Week 11 Collab Session - Ratios, Odss, Chi-square Tests and Cross Tabulations

Foundations of Statistics - Week Eleven Collaborative Session Notes

Concise Version

Introduction

  • Host: Manjila

  • Focus: Relationship between two categorical variables, specifically cross tabulations and chi-square test.

  • Addressing questions in chat box during the session.

Acknowledgments

  • Respectful acknowledgment of the traditional owners of land across Australia, their elders, ancestors, cultures, and heritage.

Agenda for the Session

  1. Background theory on chi-square test.

  2. Exercises:

    • Cross Tabulations.

    • Full report writing.

    • Calculation of risk ratios.

  3. Q&A on chi-square test at the end of the session.

  4. Reminder: Unique feedback survey available for feedback on the foundation of statistics unit.

  5. Announcements:

    • Last week of new content; revision week upcoming.

    • Final exam scheduled for Thursday, February 12.

Confidence Check

  • Participants were encouraged to share feelings about content and exam readiness (nervous vs. confident).

  • Reassurance provided regarding learning material and examination preparation.

Review of Statistical Tests Covered

  • Overview of tests learned over past 11 weeks:

    • Binomial test

    • T-test

    • Correlation

    • Regression

    • Introduction to chi-square test.

Determining Appropriate Statistical Tests

  • Important questions to consider:

    • How many variables?

    • What type of variables? (metric or categorical)

    • What are the independent and dependent variables?

Examples of Conclusions and Corresponding Tests

  1. Conclusion: "People working full-time take longer to travel to work than those employed part-time."

    • Test: Independent sample t-test.

  2. Conclusion: "More than 42% of Australians have access to a computer at home."

    • Test: Binomial test.

  3. Conclusion: "Number of cigarettes smoked reduces after hypnosis therapy."

    • Test: Paired sample t-test.

  4. Conclusion: "People with more years of experience tend to earn higher salaries."

    • Test: Correlation (or regression).

Introduction to Chi-square Test

  • The chi-square test investigates the relationship between two categorical variables.

  • Example question: Are males more likely to be satisfied with their car than females?

    • Independent Variable: Gender

    • Dependent Variable: Satisfaction with the car.

    • Arrangement in crosstab:

      • Independent variable in columns, dependent variable in rows.

      • Grand total equals total sample size.

Crosstabulation Example

  • Sample distribution with 100 males and 50 females; satisfaction levels noted.

  • Example provided for males: 20 satisfied, demonstrating how to interpret values in the crosstab.

SPSS Procedure for Chi-square Test

  • Instructions on running chi-square in SPSS:

    1. Go to descriptive statistics, select cross tabs.

    2. Move independent and dependent variables to the correct boxes.

    3. Select statistics and choose chi-square.

    4. Ensure “column percentages” is selected.

    5. Continue to generate output.

Practice Questions Using SPSS Data

  1. Calculate total respondents in poor health.

  2. Calculate total respondents with a good diet.

  3. Determine respondents with good diet and excellent health (intersecting data).

  4. Calculate percentage of respondents with good diet in excellent health:

    • Formula for percentage: rac{37}{80} imes 100 = 46.25 ext{%}

  5. Similar calculation for those in poor diet with excellent health leading to rac{17}{70} imes 100 = 24.29 ext{%} .

Chi-square Test Output Analysis

  • SPSS output relevant for reporting results and determining significance.

  • Important values to include in reports:

    • Pearson chi-square value: 8.222

    • Degrees of freedom: 2

    • P-value: 0.016

  • Report format for chi-square:

    • χ2(2,N=150)=8.222,p=0.016\chi^2(2, N=150) = 8.222, p = 0.016.

Report Writing for Chi-square Test

Structure for Writing Report

  1. State the research question/hypothesis.

  2. Introduce sample specifics (size, nature).

  3. Describe sample relationship (percentages if significant).

  4. State the test conducted (chi-square) and its significance.

  5. Report chi-square statistic and p-value.

  6. State if the hypothesis was supported.

Sample Report Exemplar

  • Sample report based on hypothesis: "People with good diet have different health outcomes compared to poor diets."

  • Summary with statistics and interpretations included only when results are significant (e.g., difference in health status).

Reporting Non-significant Results

  • If p-value exceeds 0.05, note that the relationship is not significant and skip details on comparative percentages.

Introduction to Risk Ratios and Odds Ratios

  • Definitions:

    • Risk: Probability of an event occurring out of total instances (e.g., selecting vanilla ice cream).

    • Relative risk: Ratio of risks between two events (e.g., vanilla vs. chocolate ice cream).

    • Odds: Ratio of an event occurring vs. not occurring.

