Key T-Test Findings
T-Test Key Findings
Executive Summary — overview — High-level t-test results and key findings
Company: Test Corp
Objective: Compare mean differences between control and treatment groups
| Group | N | Mean | SD | SE | Min | Q1 | Median | Q3 | Max |
|---|---|---|---|---|---|---|---|---|---|
| Control | 50.000 | 99.465 | 17.272 | 2.443 | 60.153 | 90.517 | 98.494 | 109.761 | 134.300 |
| Treatment | 45.000 | 111.102 | 16.397 | 2.444 | 54.124 | 101.390 | 113.128 | 120.976 | 136.363 |
Executive Summary
Statistically Significant Difference: The t-test results indicate a statistically significant difference between the control and treatment groups, with a p-value of 0.0011 (below the significance level of 0.05).
Practical Significance (Effect Size): The mean difference between the groups is -11.6365 units, with a Cohen’s d effect size of -0.69, indicating a medium practical significance. This suggests that the treatment has a moderate impact on the outcome compared to the control.
Key Business Implications: The findings show that the treatment group significantly outperforms the control group. With a medium effect size, the treatment can be considered impactful in practical terms. This highlights the potential benefit and relevance of implementing the treatment in a business context to improve the targeted outcome. Consider further investigation into the specific attributes of the treatment that led to this significant effect for optimizing business strategies.
Executive Summary
Statistically Significant Difference: The t-test results indicate a statistically significant difference between the control and treatment groups, with a p-value of 0.0011 (below the significance level of 0.05).
Practical Significance (Effect Size): The mean difference between the groups is -11.6365 units, with a Cohen’s d effect size of -0.69, indicating a medium practical significance. This suggests that the treatment has a moderate impact on the outcome compared to the control.
Key Business Implications: The findings show that the treatment group significantly outperforms the control group. With a medium effect size, the treatment can be considered impactful in practical terms. This highlights the potential benefit and relevance of implementing the treatment in a business context to improve the targeted outcome. Consider further investigation into the specific attributes of the treatment that led to this significant effect for optimizing business strategies.
Actionable Insights
Recommendations — recommendations — Actionable insights and next steps
Company: Test Corp
Objective: Compare mean differences between control and treatment groups
Recommendations
Based on the provided data profile, here are 3-5 actionable recommendations:
Review Assumptions: Since the assumptions are only partially met, it is crucial to thoroughly examine the assumptions of the statistical test being conducted. Check for potential violations such as normality, independence, and homogeneity of variances. Addressing any assumptions that are not met can improve the reliability of the results.
Interpret Effect Size: With a medium effect size, it is important to delve deeper into the practical significance of the differences between the control and treatment groups. Understand how this effect size translates into real-world impact for Test Corp. Consider whether the observed effect is meaningful from a business perspective.
Utilize Statistical Significance: Given that the results are statistically significant, leverage this information to make informed decisions. Identify the areas where these differences lie and explore why they exist. Consider implementing changes based on these significant findings to drive improvements within Test Corp.
Further Analysis: Explore additional factors that may be influencing the observed differences between the control and treatment groups. Conduct subgroup analysis or delve into specific variables to uncover more insights. This can help in identifying potential confounding variables and refining strategies.
Communicate Insights: Ensure that the insights derived from the data analysis are effectively communicated within Test Corp. Share the actionable recommendations with relevant stakeholders, such as decision-makers and team members, to facilitate informed decision-making and drive positive changes based on the results.
By following these recommendations, Test Corp can enhance its understanding of the differences between the control and treatment groups and leverage this knowledge to make strategic decisions that positively impact the company’s objectives.
Recommendations
Based on the provided data profile, here are 3-5 actionable recommendations:
Review Assumptions: Since the assumptions are only partially met, it is crucial to thoroughly examine the assumptions of the statistical test being conducted. Check for potential violations such as normality, independence, and homogeneity of variances. Addressing any assumptions that are not met can improve the reliability of the results.
Interpret Effect Size: With a medium effect size, it is important to delve deeper into the practical significance of the differences between the control and treatment groups. Understand how this effect size translates into real-world impact for Test Corp. Consider whether the observed effect is meaningful from a business perspective.
Utilize Statistical Significance: Given that the results are statistically significant, leverage this information to make informed decisions. Identify the areas where these differences lie and explore why they exist. Consider implementing changes based on these significant findings to drive improvements within Test Corp.
