Analysis Explanations

Author

Sarah Morris

Published

February 19, 2025

Comprehensive Guide to Statistical Analysis Methods Used

This guide explains the statistical analysis methods used in the study, providing context for interpreting results related to respiratory muscle training (RMT) among wind instrumentalists.

1 Descriptive Statistics

1.1 Frequency Distributions

What it shows: The count and percentage of observations in each category of a variable. How to interpret: Provides an overview of how observations are distributed across categories. Example in the study: Gender distribution shows 48.1% male, 46.5% female, 4.36% non-binary, and 0.963% not specified participants.

1.2 Measures of Central Tendency

Mean: The average value of a variable.
Median: The middle value when observations are arranged in order.
Mode: The most frequently occurring value. How to interpret: These measures indicate the typical or central value of a distribution. Example in the study: For years of playing experience, the mode was “20+ years” (41.8% of participants).

1.3 Measures of Dispersion

Standard Deviation (SD): Measures the amount of variation or dispersion from the mean.
Range: The difference between the maximum and minimum values.
Interquartile Range (IQR): The range between the first and third quartiles. How to interpret: Larger values indicate greater variability in the data. Example in the study: For frequency of playing, the SD was 0.986 on a scale of 1-5.

1.4 Inferential Statistics

1.5 Chi-Square Tests

Chi-Square Test of Independence

What it shows: Whether there is a significant association between two categorical variables. How to interpret:

The p-value indicates whether the association is statistically significant (typically p < 0.05).
Examine standardized residuals (values > |1.96| indicate significant contributions to the chi-square statistic). Example in the study: Chi-square test between gender and RMT usage (χ² = 13.754, df = 2, p = 0.001031), indicating a significant association.

Chi-Square Goodness-of-Fit Test

What it shows: Whether the observed frequency distribution differs from an expected distribution. How to interpret: A significant p-value indicates the observed distribution differs from the expected distribution. Example in the study: Chi-square test for country of education (χ² = 1111.3, df = 5, p < 0.001), showing distribution is not equal.

1.6 Effect Size Measures

Cramer’s V

What it shows: The strength of association between categorical variables. How to interpret:

0.1: Small effect
0.3: Medium effect
0.5: Large effect Example in the study: For the association between gender and RMT usage, Cramer’s V = 0.094, indicating a small effect.

Odds Ratio

What it shows: The ratio of the odds of an event occurring in one group to the odds in another group. How to interpret:

OR = 1: No association
OR > 1: Positive association
OR < 1: Negative association Example in the study: For teaching income and RMT use, OR = 0.384, indicating lower odds of having teaching income for non-RMT users.

1.7 T-Tests and Non-Parametric Alternatives

Independent Samples T-Test

What it shows: Whether the means of two independent groups differ significantly. How to interpret: A significant p-value (< 0.05) indicates the means differ more than would be expected by chance. Example in the study: T-test comparing playing ability between RMT users and non-users (t = 6.125, p < 0.001).

Mann-Whitney U Test (Wilcoxon Rank Sum Test)

What it shows: Whether there are differences in the distributions of two groups when data isn’t normally distributed. How to interpret: Similar to the t-test, but uses ranks instead of actual values. Example in the study: Mann-Whitney test for symptom frequency (W = 126447, p < 0.001), showing RMT users report more frequent symptoms.

1.8 Analysis of Variance (ANOVA)

What it shows: Whether there are significant differences among the means of three or more groups. How to interpret: A significant F-statistic and p-value indicate at least one group mean differs from the others. Example in the study: ANOVA for perceived importance of body parts (F = 175.515, p < 0.001).

Post-hoc Tests

What it shows: Which specific group means differ after finding a significant ANOVA result. How to interpret: Examine the p-values for each pairwise comparison, often with correction for multiple comparisons. Example in the study: Pairwise comparisons of age groups with Bonferroni correction identified significant differences between 30-39 age group and others.

1.9 Regression Analysis

Logistic Regression

What it shows: The relationship between predictor variables and a binary outcome variable. How to interpret:

Coefficients represent the log odds of the outcome for a one-unit change in the predictor.
Exponentiated coefficients represent odds ratios. Example in the study: Logistic regression of RMT usage on playing ability (Advanced players had 1.972 times higher odds of using RMT compared to beginners).

2 Specialized Analysis Techniques

2.1 Fisher’s Exact Test

What it shows: Association between categorical variables when sample sizes are small. How to interpret: Similar to chi-square test but more accurate for small samples. Example in the study: Fisher’s exact test for country of residence and RMT usage (p < 0.001).

2.2 Multiple Comparisons Corrections

Bonferroni Correction

What it shows: Adjusted p-values to account for multiple statistical tests. How to interpret: Divides the significance level by the number of tests to control the family-wise error rate. Example in the study: Bonferroni-adjusted p-values for pairwise comparisons between age groups.