    • Odds Ratio: Ratio comparing two events to see which is more likely to occur.

Example with Aspirin and Heart Attack

  • Total Sample Size: 250

    • Aspirin Group: 150 (15 had a stroke).

    • Placebo Group: 100 (20 had a stroke).

  • Calculation Steps for Relative Risk:

    1. Risk in Aspirin = 15150=0.1\frac{15}{150} = 0.1

    2. Risk in Placebo = 20100=0.2\frac{20}{100} = 0.2

    3. Relative Risk = 0.10.2=0.5\frac{0.1}{0.2} = 0.5.

    • Interpretation: Participants using aspirin have half the risk of a stroke compared to placebo users.

    • Value of 1 indicates no difference in risk between groups.

Summary of Learning Tasks

  1. Complete Lab 11 Report for chi-square test.

  2. Watch module on relative risk and odds ratio.

  3. Update topic tests on statistics content.

  4. Encouragement to engage in exercises and seek help if needed.

Conclusion

  • Emphasis on preparation for final exam.

  • Encourage practice and revision of all topics covered.

  • Thank fans for attending, invitation to reach out with questions.

Detailed Version

Introduction

  • Host: Manjila, experienced in statistical methods and engaging in educational sessions.

  • Focus: An in-depth exploration of the relationship between two categorical variables, emphasizing the significance of cross tabulations and the chi-square test.

  • Session format includes addressing participant queries via the chat box, ensuring interactive learning.

Acknowledgments

  • Respectfully acknowledging the traditional owners of the land across Australia, recognizing their elders, ancestors, cultures, and heritage, which underpins a commitment to inclusivity in the educational setting.

Agenda for the Session

  1. Detailed background theory on the chi-square test, including conditions for applicability and its role in statistical analysis of categorical data.

  2. Hands-on exercises:

    • Comprehensive exploration of Cross Tabulations, illustrating data segregation and comparison between categories.

    • Emphasis on Full Report Writing, focusing on the structure and clarity needed for effective communication of results.

    • Calculation of risk ratios, including practical applications in real-world scenarios.

  3. Q&A session focused on the chi-square test at the end, allowing participants to clarify doubts and solidify their understanding.

  4. Reminder: Unique feedback survey available for participants' insights on the Foundations of Statistics unit, encouraging continuous improvement of the course.

  5. Announcements:

    • Importance of current week as the last week for introducing new content while anticipating an upcoming revision week for consolidation of learned material.

    • Final exam scheduled for Thursday, February 12, stressing the importance of comprehensive understanding for proper preparation.

Confidence Check

  • Encouragement for participants to share their feelings about the session's content and readiness for exams, with attention to a spectrum of emotions from nervousness to confidence, fostering a supportive learning environment.

  • Reassurance provided regarding mastery of learning materials and effective examination preparation strategies.

Review of Statistical Tests Covered

  • Comprehensive overview of various statistical tests learned over the past 11 weeks, enhancing understanding of when and how to apply each:

    • Binomial test: assessing proportions.

    • T-test: comparing means across groups.

    • Correlation: measuring relationships between continuous variables.

    • Regression: exploring dependencies among variables.

    • Introduction to chi-square test: foundational knowledge for analyzing categorical data.

Determining Appropriate Statistical Tests

  • Key considerations for selecting statistical tests:

    • Number of variables involved in the study.

    • Types of variables (metric or categorical).

    • Identification of independent and dependent variables within the analysis.

Examples of Conclusions and Corresponding Tests

  1. Conclusion: "People working full-time take longer to travel to work than those employed part-time."

    • Test: Independent sample t-test, allowing for comparisons between two distinct groups.

  2. Conclusion: "More than 42% of Australians have access to a computer at home."

    • Test: Binomial test, suited for determining proportions in categorical data.

  3. Conclusion: "Number of cigarettes smoked reduces after hypnosis therapy."

    • Test: Paired sample t-test, utilized for within-subject comparisons before and after treatment phases.

  4. Conclusion: "People with more years of experience tend to earn higher salaries."

    • Test: Correlation (or regression), facilitating insight into relationships between years of experience and salary variables.

Introduction to Chi-square Test

  • The chi-square test is central to investigating relationships between two categorical variables, providing robust insights in categorical data analysis.

  • Example question: Are males more likely to be satisfied with their car than females?

    • Independent Variable: Gender, positioned in columns for clarity in analysis.

    • Dependent Variable: Satisfaction with the car, arranged in rows.

    • Structure in crosstab: Clearly defined to ensure a grand total that equals the total sample size, allowing for visualization of relationships.

Crosstabulation Example

  • Sample distribution featuring 100 males and 50 females; satisfaction levels noted for an accurate interpretation of the data.