Further Analysis: Explore additional factors that may be influencing the observed differences between the control and treatment groups. Conduct subgroup analysis or delve into specific variables to uncover more insights. This can help in identifying potential confounding variables and refining strategies.
Communicate Insights: Ensure that the insights derived from the data analysis are effectively communicated within Test Corp. Share the actionable recommendations with relevant stakeholders, such as decision-makers and team members, to facilitate informed decision-making and drive positive changes based on the results.
By following these recommendations, Test Corp can enhance its understanding of the differences between the control and treatment groups and leverage this knowledge to make strategic decisions that positively impact the company’s objectives.
T-Test Analysis
T-Test Statistics
Statistical Test Results test_results Detailed t-test statistics and conclusions
| Test | Statistic | p_value | Conclusion |
|---|---|---|---|
| t-test | -3.368 | 0.001 | Significant difference |
| Levene's Test | 0.207 | 0.650 | Equal variances |
| Shapiro-Wilk (Group 1) | 0.980 | 0.561 | Normal |
| Shapiro-Wilk (Group 2) | 0.939 | 0.019 | Non-normal |
Statistical Test Results
Based on the provided t-test results with a Welch’s t-test method, the key findings are as follows:
T-Statistic and P-Value:
Confidence Interval:
Conclusion:
Overall, the statistical analysis indicates that there is a significant difference between the control and treatment groups, providing valuable insights for decision-making and potentially influencing business strategies or interventions.
Statistical Test Results
Based on the provided t-test results with a Welch’s t-test method, the key findings are as follows:
T-Statistic and P-Value:
Confidence Interval:
Conclusion:
Overall, the statistical analysis indicates that there is a significant difference between the control and treatment groups, providing valuable insights for decision-making and potentially influencing business strategies or interventions.
Practical Significance
Effect Size Analysis effect_size Magnitude and practical significance of differences
| Measure | Value |
|---|---|
| Mean Difference | -11.637 |
| Cohen's d | -0.69 |
| Effect Magnitude | Medium |
| Statistical Power | 91.4% |
Effect Size
The Cohen’s d of -0.69 indicates a medium effect size. This suggests that there is a moderate practical significance to the observed difference between the Control and Treatment groups.
In practical terms, a medium effect size like this could imply that the Treatment group shows a meaningful reduction in the outcome being studied compared to the Control group.
Decision-making beyond statistical significance should take into account not only whether the results are statistically significant (which indicates whether the findings are likely not due to chance) but also whether the effect size is practically significant. In this case, even though the mean difference is statistically significant, the medium effect size suggests that the Treatment’s impact is not only statistically real but also practically meaningful. This implies that implementing the Treatment could lead to a substantive and noticeable change in the outcome of interest.
Therefore, when assessing the importance of these findings, considering the effect size alongside statistical significance can provide more comprehensive insights for decision-making and practical implications.
Effect Size
The Cohen’s d of -0.69 indicates a medium effect size. This suggests that there is a moderate practical significance to the observed difference between the Control and Treatment groups.
In practical terms, a medium effect size like this could imply that the Treatment group shows a meaningful reduction in the outcome being studied compared to the Control group.
Decision-making beyond statistical significance should take into account not only whether the results are statistically significant (which indicates whether the findings are likely not due to chance) but also whether the effect size is practically significant. In this case, even though the mean difference is statistically significant, the medium effect size suggests that the Treatment’s impact is not only statistically real but also practically meaningful. This implies that implementing the Treatment could lead to a substantive and noticeable change in the outcome of interest.
Therefore, when assessing the importance of these findings, considering the effect size alongside statistical significance can provide more comprehensive insights for decision-making and practical implications.
Distribution Analysis
Distribution by Group
Group Comparison — Visual comparison of group distributions
Group Comparison
The group comparison data indicates a mean difference of -11.6365 between “Control” (mean of 99.4649) and “Treatment” (mean of 111.1015) groups. This observed difference suggests that, on average, the “Treatment” group scored higher compared to the “Control” group.
Practically, this difference could have important implications depending on the context of the study. For instance, in a medical trial, a mean score difference of -11.6365 could indicate that the treatment has a measurable effect on the outcome being studied. Further investigation would be needed to understand the significance and relevance of this difference in real-world applications.
