Lecture 3: Basic Statistics 1

• mean =


  sum of the observations/ number of observations (Average)
• Definition of median


  the level below (OR ABOVE) half of the observations fall
• What should you do if you have an odd number when calculating the median?

  If you have an odd number, divide by 2 and round up to get the position of the median.
• What should you do if you have an even number when calculating the median?


  If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median
• Definition of mode


  most frequent occurrence of observations
• What is the word for two modes? What is the word for three modes?

  bimodal; trimodal
• Mean=

  Median=

  Mode=

  average value

  middle value

  most common value
• population mean =


  μ (mu)
• population standard deviation (sd)=


  sigma (σ)
• population variance


  sigma squared (σ2)
• What does negatively skewed look like?

  negative direction (to the left)
• What does normal mean?


  No skew (normal curve/perfectly symmetrical)
• What does positively skewed look like?

  Positive direction (to the right)
• When should you use median versus mean?

  Median is better than mean for skewed data
• Probability definition (Pr)


  the numerical expression of the likelihood of occurrence
• True or false: probability can be expressed in fractions, decimal fractions, or percent

  True
• Simple probability definition


  at the likelihood of one event occurring
• Conditional probability definition


  looks at two events occurring in relation to one another. It looks at the probability of a second event occurring based on the probability of the first event occurring.
• Independent events definition:


  are those events whose occurrence is not dependent on any other event- (Can occur at the same time as the other event)
• Mutually exclusive events definition


  events that cannot occur at the same time
• What is the multiplication rule?


  used to calculate the probability of independent events both occurring. (A and B)
• Multiplication rule formula:


  Pr (A and B) = Pr (A) x Pr (B)
• Definition of the addition rule:

  used to calculate the probability of independent events either occurring. (A or B)
• Formula for addition rule:


  Pr (A or B) = Pr (A) + Pr (B)
• Addition rule when NOT mutually exclusive- BOTH CAN HAPPEN AT THE SAME TIME FORMULA:


  Pr (A) + Pr (B) - Pr (A and B)
• Definition of target population:

  The population to which it might be possible to extrapolate results from a study
• Definition of Study/Source Population:


  The population from which the study subjects are drawn
• Definition of Sampling frame:

  Are available and we are able to sample
• Sample definition:


  Consists of the individuals that end up in the study
• What are the 2 types of measurement errors:

  Random error (imprecision) and Systematic error (bias)
• Sampling error definition:


  is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others
• What are some examples of sampling error?


  Self-selection bias

  Survivorship bias Healthy worker bias
• True or False: Random sampling does not allow the reduction of systematic bias

  False (Reducing systematic bias through random sampling)
• Random sampling definition


  A selection process that gives each member of the population being studied an equal chance to be chosen
• What are the 4 types of random sampling?

  Simple, systematic, stratified, cluster
• Standard error of measurement (random error) definition


  Standard Error of Measurement is the variability ofa sample statistic
• What are sources of variation:


  Natural variations (ex. morning versus night) Imprecise instruments Individual differences (ex. subjective pain rating)
• What are Confidence Intervals (CI)


  surround point estimate with margin or error
• True or False: confidence intervals address random error only!

  True
• What is confidence level?

  a measure of the degree of reliability of a confidence interval. (the higher the confidence level the more strongly we believe the value of the parameter being estimated lies within the interval)