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S519 Statistical Sessions

This wrap-up summarizes the key topics covered in our statistical sessions, including descriptive statistics, normal distributions, hypothesis testing, t-test, ANOVA, correlation, linear regression, and chi-square analysis.

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S519 Statistical Sessions

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  1. S519 Statistical Sessions Wrap up

  2. Things we’ve covered • Descriptive Statistics • Normal Distributions • Z-test • Hypothesis Testing • T-test • ANOVA • Correlation • Linear regression • Chi-square

  3. Descriptive Statistics • Central Tendency • Mean • Median • Mode • Variance • Range • Standard deviation • Variance

  4. Normal Distributions • Skewness • Kurtosis

  5. Z-test

  6. Hypothesis Testing • State the hypothesis • Null hypothesis • Research hypothesis • Directional • Non-directional • Set decision criteria • Collect data and compute sample statistic • Make a decision (accept/reject)

  7. T-test

  8. T-test • Degree of freedom=n-1 • TTEST (array1, array2, tails, type) • array1 = the cell address for the first set of data • array2 = the cell address for the second set of data • tails: 1 = one-tailed, 2 = two-tailed • type: 1 = a paired t test; 2 = a two-sample test (independent with equal variances); 3 = a two-sample test with unequal variances

  9. ANOVA • Analysis of Variance • A hypothesis-testing procedure used to evaluate mean differences between two or more treatments (or populations). • Advantages: • 1) Can work with more than two samples. • 2) Can work with more than one independent variable

  10. ANOVA • In ANOVA an independent or quasi-independent variable is called a factor. • Factor = independent (or quasi-independent) variable. • Levels = number of values used for the independent variable. • One factor → “single-factor design” • More than one factor → “factorial design”

  11. ANOVA • Df for independent ANOVA • Between-group degree of freedom=k-1 • k: number of groups • Within-group degree of freedom=N-k • N: total sample size • Df for dependent ANOVA • Between-group degree of freedom=k-1 • k: number of groups • Within-group degree of freedom=N-k • N: total sample size • Between-subject degree of freedom=n-1 • n: number of subjects • Error degree of freedom=(N-k)-(n-1)

  12. ANOVA • Three different ANOVA: • Independent measures design: Groups are samples of independent measurements (different people) ANOVA: single factor • Dependent measures design: Groups are samples of dependent measurements (usually same people at different times) “Repeated measures” ANOVA: two factors without replication • Factorial ANOVA (more than one factor) ANOVA: two factors with replication

  13. Correlation • Pearson correlation • CORREL function or Pearson function • Toolpak for more than two variables (matrix) • The correlation represents the association between two or more variables • It has nothing to do with causality (there is no cause relation between two correlated variables)

  14. Correlation

  15. Correlation

  16. Linear regression • Y’ = bX + a • b = SLOPE() • a = INTERCEPT()

  17. Chi-square • Non-parametric vs. parametric • O: the observed frequency • E: the expected frequency • df=r-1 (r= number of categories)

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