Additionally, since the test type is specified as two-sided with unequal variances assumed, it suggests that the mean difference is not likely due to random chance. The confidence level of 95% implies that there is a high degree of certainty in the observed mean difference.
In conclusion, the mean difference of -11.6365 between the two groups in the group comparison data highlights a significant contrast that warrants further research to better comprehend the practical implications of this distinction.
Group Comparison
The group comparison data indicates a mean difference of -11.6365 between “Control” (mean of 99.4649) and “Treatment” (mean of 111.1015) groups. This observed difference suggests that, on average, the “Treatment” group scored higher compared to the “Control” group.
Practically, this difference could have important implications depending on the context of the study. For instance, in a medical trial, a mean score difference of -11.6365 could indicate that the treatment has a measurable effect on the outcome being studied. Further investigation would be needed to understand the significance and relevance of this difference in real-world applications.
Additionally, since the test type is specified as two-sided with unequal variances assumed, it suggests that the mean difference is not likely due to random chance. The confidence level of 95% implies that there is a high degree of certainty in the observed mean difference.
In conclusion, the mean difference of -11.6365 between the two groups in the group comparison data highlights a significant contrast that warrants further research to better comprehend the practical implications of this distinction.
Density Comparison
Density Comparison
Distribution Analysis — Density plots and histograms of group distributions
Distribution Analysis
Based on the provided data profile for Distribution Analysis, we have two groups: Control and Treatment. Here are insights on the shape, spread, and central tendency of each group’s distribution:
Control Group (n=50):
Treatment Group (n=45):
Comparison and Notable Patterns:
To conduct a more thorough analysis and visualize the distributions for a better understanding, generating density plots and histograms as intended in the data profile could help in further examining the data patterns and outliers.
Distribution Analysis
Based on the provided data profile for Distribution Analysis, we have two groups: Control and Treatment. Here are insights on the shape, spread, and central tendency of each group’s distribution:
Control Group (n=50):
Treatment Group (n=45):
Comparison and Notable Patterns:
To conduct a more thorough analysis and visualize the distributions for a better understanding, generating density plots and histograms as intended in the data profile could help in further examining the data patterns and outliers.
Practical Significance
Practical Significance
Effect Size Analysis effect_size Magnitude and practical significance of differences
| Measure | Value |
|---|---|
| Mean Difference | -11.637 |
| Cohen's d | -0.69 |
| Effect Magnitude | Medium |
| Statistical Power | 91.4% |
Effect Size
The Cohen’s d of -0.69 indicates a medium effect size. This suggests that there is a moderate practical significance to the observed difference between the Control and Treatment groups.
In practical terms, a medium effect size like this could imply that the Treatment group shows a meaningful reduction in the outcome being studied compared to the Control group.
Decision-making beyond statistical significance should take into account not only whether the results are statistically significant (which indicates whether the findings are likely not due to chance) but also whether the effect size is practically significant. In this case, even though the mean difference is statistically significant, the medium effect size suggests that the Treatment’s impact is not only statistically real but also practically meaningful. This implies that implementing the Treatment could lead to a substantive and noticeable change in the outcome of interest.
Therefore, when assessing the importance of these findings, considering the effect size alongside statistical significance can provide more comprehensive insights for decision-making and practical implications.
Effect Size
The Cohen’s d of -0.69 indicates a medium effect size. This suggests that there is a moderate practical significance to the observed difference between the Control and Treatment groups.
In practical terms, a medium effect size like this could imply that the Treatment group shows a meaningful reduction in the outcome being studied compared to the Control group.
Decision-making beyond statistical significance should take into account not only whether the results are statistically significant (which indicates whether the findings are likely not due to chance) but also whether the effect size is practically significant. In this case, even though the mean difference is statistically significant, the medium effect size suggests that the Treatment’s impact is not only statistically real but also practically meaningful. This implies that implementing the Treatment could lead to a substantive and noticeable change in the outcome of interest.
Therefore, when assessing the importance of these findings, considering the effect size alongside statistical significance can provide more comprehensive insights for decision-making and practical implications.
Range of Effect
Confidence Intervals confidence_intervals Confidence interval for mean difference
Confidence Intervals
The provided confidence interval is for the mean difference between two groups (Control and Treatment).
Mean Difference: The mean difference between the groups is calculated to be -11.6365.
