2/17/2023

Return to calculations for normal distributions - see !Class-csv-Rscripts\NormalDistributionCalcs.R

Assessing Normality

• Should we use the normal model for a given data set?
• 68-95-99.7 Rule
• Normal Quantile Plots - qqnorm in R
• Other Visual Displays

Class Activity on using qqplots to assess Normality

• Open the R script QQPlot.R to conduct simulations that will help you develop your understand of these new plots.
• The script simulates data from normal distributions, uniform distributions, and t distributions. Look at the histograms and qqplots carefully. You can run the commands multiple times to help you distinguish general trends from chance variation.
• Describe each of the plots. Can you explain how the differences in the distributions are appearing on the normal probability plots?
• Use appropriate methods for assessing normality to see if the normal distribution would be an appropriate model for the quantitative variables from our Data Survey on Day 1.

Binomial Experiments (A generalization of the discrete RV lab problem on the number of patients who experience side effects)

• Each random trial can result in one of only two possible outcomes.  This is called a Bernoulli trial.
• We collect data from Bernoulli trials satisfying the following:
  • there are n trials;
  • the n trials are independent; and
  • the probability of “success” remains constant from trial to trial.
• Binomial Distribution - If X is the number of successes in n independent Bernoulli trials, then P(X=k)=n!/[k!*(n-k)!]*p^k*(1-p)^n-k, for k=0, 1, ..., n.
• Using RStudio for Binomial Probability Calculations 
  • dbinom() or pbinom() or qbinom()

The mean (expected value) and standard deviation of a binomial random variable

• Mean (or Expected Value) of X is n*p
• Variance of X is n*p*(1-p)
• The standard deviation of X is the square root of the variance.

Binomial Random Variables - See handout

• We will have a problem session on Monday, if you want to see some of these problems worked out by your peers.

Please read Sections 4.4 and 4.5 for class on Monday.