOVA table along with the F-statistic and p-values. Understanding how to set up and interpret this output is crucial for providing evidence to support or reject the research hypothesis. This step directly leads to statistical conclusions that answer the original research question.

Setting Up the Analysis

To perform One-Way ANOVA:

• Go to Analyze > Compare Means > One-Way ANOVA
• Set "relieftime" as the dependent variable and "drug" as the factor
• Click OK to generate the output

Interpreting the ANOVA Output

The output includes the ANOVA table with:

• Sum of Squares
• Degrees of Freedom
• Mean Squares
• F-statistic
• Significance level (p-value)

In the arthritis example:

• The F value was 12.723 with a significance level of 0.000, leading to rejection of the null hypothesis that all group means are equal.

Post Hoc Analysis to Identify Group Differences

Post hoc analysis is necessary when the ANOVA indicates that there are statistically significant differences among groups. This step helps pinpoint exactly which groups differ from each other, providing deeper insight into the data. SPSS offers multiple post hoc tests such as Tukey, LSD, and Scheffe, each with its own level of conservatism. Selecting the right test and interpreting the output correctly is essential for drawing meaningful and defensible conclusions. This part of the analysis is especially valuable in assignments where precise comparisons are required.

Running Post Hoc Tests

Since the null hypothesis was rejected, post hoc tests help identify which specific group means differ:

• Click "Post Hoc" in the ANOVA window
• Select options such as LSD, Tukey, and Scheffe
• Click Continue and OK

Interpreting Post Hoc Results

• Tukey and Scheffe results display homogeneous subsets
• The group means for T50 (12.80 minutes) and T15 (20.40 minutes) showed the largest difference
• However, not all group differences are statistically significant

For example, the difference between T50 and control was not significant.

Performing Contrast Analysis in SPSS

Contrast analysis offers a more focused approach by testing specific hypotheses about group differences, rather than all possible comparisons. It is particularly useful in research scenarios where theoretical expectations exist. SPSS allows users to set custom contrasts and compute significance levels for each one. Properly constructing and interpreting contrasts not only adds depth to the analysis but also demonstrates a higher level of statistical understanding in academic assignments. Contrasts provide a valuable alternative or complement to post hoc testing.

Planning Contrasts

Contrasts are specific comparisons designed before running the experiment. Three contrasts were considered:

1. Control vs. all compounds
2. Low concentration (T15) vs. high concentration (T40, T50)
3. T40 vs. T50

Coefficients are assigned such that their sum equals zero, for example:

• Control vs. Compounds: (3, -1, -1, -1)
• Low vs. High: (0, 2, -1, -1)
• T40 vs. T50: (0, 0, 1, -1)

Entering Contrasts in SPSS

• Access One-Way ANOVA > Contrasts
• Enter the coefficients
• Click Next to add all planned contrasts

Interpreting Contrast Results

The contrast outputs display:

• Contrast values
• Standard Errors
• t-values
• Significance (p-values)

Significant findings in the arthritis study included:

• A significant difference between low concentration (T15) and high concentration (T40, T50) compounds (p = 0.000)
• A significant difference between T40 and T50 (p = 0.003)
• No significant difference between control and compounds (p = 0.562)

Conclusion

One-Way ANOVA is a powerful statistical method for comparing means across multiple groups and is frequently required in academic assignments. Successfully solving such assignments using SPSS involves several key steps: understanding the problem, ensuring assumptions are met through graphical analysis, conducting the ANOVA, performing post hoc tests when necessary, and applying contrast analysis for targeted comparisons. Presenting results clearly and accurately is equally important. By following this structured approach, you can not only complete your statistics assignments effectively but also gain valuable statistical skills applicable in both academic and professional contexts. For those seeking additional help with SPSS assignment, professional guidance can make the process smoother and more efficient.