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FoSSA: Fundamentals of Statistical Software & Analysis

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  1. Course Information

    Meet the Teaching Team
  2. Course Dataset 1
  3. Course Dataset 2
  4. MODULE A1: INTRODUCTION TO STATISTICS USING R, STATA, AND SPSS
    A1.1 What is Statistics?
  5. A1.2.1a Introduction to Stata
  6. A1.2.2b: Introduction to R
  7. A1.2.2c: Introduction to SPSS
  8. A1.3: Descriptive Statistics
  9. A1.4: Estimates and Confidence Intervals
  10. A1.5: Hypothesis Testing
  11. A1.6: Transforming Variables
  12. End of Module A1
    1 Quiz
  13. MODULE A2: POWER & SAMPLE SIZE CALCULATIONS
    A2.1 Key Concepts
  14. A2.2 Power calculations for a difference in means
  15. A2.3 Power Calculations for a difference in proportions
  16. A2.4 Sample Size Calculation for RCTs
  17. A2.5 Sample size calculations for cross-sectional studies (or surveys)
  18. A2.6 Sample size calculations for case-control studies
  19. End of Module A2
    1 Quiz
  20. MODULE B1: LINEAR REGRESSION
    B1.1 Correlation and Scatterplots
  21. B1.2 Differences Between Means (ANOVA 1)
  22. B1.3 Univariable Linear Regression
  23. B1.4 Multivariable Linear Regression
  24. B1.5 Model Selection and F-Tests
  25. B1.6 Regression Diagnostics
  26. End of Module B1
    1 Quiz
  27. MODULE B2: MULTIPLE COMPARISONS & REPEATED MEASURES
    B2.1 ANOVA Revisited - Post-Hoc Testing
  28. B2.2 Correcting For Multiple Comparisons
  29. B2.3 Two-way ANOVA
  30. B2.4 Repeated Measures and the Paired T-Test
  31. B2.5 Repeated Measures ANOVA
  32. End of Module B2
    1 Quiz
  33. MODULE B3: NON-PARAMETRIC MEASURES
    B3.1 The Parametric Assumptions
  34. B3.2 Mann-Whitney U Test
  35. B3.3 Kruskal-Wallis Test
  36. B3.4 Wilcoxon Signed Rank Test
  37. B3.5 Friedman Test
  38. B3.6 Spearman's Rank Order Correlation
  39. End of Module B3
    1 Quiz
  40. MODULE C1: BINARY OUTCOME DATA & LOGISTIC REGRESSION
    C1.1 Introduction to Prevalence, Risk, Odds and Rates
  41. C1.2 The Chi-Square Test and the Test For Trend
  42. C1.3 Univariable Logistic Regression
  43. C1.4 Multivariable Logistic Regression
  44. End of Module C1
    1 Quiz
  45. MODULE C2: SURVIVAL DATA
    C2.1 Introduction to Survival Data
  46. C2.2 Kaplan-Meier Survival Function & the Log Rank Test
  47. C2.3 Cox Proportional Hazards Regression
  48. C2.4 Poisson Regression
  49. End of Module C2
    1 Quiz

Learning Outcomes

By the end of this section, students will be able to:

  • Explore the data with correlations and scatterplots.
  • Use an ANOVA to test for a difference in means across a categorical variable. 
  • Conduct univariable and multivariable linear regression
  • Check the regression diagnostics of a linear model.

You can download a copy of the slides here: B1.2 Differences Between Means (ANOVA I)

Video B1.2 – One-Way ANOVA (12 minutes)

B1.2 PRACTICAL: Stata

The ANOVA procedure allows us to establish whether there is evidence that the mean SBP values across the BMI groups are not all equal. You use an ANOVA to test for differences in means across levels of a categorical variable (not a continuous one).

The anova command in Stata is setup as follows:

anova varname [termlist], [options]

where ‘termlistis a factor-variable list (i.e. a categorical variable). We will not be using any of the options here.

Now compare mean SBP in the four groups of BMI using ANOVA, the Stata code you will need is:

 anova sbp bmi_grp4

Question B1.2a: Is there a significant difference in mean SBP across the BMI groups?

Answer

The result indicates there are differences in mean SBP across the four categories of BMI as the p-value of 0.0001 is highly significant.

Note that an ANVOA it is a global test and does not tell us which BMI groups are significantly different from each other. You will learn how to produce comparisons of all possible pairings of the BMI groups, as well as many other uses of the ANOVA test in Module B2.

B1.2 PRACTICAL: SPSS

The ANOVA procedure allows us to establish whether there is evidence that the mean SBP values across the BMI groups are not all equal. You use an ANOVA to test for differences in means across levels of a categorical variable (not a continuous one).

We are going to use this to test for a significant difference in mean SBP across the BMI groups.

There are actually multiple ways to get to the same outcome in SPSS. The simplest way, if you know you are not going to need to consider any other variables is as follows.

Select

Analyze >> Compare Means and Proportions >> One-Way ANOVA

The move the continuous variable (in this case SBP) into the Dependant List and the Categorical variable (BMI group) into the Factor box. Then press ‘OK’ to run the test.

Answer

The result indicates there are differences in mean SBP across the four categories of BMI as the p-value < 0.001 is highly significant.

Note that an ANVOA it is a global test and does not tell us which BMI groups are significantly different from each other. You will learn how to produce comparisons of all possible pairings of the BMI groups, as well as many other uses of the ANOVA test in Module B2.

B1.2 PRACTICAL: R

ANOVA
We use aov() to perform ANOVA, and we get a summary of the ANOVA table using summary().
aov() can be used in two ways as follows:

    • fit3 <- aov(y ~ x, data=my.data)
    • fit3 <- aov(my.data$y ~ my.data$x)

To create a summary of ANOVA we can use summary(fit3).
white.data$bmi_fact<-factor(white.data$bmi_grp4)

fit3<-aov(sbp~bmi_fact, data=white.data)
summary(fit3)

Question B1.2: Compare SBP in the four groups using ANOVA. Is there a significant relationship between SBP and BMI groups?

Answer

> fit3<-aov(sbp~bmi_fact, data=white.data)
> summary(fit3)
              Df  Sum Sq Mean Sq F value   Pr(>F)    
bmi_fact       3    6451  2150.4   7.024 0.000104 ***
Residuals   4297 1315528   306.2                     

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
26 observations deleted due to missingness

The result indicates there are differences in SBP across the four categories of BMI as the p-value of 0.0001 is highly significant.

However, an ANOVA a global test and does not tell us which BMI groups are significantly different from each other. You will learn how to produce comparisons of all possible pairings of the BMI groups, as well as many other aspects of the ANOVA test in Module B2.

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