Confidence Interval: The confidence interval ranges from -18.4989 to -4.7742 at a confidence level of 95%. This means that we are 95% confident that the true difference in means falls within this interval.
Interpretation:
Range of Plausible Values: The range of plausible values for the true difference in means is between -18.4989 and -4.7742. This suggests that we are quite confident that the actual difference lies within this range.
Statistical Significance: Since the confidence interval does not contain zero (CI_contains_zero: “No”), this indicates that there is a statistically significant difference between the groups.
In summary, based on the confidence interval provided, we can conclude that there is a statistically significant difference between the Control and Treatment groups, with a mean difference estimated to be between -18.4989 and -4.7742. This information aids in understanding the potential impact of the treatment compared to the control.
Confidence Intervals
The provided confidence interval is for the mean difference between two groups (Control and Treatment).
Mean Difference: The mean difference between the groups is calculated to be -11.6365.
Confidence Interval: The confidence interval ranges from -18.4989 to -4.7742 at a confidence level of 95%. This means that we are 95% confident that the true difference in means falls within this interval.
Interpretation:
Range of Plausible Values: The range of plausible values for the true difference in means is between -18.4989 and -4.7742. This suggests that we are quite confident that the actual difference lies within this range.
Statistical Significance: Since the confidence interval does not contain zero (CI_contains_zero: “No”), this indicates that there is a statistically significant difference between the groups.
In summary, based on the confidence interval provided, we can conclude that there is a statistically significant difference between the Control and Treatment groups, with a mean difference estimated to be between -18.4989 and -4.7742. This information aids in understanding the potential impact of the treatment compared to the control.
Study Adequacy
Statistical Power power_analysis Statistical power and sample size adequacy
Statistical Power
The statistical power of the study is reported to be 0.9136, indicating a high probability (91.36%) of detecting a true effect if it exists. With a Cohen’s d effect size of -0.69 and a sample size of 95, the study is deemed to have adequate power.
Implications for future studies:
Sample Size: The high statistical power achieved with 95 total samples suggests that the sample size was sufficient to detect the observed effect size. In future studies, maintaining a sample size around this level may be appropriate for similar effect sizes.
Effect Size: The negative Cohen’s d value of -0.69 indicates a medium to large effect size. Researchers should consider effect sizes from past studies or pilot studies to inform power analyses for future research.
Confidence Level: The confidence level of 95% used in the analysis is standard but can influence power. Researchers may want to vary the confidence level in power calculations to assess its impact on sample size requirements.
Test Type and Variance Equality: The choice of a two-sided test and unequal variances can affect power calculations. Conducting sensitivity analyses with different assumptions can provide a more comprehensive understanding of power requirements.
In conclusion, the study demonstrated high statistical power to detect the observed effect size, indicating that the sample size was adequate. Researchers should carefully consider effect sizes, confidence levels, and test assumptions in planning future studies to ensure adequate power for meaningful results.
Statistical Power
The statistical power of the study is reported to be 0.9136, indicating a high probability (91.36%) of detecting a true effect if it exists. With a Cohen’s d effect size of -0.69 and a sample size of 95, the study is deemed to have adequate power.
Implications for future studies:
Sample Size: The high statistical power achieved with 95 total samples suggests that the sample size was sufficient to detect the observed effect size. In future studies, maintaining a sample size around this level may be appropriate for similar effect sizes.
Effect Size: The negative Cohen’s d value of -0.69 indicates a medium to large effect size. Researchers should consider effect sizes from past studies or pilot studies to inform power analyses for future research.
Confidence Level: The confidence level of 95% used in the analysis is standard but can influence power. Researchers may want to vary the confidence level in power calculations to assess its impact on sample size requirements.
Test Type and Variance Equality: The choice of a two-sided test and unequal variances can affect power calculations. Conducting sensitivity analyses with different assumptions can provide a more comprehensive understanding of power requirements.
In conclusion, the study demonstrated high statistical power to detect the observed effect size, indicating that the sample size was adequate. Researchers should carefully consider effect sizes, confidence levels, and test assumptions in planning future studies to ensure adequate power for meaningful results.
