Tukey-Kramer Post Hoc Test after One-Way ANOVA in Excel

Dr. Todd Grande
25 Aug 201715:34
EducationalLearning
32 Likes 10 Comments

TLDRDr. Grande's video tutorial demonstrates how to perform a Tukey Kramer post hoc test in Excel following a one-way ANOVA. Using fictitious data, the video guides viewers through calculating the Tukey Kramer statistic to determine if there are significant differences between three therapy groups: CBT, existential, and psychodynamic. The tutorial explains the process of comparing the calculated Q statistic with a critical value from the studentized range distribution table, emphasizing the importance of selecting the correct table based on alpha levels and degrees of freedom.

Takeaways
  • 🔍 The video demonstrates how to conduct the Tukey-Kramer post hoc test after performing ANOVA in Excel.
  • 🧪 The dataset used in the example is fictitious, representing scores from psychometric instruments measuring motivation levels.
  • 📊 Three levels of the independent variable (treatment) are considered: CBT (Cognitive Behavioral Therapy), Existential Therapy, and Psychodynamic Therapy.
  • 🔎 A one-way ANOVA is first performed to determine if there are differences between the groups.
  • ❓ The ANOVA test reveals a statistically significant difference, but it does not indicate where the differences lie.
  • 📈 The Tukey-Kramer test is chosen for post hoc analysis because it handles unequal sample sizes and controls for Type I errors.
  • 🧮 Step-by-step instructions are given for calculating the absolute differences, sample sizes, standard error, and the Q statistic for each pairwise comparison.
  • 📐 The Q statistics are compared against critical values from the studentized range distribution (Q table) to determine significance.
  • ✅ Significant differences are found between Psychodynamic and CBT, as well as between Existential and Psychodynamic therapies.
  • ❌ No significant difference is found between CBT and Existential therapies.
  • 📜 Viewers are advised to ensure they use the correct Q table for their alpha value and degrees of freedom.
Q & A

  • What is the purpose of the Tookie Kramer test in the context of this video?

    -The Tookie Kramer test is used for post hoc analysis after an ANOVA to determine if there are significant differences between the means of different groups, specifically in cases with unequal sample sizes.

  • What is the null hypothesis in the context of this video?

    -The null hypothesis is that there is no significant difference between the means of the groups being compared, such as the levels of motivation among participants receiving different types of therapy.

  • What are the three levels of the independent variable 'treatment' mentioned in the video?

    -The three levels of the independent variable 'treatment' are cognitive behavioral therapy (CBT), existential therapy, and psychodynamic therapy.

  • Why is the one-way ANOVA performed before the Tookie Kramer test?

    -The one-way ANOVA is performed to test if there is any significant difference among the group means before conducting pairwise comparisons with the Tookie Kramer test.

  • What does the result of the ANOVA reveal about the group means?

    -The result of the ANOVA reveals whether there is at least one significant difference among the group means, but it does not specify which groups differ or the number of differences.

  • What is the significance of the p-value obtained from the ANOVA in the video?

    -The p-value of 0.3% is less than the alpha level of 0.05, indicating a statistically significant difference among the group means, which justifies further analysis with the Tookie Kramer test.

  • What is the formula for calculating the standard error used in the video?

    -The formula for calculating the standard error is the square root of one half times the mean square error divided by the sum of the reciprocals of the sample sizes of the two groups being compared.

  • How is the Q statistic calculated in the Tookie Kramer test?

    -The Q statistic is calculated by dividing the absolute value of the difference between group means by the standard error of those means.

  • What is the critical value used for comparison with the Q statistic in the video?

    -The critical value used for comparison with the Q statistic is obtained from the studentized range distribution table (Q table), which is 3.4 in this case for an alpha of 0.05 and degrees of freedom of 60.

  • What conclusion can be drawn when the Q statistic is greater than the critical value?

    -If the Q statistic is greater than the critical value, it suggests that there is a significant difference between the group means, and the null hypothesis is rejected.

  • What does it mean to fail to reject the null hypothesis in the context of the Tookie Kramer test?

    -Failing to reject the null hypothesis means that there is not enough evidence to conclude that there is a significant difference between the group means being compared.

Outlines
00:00
📊 Introduction to Tookie Kramer Test in Excel

Dr. Grande introduces a video tutorial on how to conduct the Tookie Kramer test following an ANOVA analysis in Excel. The video aims to guide viewers through the process of using fictitious data to calculate the Tookie Kramer statistic and compare it with a Studentized range (Q) table. The purpose is to determine if there is a significant difference in motivation levels among participants who received different types of therapy: CBT, existential, and psychodynamic. The video emphasizes the importance of first conducting a one-way ANOVA to establish if there is any difference among the groups before proceeding with the post hoc test for pairwise comparisons.

05:01
🔍 Step-by-Step ANOVA and Q Statistic Calculation

The script details the step-by-step process of performing a one-way ANOVA in Excel, including how to input data, set parameters, and interpret the results. It explains the significance of the F-statistic and p-value in determining whether there is a statistically significant difference among the therapy groups. The video then moves on to calculating the Q statistic for each pairwise comparison by finding the absolute difference in means, determining sample sizes, and calculating the standard error. The formula for the Q statistic is provided, and the process of autofilling calculations for all pairwise comparisons is demonstrated.