2.3 Standardized Residuals

What it shows: The contribution of each cell to the chi-square statistic. How to interpret: Values greater than |1.96| indicate cells that significantly contribute to the chi-square statistic at p < 0.05. Example in the study: Standardized residuals for frequency of playing showed values of 9.61 for “Everyday” in the “MAX” category.

3 Visualizing Results

3.1 Reading Graphical Presentations

Bar Charts and Histograms

What they show: Frequency distributions of categorical or binned continuous variables. How to interpret: The height of each bar represents the frequency or percentage in that category.

Box Plots

What they show: Distribution summary with median, quartiles, and outliers. How to interpret: The box shows the IQR, the line inside the box is the median, and whiskers extend to the range (excluding outliers).

Error Bars

What they show: Uncertainty or variability in measurements. How to interpret: Typically represent standard errors, standard deviations, or confidence intervals.

4 Interpreting Confidence Intervals

What they show: A range of values likely to contain the true population parameter. How to interpret:

Wider intervals indicate less precision.
Non-overlapping confidence intervals between groups suggest significant differences. Example in the study: 95% confidence intervals for disorder prevalence rates (e.g., General Anxiety: 40.9% to 48.2%).

5 Statistical Significance vs. Practical Significance

Statistical significance: Indicates that results are unlikely due to chance (p < 0.05). Practical significance: Indicates that results are meaningful in a real-world context. How to distinguish:

Look at effect sizes (Cramer’s V, Cohen’s d, odds ratios) to determine practical importance.
With large samples, even tiny differences can be statistically significant without practical importance. Example in the study: While many associations with RMT were statistically significant, effect sizes varied from small (Cramer’s V = 0.089 for years of playing) to large (Cramer’s V = 0.533 for opinions on device effectiveness).

6 Limitations in Statistical Analysis

Missing data: Can affect results if not randomly distributed.
Multiple testing: Increases the chance of false positives if not corrected.
Causality: Statistical associations do not necessarily imply causation.
Sampling bias: Results may not generalize if the sample isn’t representative.

Understanding these statistical concepts helps in critically evaluating the findings related to respiratory muscle training practices, their associations with demographic factors, and their potential impact on wind instrumentalists’ performance and experiences.