Test Validity Assessment
Test Validity
Assumptions Check assumptions Validation of t-test assumptions
| Test | Statistic | p_value | Conclusion |
|---|---|---|---|
| Levene's Test | 0.207 | 0.650 | Equal variances |
| Shapiro-Wilk (Group 1) | 0.980 | 0.561 | Normal |
| Shapiro-Wilk (Group 2) | 0.939 | 0.019 | Non-normal |
Assumptions Check
Based on the provided data profile, the assumptions for a t-test are partially met and partially violated:
Equal Variances:
Normality:
If the normality assumption is violated, the implications are as follows:
In this case, since the assumption of normality is not met for Group 2, and the assumption of equal variances is met, you can still proceed with the t-test analysis if the sample size is large enough. However, if the sample size is small, it would be advisable to consider alternative non-parametric tests that do not rely on the normality assumption.
Assumptions Check
Based on the provided data profile, the assumptions for a t-test are partially met and partially violated:
Equal Variances:
Normality:
If the normality assumption is violated, the implications are as follows:
In this case, since the assumption of normality is not met for Group 2, and the assumption of equal variances is met, you can still proceed with the t-test analysis if the sample size is large enough. However, if the sample size is small, it would be advisable to consider alternative non-parametric tests that do not rely on the normality assumption.
Q-Q Plot Analysis
Q-Q Plots
Normality Diagnostics — Q-Q plots for normality assessment
Normality Check
The Shapiro-Wilk tests were conducted to assess the normality assumption for two groups: Control and Treatment. The p-value for the Shapiro-Wilk test in the Control group was 0.5611, indicating that the data in this group likely follow a normal distribution. However, for the Treatment group, the p-value was 0.0192, suggesting that the data in this group do not follow a normal distribution.
Given that the normality assumption was not met for the Treatment group based on the Shapiro-Wilk test, it is essential to interpret the Q-Q plots to further evaluate the normality of the data. Q-Q plots provide a visual assessment of how closely the data points align with the theoretical quantiles of a normal distribution. In this case, you would expect to see points on the Q-Q plot forming a relatively straight line if the data are normally distributed.
If the Q-Q plot for the Control group shows points aligning relatively well around a straight line, this would support the interpretation from the Shapiro-Wilk test that the data in the Control group are likely normally distributed.
For the Treatment group, if the Q-Q plot deviates noticeably from a straight line, with points showing a curved pattern or significant deviations, it would further confirm that the data in this group do not follow a normal distribution.
In conclusion, based on the Shapiro-Wilk test results and the visual inspection of Q-Q plots, it can be said that the normality assumption is reasonable for the Control group but not met for the Treatment group. This information is crucial when deciding on appropriate statistical tests or methodologies that rely on the assumption of normality.
Normality Check
The Shapiro-Wilk tests were conducted to assess the normality assumption for two groups: Control and Treatment. The p-value for the Shapiro-Wilk test in the Control group was 0.5611, indicating that the data in this group likely follow a normal distribution. However, for the Treatment group, the p-value was 0.0192, suggesting that the data in this group do not follow a normal distribution.
Given that the normality assumption was not met for the Treatment group based on the Shapiro-Wilk test, it is essential to interpret the Q-Q plots to further evaluate the normality of the data. Q-Q plots provide a visual assessment of how closely the data points align with the theoretical quantiles of a normal distribution. In this case, you would expect to see points on the Q-Q plot forming a relatively straight line if the data are normally distributed.
If the Q-Q plot for the Control group shows points aligning relatively well around a straight line, this would support the interpretation from the Shapiro-Wilk test that the data in the Control group are likely normally distributed.
For the Treatment group, if the Q-Q plot deviates noticeably from a straight line, with points showing a curved pattern or significant deviations, it would further confirm that the data in this group do not follow a normal distribution.
In conclusion, based on the Shapiro-Wilk test results and the visual inspection of Q-Q plots, it can be said that the normality assumption is reasonable for the Control group but not met for the Treatment group. This information is crucial when deciding on appropriate statistical tests or methodologies that rely on the assumption of normality.
Statistical Adequacy
Study Adequacy
Statistical Power power_analysis Statistical power and sample size adequacy
Statistical Power
The statistical power of the study is reported to be 0.9136, indicating a high probability (91.36%) of detecting a true effect if it exists. With a Cohen’s d effect size of -0.69 and a sample size of 95, the study is deemed to have adequate power.
Implications for future studies:
Sample Size: The high statistical power achieved with 95 total samples suggests that the sample size was sufficient to detect the observed effect size. In future studies, maintaining a sample size around this level may be appropriate for similar effect sizes.
