Lecture 3 - Basic Statistics I

Made by Harley Chase and Kylee Wood

What are the indices of central tendency used to describe the typical or central value in a distribution?

Mean, Median, Mode

Why are central tendency measures useful in veterinary medicine?

• Help you understand & critically evaluate the medical research literature

• Understand your patients’ values in relation to the larger population

• Understand biological variability

What is the (sum of the observations / # of observations)?

Mean

What is the level below (or above) half of the observations fall (50 percentile)?

Median

How do you calculate Median?

1. Arrange your #s in numerical order

2. Count how many #s you have

3. Odd # - find # in middle / Even # - average with 2 #s in middle

What is the most frequent occurrence of observations?

Mode

T or F: You can have more than one mode.

True

What is it called when you have 2 modes?

Bimodal

What is it called when you have 3 modes?

Trimodal

What is the average value?

Mean

What is the middle value?

Median

What is the most common value?

Mode

What is the notation for population mean?

“mu” = μ

What is the notation for population standard deviation (sd)?

“sigma” = σ

What is the notation for population variance?

“sigma squared” = σ²

How will a Negatively skewed Distribution on a Bell Curve appear?

Curve on the right and tail going to the left

How will a Positively skewed Distribution on a Bell Curve appear?

Curve to the left and tail going to the right

How will a Normal Distribution appear?

No skew - Normal Bell Curve - A perfectly symmetrical distribution

What type of Distribution is seen in the following graph?

What type of Distribution is seen in the following graph?

What type of Distribution is seen in the following graph?

When is it better to use median vs. mean? Why?

For skewed data - Outliers can greatly skew the mean

What is the skew in the direction of?

The tail of the curve

What is the numerical expression of the likelihood of occurrence?

Probability (Pr)

How can Probability (Pr) be expressed?

• Fractions

• Decimal Fractions

• Percent

What type of Probability (Pr) is associated with the likelihood of 1 event occurring?

Simple Probability

What type of Probability (Pr) is associated with looking at 2 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?

Conditional Probability

What is used to calculate the probabilities of independent events?

Complex Probabilities (Multiplication and Addition Rules)

What are we looking to answer in regards to the probability of 2 types of events?

• 1st when both events occur (A and B)

• 2nd when either event occurs (A or B)

What are those events whose occurrence is NOT dependent on any other event and can occur at the same time as the other event?

Independent Events

What are events that cannot occur at the same time?

Mutually Exclusive Events

What is used to calculate the probability of independent events BOTH occurring (A and B)?

Multiplication Rule

What is the formula for the Multiplication Rule?

Pr (A and B) = Pr (A) x Pr (B)

What is used to calculate the probability of independent events EITHER occurring (A or B)?

Addition Rule

What is the formula for the Addition Rule?

Pr (A or B) = Pr (A) + Pr (B)

When can both rules occur at the same time?

When NOT mutually exclusive

What is the population to which it might be possible to extrapolate results from a study?

Target Population

What is the population from which the study subjects are drawn?

Study/Source Population

What are available and we are able to sample?

Sampling Frame

What consists of the individuals (animals or groups of animals) that end up in the study?

Sample

What is the collection of individuals, items or measurements that we want to study and make inferences about?

Target Population

What is the goal of designing a study?

To accurately reflect your population of interest

What are all measurements susceptible to?

Error

What are the 2 types of measurement errors?

• Random Error (Imprecision)

• Systematic Error (Bias)

What type of error is a sampling error?

A form of systematic error

What 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?

Sampling Error

What are the following examples of?

• Self-selection Bias

• Survivorship Bias

• Healthy Worker Bias

T or F: Systematic bias can be reduced through random sampling.

True

What is a selection process that gives each member of the population being studied an equal chance to be chosen?

Random Sampling

What are the 4 types of random sampling?

• Simple Random Sample

• Systematic Sample

• Stratified Sample

• Cluster Sample

What is random sampling an attempt to do?

To replicate the characteristics of the Target Populating using a sample

What does NOT guarantee a replication of Target Population characteristics?

Unbiased random sampling

What is the variability of a sample statistic or a random error?

Standard Error of Measurement

What are sources of variation associated with standard error of measurement (random error)?

• Natural Variations (ex. morning vs. night)

• Imprecise Instruments

• Individual Differences (ex. subjective pain rating)

What do Confidence Intervals (CI) surround point estimate with?

Margin of Error

T or F: a 95% CI for a mean has a 95% chance of capturing the “true” mean.

True

What quantifies precision of estimate?

Confidence Interval (CI) Width

What do Confidence Intervals address?

Random Error only

What is a measure of the degree of reliability of a confidence interval?

Confidence Level

Confidence Level is denoted as 100(1-α)%, where α usually equals what?

0.1, 0.05 or 0.01

What are the most frequently used confidence levels?

90%, 95% and 99%

What does a confidence level of 95% imply?

That 95% of all samples would include the true value of the parameter estimated

The higher the ________ ________, the more strongly we believe that the true value of the parameter being estimated lies within the interval.

Confidence Level