--- title: "Analysis Explanations" author: "Sarah Morris" date: "2025-02-19" format: html: toc: true toc-depth: 2 toc-title: "Table of Contents" toc-location: right number-sections: true theme: cosmo code-fold: true code-tools: true highlight-style: github execute: echo: true warning: false error: false --- Comprehensive Guide to Statistical Analysis Methods Used This guide explains the statistical analysis methods used in the study, providing context for interpreting results related to respiratory muscle training (RMT) among wind instrumentalists. # Descriptive Statistics ## Frequency Distributions **What it shows:** The count and percentage of observations in each category of a variable. **How to interpret:** Provides an overview of how observations are distributed across categories. **Example in the study:** Gender distribution shows 48.1% male, 46.5% female, 4.36% non-binary, and 0.963% not specified participants. ## Measures of Central Tendency - **Mean:** The average value of a variable. - **Median:** The middle value when observations are arranged in order. - **Mode:** The most frequently occurring value. **How to interpret:** These measures indicate the typical or central value of a distribution. **Example in the study:** For years of playing experience, the mode was "20+ years" (41.8% of participants). ## Measures of Dispersion - **Standard Deviation (SD):** Measures the amount of variation or dispersion from the mean. - **Range:** The difference between the maximum and minimum values. - **Interquartile Range (IQR):** The range between the first and third quartiles. **How to interpret:** Larger values indicate greater variability in the data. **Example in the study:** For frequency of playing, the SD was 0.986 on a scale of 1-5. ## Inferential Statistics ## Chi-Square Tests **Chi-Square Test of Independence** **What it shows:** Whether there is a significant association between two categorical variables. **How to interpret:** - The p-value indicates whether the association is statistically significant (typically p \< 0.05). - Examine standardized residuals (values \> \|1.96\| indicate significant contributions to the chi-square statistic). **Example in the study:** Chi-square test between gender and RMT usage (χ² = 13.754, df = 2, p = 0.001031), indicating a significant association. **Chi-Square Goodness-of-Fit Test** **What it shows:** Whether the observed frequency distribution differs from an expected distribution. **How to interpret:** A significant p-value indicates the observed distribution differs from the expected distribution. **Example in the study:** Chi-square test for country of education (χ² = 1111.3, df = 5, p \< 0.001), showing distribution is not equal. ## Effect Size Measures **Cramer's V** **What it shows:** The strength of association between categorical variables. **How to interpret:** - 0.1: Small effect - 0.3: Medium effect - 0.5: Large effect **Example in the study:** For the association between gender and RMT usage, Cramer's V = 0.094, indicating a small effect. **Odds Ratio** **What it shows:** The ratio of the odds of an event occurring in one group to the odds in another group. **How to interpret:** - OR = 1: No association - OR \> 1: Positive association - OR \< 1: Negative association **Example in the study:** For teaching income and RMT use, OR = 0.384, indicating lower odds of having teaching income for non-RMT users. ## T-Tests and Non-Parametric Alternatives **Independent Samples T-Test** **What it shows:** Whether the means of two independent groups differ significantly. **How to interpret:** A significant p-value (\< 0.05) indicates the means differ more than would be expected by chance. **Example in the study:** T-test comparing playing ability between RMT users and non-users (t = 6.125, p \< 0.001). **Mann-Whitney U Test (Wilcoxon Rank Sum Test)** **What it shows:** Whether there are differences in the distributions of two groups when data isn't normally distributed. **How to interpret:** Similar to the t-test, but uses ranks instead of actual values. **Example in the study:** Mann-Whitney test for symptom frequency (W = 126447, p \< 0.001), showing RMT users report more frequent symptoms. ## Analysis of Variance (ANOVA) **What it shows:** Whether there are significant differences among the means of three or more groups. **How to interpret:** A significant F-statistic and p-value indicate at least one group mean differs from the others. **Example in the study:** ANOVA for perceived importance of body parts (F = 175.515, p \< 0.001). **Post-hoc Tests** **What it shows:** Which specific group means differ after finding a significant ANOVA result. **How to interpret:** Examine the p-values for each pairwise comparison, often with correction for multiple comparisons. **Example in the study:** Pairwise comparisons of age groups with Bonferroni correction identified significant differences between 30-39 age group and others. ## Regression Analysis **Logistic Regression** **What it shows:** The relationship between predictor variables and a binary outcome variable. **How to interpret:** - Coefficients represent the log odds of the outcome for a one-unit change in the predictor. - Exponentiated coefficients represent odds ratios. **Example in the study:** Logistic regression of RMT usage on playing ability (Advanced players had 1.972 times higher odds of using RMT compared to beginners). # Specialized Analysis Techniques ## Fisher's Exact Test **What it shows:** Association between categorical variables when sample sizes are small. **How to interpret:** Similar to chi-square test but more accurate for small samples. **Example in the study:** Fisher's exact test for country of residence and RMT usage (p \< 0.001). ## Multiple Comparisons Corrections **Bonferroni Correction** **What it shows:** Adjusted p-values to account for multiple statistical tests. **How to interpret:** Divides the significance level by the number of tests to control the family-wise error rate. **Example in the study:** Bonferroni-adjusted p-values for pairwise comparisons between age groups. ## Standardized Residuals **What it shows:** The contribution of each cell to the chi-square statistic. **How to interpret:** Values greater than \|1.96\| indicate cells that significantly contribute to the chi-square statistic at p \< 0.05. **Example in the study:** Standardized residuals for frequency of playing showed values of 9.61 for "Everyday" in the "MAX" category. # Visualizing Results ## Reading Graphical Presentations **Bar Charts and Histograms** **What they show:** Frequency distributions of categorical or binned continuous variables. **How to interpret:** The height of each bar represents the frequency or percentage in that category. **Box Plots** **What they show:** Distribution summary with median, quartiles, and outliers. **How to interpret:** The box shows the IQR, the line inside the box is the median, and whiskers extend to the range (excluding outliers). **Error Bars** **What they show:** Uncertainty or variability in measurements. **How to interpret:** Typically represent standard errors, standard deviations, or confidence intervals. # Interpreting Confidence Intervals **What they show:** A range of values likely to contain the true population parameter. **How to interpret:** - Wider intervals indicate less precision. - Non-overlapping confidence intervals between groups suggest significant differences. **Example in the study:** 95% confidence intervals for disorder prevalence rates (e.g., General Anxiety: 40.9% to 48.2%). # Statistical Significance vs. Practical Significance **Statistical significance:** Indicates that results are unlikely due to chance (p \< 0.05). **Practical significance:** Indicates that results are meaningful in a real-world context. **How to distinguish:** - Look at effect sizes (Cramer's V, Cohen's d, odds ratios) to determine practical importance. - With large samples, even tiny differences can be statistically significant without practical importance. **Example in the study:** While many associations with RMT were statistically significant, effect sizes varied from small (Cramer's V = 0.089 for years of playing) to large (Cramer's V = 0.533 for opinions on device effectiveness). # Limitations in Statistical Analysis - **Missing data:** Can affect results if not randomly distributed. - **Multiple testing:** Increases the chance of false positives if not corrected. - **Causality:** Statistical associations do not necessarily imply causation. - **Sampling bias:** Results may not generalize if the sample isn't representative. Understanding these statistical concepts helps in critically evaluating the findings related to respiratory muscle training practices, their associations with demographic factors, and their potential impact on wind instrumentalists' performance and experiences.