Effect Size: The negative Cohen’s d value of -0.69 indicates a medium to large effect size. Researchers should consider effect sizes from past studies or pilot studies to inform power analyses for future research.
Confidence Level: The confidence level of 95% used in the analysis is standard but can influence power. Researchers may want to vary the confidence level in power calculations to assess its impact on sample size requirements.
Test Type and Variance Equality: The choice of a two-sided test and unequal variances can affect power calculations. Conducting sensitivity analyses with different assumptions can provide a more comprehensive understanding of power requirements.
In conclusion, the study demonstrated high statistical power to detect the observed effect size, indicating that the sample size was adequate. Researchers should carefully consider effect sizes, confidence levels, and test assumptions in planning future studies to ensure adequate power for meaningful results.
Statistical Power
The statistical power of the study is reported to be 0.9136, indicating a high probability (91.36%) of detecting a true effect if it exists. With a Cohen’s d effect size of -0.69 and a sample size of 95, the study is deemed to have adequate power.
Implications for future studies:
Sample Size: The high statistical power achieved with 95 total samples suggests that the sample size was sufficient to detect the observed effect size. In future studies, maintaining a sample size around this level may be appropriate for similar effect sizes.
Effect Size: The negative Cohen’s d value of -0.69 indicates a medium to large effect size. Researchers should consider effect sizes from past studies or pilot studies to inform power analyses for future research.
Confidence Level: The confidence level of 95% used in the analysis is standard but can influence power. Researchers may want to vary the confidence level in power calculations to assess its impact on sample size requirements.
Test Type and Variance Equality: The choice of a two-sided test and unequal variances can affect power calculations. Conducting sensitivity analyses with different assumptions can provide a more comprehensive understanding of power requirements.
In conclusion, the study demonstrated high statistical power to detect the observed effect size, indicating that the sample size was adequate. Researchers should carefully consider effect sizes, confidence levels, and test assumptions in planning future studies to ensure adequate power for meaningful results.
Range of Effect
Confidence Intervals confidence_intervals Confidence interval for mean difference
Confidence Intervals
The provided confidence interval is for the mean difference between two groups (Control and Treatment).
Mean Difference: The mean difference between the groups is calculated to be -11.6365.
Confidence Interval: The confidence interval ranges from -18.4989 to -4.7742 at a confidence level of 95%. This means that we are 95% confident that the true difference in means falls within this interval.
Interpretation:
Range of Plausible Values: The range of plausible values for the true difference in means is between -18.4989 and -4.7742. This suggests that we are quite confident that the actual difference lies within this range.
Statistical Significance: Since the confidence interval does not contain zero (CI_contains_zero: “No”), this indicates that there is a statistically significant difference between the groups.
In summary, based on the confidence interval provided, we can conclude that there is a statistically significant difference between the Control and Treatment groups, with a mean difference estimated to be between -18.4989 and -4.7742. This information aids in understanding the potential impact of the treatment compared to the control.
Confidence Intervals
The provided confidence interval is for the mean difference between two groups (Control and Treatment).
Mean Difference: The mean difference between the groups is calculated to be -11.6365.
Confidence Interval: The confidence interval ranges from -18.4989 to -4.7742 at a confidence level of 95%. This means that we are 95% confident that the true difference in means falls within this interval.
Interpretation:
Range of Plausible Values: The range of plausible values for the true difference in means is between -18.4989 and -4.7742. This suggests that we are quite confident that the actual difference lies within this range.
Statistical Significance: Since the confidence interval does not contain zero (CI_contains_zero: “No”), this indicates that there is a statistically significant difference between the groups.
In summary, based on the confidence interval provided, we can conclude that there is a statistically significant difference between the Control and Treatment groups, with a mean difference estimated to be between -18.4989 and -4.7742. This information aids in understanding the potential impact of the treatment compared to the control.
Practical Significance
Effect Size Analysis effect_size Magnitude and practical significance of differences
| Measure | Value |
|---|---|
| Mean Difference | -11.637 |
| Cohen's d | -0.69 |
| Effect Magnitude | Medium |
| Statistical Power | 91.4% |
Effect Size
The Cohen’s d of -0.69 indicates a medium effect size. This suggests that there is a moderate practical significance to the observed difference between the Control and Treatment groups.