10:02
📈 Comparing Q Statistics with Critical Values

After calculating the Q statistics for each pairwise comparison, the video script explains how to compare these values with critical values obtained from the Studentized range (Q) table. It discusses the importance of selecting the correct critical value based on the number of groups and the within-groups degrees of freedom. The script highlights the conservative nature of the Tukey-Kramer test in controlling for Type 1 error and its suitability for unequal sample sizes. The video demonstrates how to determine whether to reject or fail to reject the null hypothesis based on the comparison of Q statistics with the critical value.

15:03
🎓 Conclusion and Considerations for the Tukey-Kramer Test

The final paragraph wraps up the video with a summary of the key points and considerations when performing the Tukey-Kramer post hoc test after an ANOVA in Excel. It emphasizes the importance of using the correct Q table for the chosen alpha level and understanding the degrees of freedom for both the error and the number of groups. The script provides guidance on interpreting the Q statistic results and making decisions about the null hypothesis for each pairwise comparison. The video concludes by hoping that viewers found the tutorial helpful and thanks them for watching.

Mindmap
Keywords
💡Dr. Grande
Dr. Grande is the presenter of the video, an expert who guides viewers through the process of conducting a specific statistical test in Excel. The keyword is significant as it establishes the authority and reliability of the information being shared, and it is used throughout the script to refer to the presenter's guidance and expertise.
💡Tukey Kramer test
The Tukey Kramer test is a post hoc statistical test used after ANOVA to determine which groups differ significantly from each other. In the context of the video, it is the main focus, as the script walks through the steps of performing this test in Excel. The test is essential for understanding the differences between groups after an initial ANOVA has indicated a significant overall effect.
💡ANOVA
ANOVA, or Analysis of Variance, is a statistical method used to compare means of more than two groups. It is the prerequisite test before conducting the Tukey Kramer test. In the video, ANOVA is used to determine if there are any differences among the three therapy groups, and its results are a key factor in deciding whether to proceed with the Tukey Kramer test.
💡Excel
Excel is the software used in the video to demonstrate the statistical tests. It is a widely used tool for data analysis and is the platform through which Dr. Grande illustrates the process of conducting the Tukey Kramer test. The script provides step-by-step instructions on how to navigate Excel to perform the necessary calculations.
💡Cognitive Behavioral Therapy (CBT)
CBT is one of the three treatment types compared in the video's example dataset. It represents a level of the independent variable in the study, and the script uses it to illustrate how the Tukey Kramer test can be applied to compare the effectiveness of different therapies on motivation levels.
💡Existential therapy
Existential therapy is another treatment type in the dataset, serving as a comparative group against CBT and psychodynamic therapy. The script discusses this therapy type to demonstrate the process of comparing different treatment effects on the dependent variable, which is the level of motivation.
💡Psychodynamic therapy
Psychodynamic therapy is the third treatment type in the dataset. The script uses this therapy as part of the pairwise comparisons to determine if there are significant differences in motivation levels among the different therapy groups.
💡Dependent variable
The dependent variable in the context of the video is the level of motivation, which is measured using a psychometric instrument. It is the outcome that the study is interested in and is compared across the different therapy groups to determine if there are any significant differences.
💡Independent variable
The independent variable in the video is the type of therapy received by the participants, which has three levels: CBT, existential, and psychodynamic therapy. It is the variable that the researcher manipulates or selects to observe its effect on the dependent variable.
💡Type 1 error
A Type 1 error occurs when the null hypothesis is incorrectly rejected when it is actually true. In the script, the Tukey Kramer test is described as a conservative test that controls well for Type 1 errors, emphasizing the importance of avoiding false conclusions about significant differences between groups.
💡Null hypothesis
The null hypothesis is a statistical assumption that there is no difference between groups. In the context of the video, the null hypothesis is tested for each pairwise comparison of therapy groups. If the Tukey Kramer test statistic exceeds the critical value, the null hypothesis is rejected, indicating a significant difference between the groups.
Highlights

Introduction to Dr. Grande's video on conducting the Tukey Kramer test after ANOVA in Excel.

Fictitious data is used for the example to demonstrate the Tukey Kramer statistic calculation.

Explanation of the variables involved: CBT, existential therapy, and psychodynamic therapy as levels of the same independent variable.

Assumption that scores represent levels of motivation measured by a psychometric instrument.

Description of the one-way ANOVA process to determine if there are differences among the three therapy groups.

The result of ANOVA does not specify where the differences lie, necessitating a post hoc test.

Selection of the Tukey Kramer post hoc test for its conservative nature and suitability for unequal sample sizes.

Step-by-step guide on performing one-way ANOVA in Excel, including defining input range and output range.

Interpretation of ANOVA results, including F-statistic and p-value, to determine statistical significance.

Calculation of the absolute value of differences between pairwise comparisons of therapy groups.

Determination of sample sizes for the groups involved in pairwise comparisons.

Formula and calculation of the standard error for pairwise comparisons.

Explanation of how to calculate the Q statistic using the absolute difference and standard error.

Identification of the highest Q statistic value indicating the most significant difference.

Comparison of Q statistic values to the critical value from the studentized range distribution of Q.

Decision-making process based on the comparison of Q statistic to critical value: rejecting or failing to reject the null hypothesis.

Practical application of the Tukey Kramer test in determining differences between psychodynamic and CBT, and existential and psychodynamic therapies.

Conclusion and summary of the video's content, emphasizing the importance of the Tukey Kramer test after ANOVA.

Transcripts

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Related Tags
ANOVA TestPost-Hoc AnalysisExcel TutorialStatistical MethodCognitive TherapyExistential TherapyPsychodynamic TherapyHypothesis TestingType 1 ErrorStudentized QStatistical Significance