Lecture 3 - Basic Statistics I

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

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Made by Harley Chase and Kylee Wood

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1

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

Mean, Median, Mode

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2

Why are central tendency measures useful in veterinary medicine?

  • Help you understand & critically evaluate the medical research literature

  • Understand your patientsā€™ values in relation to the larger population

  • Understand biological variability

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3

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

Mean

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4

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

Median

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5

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

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6

What is the most frequent occurrence of observations?

Mode

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7

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

True

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8

What is it called when you have 2 modes?

Bimodal

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9

What is it called when you have 3 modes?

Trimodal

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10

What is the average value?

Mean

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11

What is the middle value?

Median

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12

What is the most common value?

Mode

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13

What is the notation for population mean?

ā€œmuā€ = Ī¼

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14

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

ā€œsigmaā€ = Ļƒ

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15

What is the notation for population variance?

ā€œsigma squaredā€ = ĻƒĀ²

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16

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

Curve on the right and tail going to the left

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17

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

Curve to the left and tail going to the right

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18

How will a Normal Distribution appear?

No skew - Normal Bell Curve - A perfectly symmetrical distribution

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19

What type of Distribution is seen in the following graph?

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20

What type of Distribution is seen in the following graph?

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21

What type of Distribution is seen in the following graph?

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22

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

For skewed data - Outliers can greatly skew the mean

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23

What is the skew in the direction of?

The tail of the curve

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24

What is the numerical expression of the likelihood of occurrence?

Probability (Pr)

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25

How can Probability (Pr) be expressed?

  • Fractions

  • Decimal Fractions

  • Percent

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26

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

Simple Probability

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27

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

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28

What is used to calculate the probabilities of independent events?

Complex Probabilities (Multiplication and Addition Rules)

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29

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)

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30

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

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31

What are events that cannot occur at the same time?

Mutually Exclusive Events

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32

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

Multiplication Rule

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33

What is the formula for the Multiplication Rule?

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

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34

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

Addition Rule

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35

What is the formula for the Addition Rule?

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

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36

When can both rules occur at the same time?

When NOT mutually exclusive

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37

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

Target Population

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38

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

Study/Source Population

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39

What are available and we are able to sample?

Sampling Frame

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40

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

Sample

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41

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

Target Population

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42

What is the goal of designing a study?

To accurately reflect your population of interest

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43

What are all measurements susceptible to?

Error

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44

What are the 2 types of measurement errors?

  • Random Error (Imprecision)

  • Systematic Error (Bias)

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45

What type of error is a sampling error?

A form of systematic error

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46

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

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47

What are the following examples of?

  • Self-selection Bias

  • Survivorship Bias

  • Healthy Worker Bias

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48

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

True

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49

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

Random Sampling

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50

What are the 4 types of random sampling?

  • Simple Random Sample

  • Systematic Sample

  • Stratified Sample

  • Cluster Sample

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51

What is random sampling an attempt to do?

To replicate the characteristics of the Target Populating using a sample

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52

What does NOT guarantee a replication of Target Population characteristics?

Unbiased random sampling

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53

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

Standard Error of Measurement

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54

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)

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55

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

Margin of Error

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56

T or F: a 95% CI for a mean has a 95% chance of capturing the ā€œtrueā€ mean.

True

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57

What quantifies precision of estimate?

Confidence Interval (CI) Width

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58

What do Confidence Intervals address?

Random Error only

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59

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

Confidence Level

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60

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

0.1, 0.05 or 0.01

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61

What are the most frequently used confidence levels?

90%, 95% and 99%

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62

What does a confidence level of 95% imply?

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

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63

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

Confidence Level

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