In practical terms, a medium effect size like this could imply that the Treatment group shows a meaningful reduction in the outcome being studied compared to the Control group.
Decision-making beyond statistical significance should take into account not only whether the results are statistically significant (which indicates whether the findings are likely not due to chance) but also whether the effect size is practically significant. In this case, even though the mean difference is statistically significant, the medium effect size suggests that the Treatment’s impact is not only statistically real but also practically meaningful. This implies that implementing the Treatment could lead to a substantive and noticeable change in the outcome of interest.
Therefore, when assessing the importance of these findings, considering the effect size alongside statistical significance can provide more comprehensive insights for decision-making and practical implications.
Effect Size
The Cohen’s d of -0.69 indicates a medium effect size. This suggests that there is a moderate practical significance to the observed difference between the Control and Treatment groups.
In practical terms, a medium effect size like this could imply that the Treatment group shows a meaningful reduction in the outcome being studied compared to the Control group.
Decision-making beyond statistical significance should take into account not only whether the results are statistically significant (which indicates whether the findings are likely not due to chance) but also whether the effect size is practically significant. In this case, even though the mean difference is statistically significant, the medium effect size suggests that the Treatment’s impact is not only statistically real but also practically meaningful. This implies that implementing the Treatment could lead to a substantive and noticeable change in the outcome of interest.
Therefore, when assessing the importance of these findings, considering the effect size alongside statistical significance can provide more comprehensive insights for decision-making and practical implications.
Comprehensive Summary
Descriptive Statistics
Summary Statistics summary_statistics Detailed descriptive statistics by group
| Group | N | Mean | SD | SE | Min | Q1 | Median | Q3 | Max |
|---|---|---|---|---|---|---|---|---|---|
| Control | 50.000 | 99.465 | 17.272 | 2.443 | 60.153 | 90.517 | 98.494 | 109.761 | 134.300 |
| Treatment | 45.000 | 111.102 | 16.397 | 2.444 | 54.124 | 101.390 | 113.128 | 120.976 | 136.363 |
Summary Statistics
Based on the provided data profile, we have descriptive statistics for two groups: Control and Treatment.
Control Group:
Treatment Group:
Key Characteristics:
Central Tendency:
Variability:
Sample Sizes:
These key characteristics provide insights into the central tendency, variability, and sample sizes of the two groups, which are essential for understanding and comparing their respective distributions and characteristics.
Summary Statistics
Based on the provided data profile, we have descriptive statistics for two groups: Control and Treatment.
Control Group:
Treatment Group:
Key Characteristics:
Central Tendency:
Variability:
Sample Sizes:
These key characteristics provide insights into the central tendency, variability, and sample sizes of the two groups, which are essential for understanding and comparing their respective distributions and characteristics.
Key Findings and Technical Details
Actionable Insights
Recommendations — recommendations — Actionable insights and next steps
Company: Test Corp
Objective: Compare mean differences between control and treatment groups
Recommendations
Based on the provided data profile, here are 3-5 actionable recommendations:
Review Assumptions: Since the assumptions are only partially met, it is crucial to thoroughly examine the assumptions of the statistical test being conducted. Check for potential violations such as normality, independence, and homogeneity of variances. Addressing any assumptions that are not met can improve the reliability of the results.
Interpret Effect Size: With a medium effect size, it is important to delve deeper into the practical significance of the differences between the control and treatment groups. Understand how this effect size translates into real-world impact for Test Corp. Consider whether the observed effect is meaningful from a business perspective.
Utilize Statistical Significance: Given that the results are statistically significant, leverage this information to make informed decisions. Identify the areas where these differences lie and explore why they exist. Consider implementing changes based on these significant findings to drive improvements within Test Corp.
Further Analysis: Explore additional factors that may be influencing the observed differences between the control and treatment groups. Conduct subgroup analysis or delve into specific variables to uncover more insights. This can help in identifying potential confounding variables and refining strategies.
Communicate Insights: Ensure that the insights derived from the data analysis are effectively communicated within Test Corp. Share the actionable recommendations with relevant stakeholders, such as decision-makers and team members, to facilitate informed decision-making and drive positive changes based on the results.
By following these recommendations, Test Corp can enhance its understanding of the differences between the control and treatment groups and leverage this knowledge to make strategic decisions that positively impact the company’s objectives.
