Lecture 4: Basic Statistics II

• Measured of central tendency:


  describe the typical or central value in a distribution (mean, median, mode)
• Measures of dispersion:


  describe the spread of the data (range, standard deviation, variance)
• Standard deviation:


  (represented by the Greek letter sigma, σ) measures the amount of variation or dispersion from the average
• A low standard deviation indicates...


  the data points tend to be very close to the mean (also called expected value)
• A high standard deviation indicates...


  the data points are spread out over a large range of values.
• Variance definition


  Variance is directly related to standard deviation. It is the square of the SD
• Variance is often depicted by what symbol:


  σ2
• What are the types of data?


  Categorical (nominal and ordinal) and Numerical (interval and ratio)
• Nominal data:


  refers to the categorically discrete data such as name (nominal sounds like name)
• Ordinal data:


  data that has a discrete ranking (order sounds like ordinal)
• Interval Data:


  Interval data is numerical data that is measured along a scale. Each point is at equal distance from one another (can be negative; zero doesn't have a meaning)
• Ratio data:


  Ratio data is interval data with a natural zero point (no negative numbers, zero is a true zero)
• Alternative hypothesis:


  statement that there is a difference between two events (treatments, tests, etc.)
• Null hypothesis:


  statement that there is no difference between two events (treatments, tests, etc.)
• Statistical significance


  the probability of rejecting the null hypothesis due to chance alone (given that the null hypothesis is true). Statistical Significance is usually expressed as a p-value.
• True or false: smaller and smaller P-values provide stronger and stronger evidence against H0

  True
• What does P-value answer?


  What is the probability of the observed test statistic?
• True or false: Small P-value ---> strong evidence ----> reject null hypothesis

  True
• If the sample data are consistent with the null hypothesis then...


  we fail to reject the null hypothesis
• If the sample data are inconsistent with the null hypothesis then...

  reject the null hypothesis
• True or false: There are only 2 options, fail to reject the null hypothesis and reject the null hypothesis

  True
• True or false you can: accept the alternative hypothesis, accept the null hypothesis , reject the alternative hypothesis

  False (you cannot)
• clinical significance:


  is the practical importance of a treatment effect—whether it has a real genuine, palpable, noticeable effect on daily life
• True or false: Statistical significance means clinical significance

  False (does not mean)
• True or false: smaller the p-value, the stronger the evidence

  True
• What is the general goal of a study?

  To reject the null hypothesis
• What are cofounding factors?

  additional variables that could influence results that are not considered in the subject population selection (unknown bias)
• What are some potential confounders?


  Age

  IQ

  Prior coursework

  Gender

  Outside work

  Marital status
• Properties of a confounder


  -exposure is associated with theconfounder-confounder is an independent risk factor for thedisease-confounder is not in casual pathway