  • Example provided for males: 20 satisfied; illustrating how to interpret and present values in the crosstab effectively.

SPSS Procedure for Chi-square Test

-Step-by-step instructions on executing the chi-square test in SPSS:

  1. Navigate to descriptive statistics and select cross tabs feature.

  2. Identify and move independent and dependent variables into designated boxes.

  3. Choose statistics, ensuring the inclusion of the chi-square option for analysis.

  4. Enable “column percentages” to enhance output clarity.

  5. Generate output seamlessly for further analysis.

Practice Questions Using SPSS Data

  1. Calculate total respondents indicating poor health to identify critical health demographics.

  2. Calculate total respondents maintaining a good diet to explore dietary habits.

  3. Determine respondents possessing a good diet and excellent health (examining overlapping data).

  4. Calculate the percentage of respondents with a good diet in excellent health:

    • Formula for percentage: \frac{37}{80} \times 100 = 46.25 \text{%}

  5. Similar calculation for individuals adhering to a poor diet yet reporting excellent health, leading to \frac{17}{70} \times 100 = 24.29 \text{%} .

Chi-square Test Output Analysis

  • Detailed analysis of SPSS output crucial for accurate reporting and determining statistical significance of results:

    • Key values to be included in reports:

      • Pearson chi-square value: 8.222, indicating the strength of the association.

      • Degrees of freedom: 2, essential for statistical interpretation.

      • P-value: 0.016, which is critical for determining significance under standard alpha levels.

  • Standard report format for presenting chi-square results:

    • χ2(2,N=150)=8.222,p=0.016\chi^2(2, N=150) = 8.222, p = 0.016, ensuring adherence to academic reporting standards.

Report Writing for Chi-square Test

Structure for Writing Report

  1. Clearly articulate the research question or hypothesis guiding the analysis.

  2. Introduce detailed sample specifics (size, nature, demographic details).

  3. Describe relationships found within the sample (consider including relevant percentages for significant findings).

  4. Clearly state the test conducted (chi-square) along with significance statements relevant to the hypothesis.

  5. Report the chi-square statistic and the accompanying p-value explicitly.

  6. Conclude whether the original hypothesis was supported based on the analysis results.

Sample Report Exemplar

  • Example of a sample report stemming from the hypothesis: "People with good diet show different health outcomes compared to those with poor diets."

  • Summary to include statistics and interpretations, focusing only on significant results to maintain clarity and relevance in reporting.

Reporting Non-significant Results

  • In instances where the p-value exceeds 0.05, note that the relationship does not achieve statistical significance, omitting detailed comparisons of percentages between categorical variables.

Introduction to Risk Ratios and Odds Ratios

  • Definitions to enhance understanding:

    • Risk: Clearly defined as the probability of an event occurring out of total instances (e.g., selecting vanilla ice cream).

    • Relative risk: Ratio utilized to compare risks between two distinct events (e.g., vanilla vs. chocolate ice cream choices).

    • Odds: Ratio representing the probability of an event occurring against non-occurrence.

    • Odds Ratio: Ratio designed to compare the likelihood of two events, yielding insights into relative likelihoods.

Example with Aspirin and Heart Attack

  • Total Sample Size outlined: 250 participants.

    • Aspirin Group: 150 participants, with 15 experiencing a stroke; critical to evaluate potential preventative effects.

    • Placebo Group: 100 participants, of whom 20 suffered a stroke; facilitates direct comparison.

  • Detailed calculation steps for Relative Risk:

    1. Risk in Aspirin group: 15150=0.1\frac{15}{150} = 0.1

    2. Risk in Placebo group: 20100=0.2\frac{20}{100} = 0.2

    3. Relative Risk evaluation: 0.10.2=0.5\frac{0.1}{0.2} = 0.5.

    • Interpretation of results: Participants utilizing aspirin exhibit half the risk of a stroke when compared to those in a placebo group.

    • Note: A value of 1 signifies no difference in risk between comparative groups.

Summary of Learning Tasks

  1. Instruction to complete Lab 11 Report for chi-square test ensuring all elements are addressed.

  2. Requirement to watch the module dedicated to relative risk and odds ratio for comprehensive understanding.

  3. Encouragement to update topic tests on statistics content to reinforce knowledge.

  4. Strong motivation to engage in practical exercises and reach out for assistance whenever needed; promoting proactive learning.

Conclusion

  • Expressed emphasis on comprehensive preparation for the upcoming final exam.

  • Encouragement for participants to engage in practice, active study, and revision of all substantive topics covered throughout the session.

  • Gratitude expressed to participants for their engagement, inviting them to reach out with any subsequent questions or concerns regarding