Recommendations
Based on the provided data profile, here are 3-5 actionable recommendations:
Review Assumptions: Since the assumptions are only partially met, it is crucial to thoroughly examine the assumptions of the statistical test being conducted. Check for potential violations such as normality, independence, and homogeneity of variances. Addressing any assumptions that are not met can improve the reliability of the results.
Interpret Effect Size: With a medium effect size, it is important to delve deeper into the practical significance of the differences between the control and treatment groups. Understand how this effect size translates into real-world impact for Test Corp. Consider whether the observed effect is meaningful from a business perspective.
Utilize Statistical Significance: Given that the results are statistically significant, leverage this information to make informed decisions. Identify the areas where these differences lie and explore why they exist. Consider implementing changes based on these significant findings to drive improvements within Test Corp.
Further Analysis: Explore additional factors that may be influencing the observed differences between the control and treatment groups. Conduct subgroup analysis or delve into specific variables to uncover more insights. This can help in identifying potential confounding variables and refining strategies.
Communicate Insights: Ensure that the insights derived from the data analysis are effectively communicated within Test Corp. Share the actionable recommendations with relevant stakeholders, such as decision-makers and team members, to facilitate informed decision-making and drive positive changes based on the results.
By following these recommendations, Test Corp can enhance its understanding of the differences between the control and treatment groups and leverage this knowledge to make strategic decisions that positively impact the company’s objectives.
T-Test Key Findings
Executive Summary — overview — High-level t-test results and key findings
Company: Test Corp
Objective: Compare mean differences between control and treatment groups
| Group | N | Mean | SD | SE | Min | Q1 | Median | Q3 | Max |
|---|---|---|---|---|---|---|---|---|---|
| Control | 50.000 | 99.465 | 17.272 | 2.443 | 60.153 | 90.517 | 98.494 | 109.761 | 134.300 |
| Treatment | 45.000 | 111.102 | 16.397 | 2.444 | 54.124 | 101.390 | 113.128 | 120.976 | 136.363 |
Executive Summary
Statistically Significant Difference: The t-test results indicate a statistically significant difference between the control and treatment groups, with a p-value of 0.0011 (below the significance level of 0.05).
Practical Significance (Effect Size): The mean difference between the groups is -11.6365 units, with a Cohen’s d effect size of -0.69, indicating a medium practical significance. This suggests that the treatment has a moderate impact on the outcome compared to the control.
Key Business Implications: The findings show that the treatment group significantly outperforms the control group. With a medium effect size, the treatment can be considered impactful in practical terms. This highlights the potential benefit and relevance of implementing the treatment in a business context to improve the targeted outcome. Consider further investigation into the specific attributes of the treatment that led to this significant effect for optimizing business strategies.
Executive Summary
Statistically Significant Difference: The t-test results indicate a statistically significant difference between the control and treatment groups, with a p-value of 0.0011 (below the significance level of 0.05).
Practical Significance (Effect Size): The mean difference between the groups is -11.6365 units, with a Cohen’s d effect size of -0.69, indicating a medium practical significance. This suggests that the treatment has a moderate impact on the outcome compared to the control.
Key Business Implications: The findings show that the treatment group significantly outperforms the control group. With a medium effect size, the treatment can be considered impactful in practical terms. This highlights the potential benefit and relevance of implementing the treatment in a business context to improve the targeted outcome. Consider further investigation into the specific attributes of the treatment that led to this significant effect for optimizing business strategies.
Methodology & Parameters
Technical Details — Complete statistical output and methodology
| Test | Statistic | p_value | Conclusion |
|---|---|---|---|
| t-test | -3.368 | 0.001 | Significant difference |
| Levene's Test | 0.207 | 0.650 | Equal variances |
| Shapiro-Wilk (Group 1) | 0.980 | 0.561 | Normal |
| Shapiro-Wilk (Group 2) | 0.939 | 0.019 | Non-normal |
Technical Details
The technical details provided insights into the statistical analysis conducted using Welch’s t-test on two groups, highlighting significant differences between them. Considering the normality and variance assumptions, it’s important to interpret the results cautiously, especially in the context of the research question at hand.
Technical Details
The technical details provided insights into the statistical analysis conducted using Welch’s t-test on two groups, highlighting significant differences between them. Considering the normality and variance assumptions, it’s important to interpret the results cautiously, especially in the context of the research question at hand.