Univariate Analysis and Data Statistics

Data Analysis Key Considerations

• Single vs. Multiple Variables:

  • Univariate analysis assesses individual variables;

  • Multivariate considers relationships among multiple variables.

• Level of Measurement:

  • Categorical

    • Nominal Measures

  • Continuous

    • Ordinal, Interval, and Ratio measures

Categorical Measures in Univariate Statistics

• Frequency Analysis:

  • Counts occurrences in response categories, essential for understanding member demographics.

Continuous Measures in Univariate Statistics

• Descriptive Statistics:

  • Describe the distribution of responses on a variable

  • Utilize measures like mean (central tendency) and standard deviation (dispersion) to interpret continuous data effectively.

Converting Continuous to Categorical Measures

• Reason for Conversion:

  • Simplifies interpretation for better decision-making.

  • Two-Box technique

    • Technique for converting interval-level rating scale into a categorical measure for presentation purposes

    • Percentage of respondents choosing one of the top two positions on a rating scale is usually reported

Confidence Intervals Overview

• Definition:

  • Confidence intervals estimate population parameters based on sample statistics, accounting for sampling errors.

• Sampling Error Calculation:

  • Involves percentage of responses, sample size related to the desired confidence level.

Central Limit Theorem & Sample Size

• Key Components in Analysis:

  • Degree of precision and confidence (e.g., 95% confidence would suggest Z-value = 1.96).

• LOOK UP FORMULA IN SLIDE 17

Confidence Intervals for Proportions

• Calculating Proportions:

  • p - (sampling error) ≤ π ≤ p + (sampling error)

    • p = relevant proportion obtained from the sample

    • π = population proportion

    • Sampling error is the desired degree of confidence (z) and the number of valid cases overall for the proportion (n) in addition to p

  • Sampling error = z sqrt{(p (1 - p)) / n}

Confidence Intervals for Means

• Approach:

  • Similar to proportions, but focus on sample means.

  • CI is calculated using standard deviation and sample size.

  • x̄ - (sampling error) ≤ 𝜇 ≤ x̄ + (sampling error)

    • x̄ = sample mean

    • 𝜇 = population mean

    • Sampling error is the desired degree of confidence (z), the sample standard deviation (s), and number of valid cases overall for the proportion (n)

• Example:

  • Mean visits to AFC were found at 9.97 (s.d. = 7.256); compute 95% CI around this mean for insights into overall member usage.

Exercise Applications: Average Income & Market Share Examples

• Calculate and interpret confidence intervals based on sample data in varied contexts (i.e., income levels of undergraduates or market share for PC).

• Each analysis involves verifying confidence levels (99%, 90%) and thoroughly interpreting the results.