PPT 1: Descriptive Statistics

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61 Terms

1

Why do we use statistics in biology?

Most things are probabilistic (data based on probabilities) rather than deterministic (data based on know facts)

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2

What is the difference between observational and experimental populations?

  • Observational- A finite population, but is difficult to count

  • Experimental- An infinite amount in the population

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3

Observational Population

A finite population that is difficult to count.

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4

What is a sample survey (or an observational study)

A study of the individuals actually present in a population (under what the investigator can control)

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5

What is a sample?

The amount of a population actually measured

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6

Observation

Descriptions of patterns in data.

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7

What is a sample unit?

An individual thing drawn from the population (e.g. an organism or a measurement)

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8

What is inference?

A generalization of an observation (as samples do not always contain all of the population)

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9

What is random sampling?

Truly random, all members of a population have a chance to be chosen

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10

What is simple random sampling?

A random sample within the whole population

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11

What is a stratified random sample?

A random sample within a group (males v females, age 1 age 2, etc)

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12

What is continuous measurement of variables?

Any value between two extremes can be selected

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13

What are discrete measurements of variables?

Fixed values are chosen between extremes (whole numbers)

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14

What are rank variables?

Indicate more or less of variables based on their rank (e.g. smallest to greatest)

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15

What are qualitative variables

Categorical variables (e.g. male/female, living/dead)

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16

What is a rate?

The quantity per unit (eg. time, mass, births per year)

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17

What are indices (or index)?

Complex derived variables (e.g. condition index: condition of body)

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18

What is the difference between accuracy an precision?

  • Accuracy- How close a value is to the true value

  • Precision- How close repeated variables are

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19

What is bias?

Departure from the true value

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20

What can frequency distribution show?

Location, dispersion, and symmetry

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21

What are examples of frequency distributions?

Symmetrical unimodal, Asymmetrical bimodal, Symmetrical uniform, Asymmetrical (skewed) unimodal, Symmetrical bimodal, Extremely skewed

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22

What is the difference between absolute and relative frequencies?

  • Absolute- The vertical axis represents the real number of observations

  • Relative- The axis represents a percentage of observations

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23

What does ∑ represent?

The sum of all of the variables

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24

What is the statistics of location (or mean)?

The position of a sample along a given dimension representing a variable

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25

What is the difference between an arithmetic mean and a weighted mean?

  • Arithmetic- The balance point of a distribution. All numbers are treated equally and have equal weight. Most commonly used

  • Weighted- The averages of the values are taken to find the mean (may be based on prevalence or the overall percentage of some variables)

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26

Why do we transform our results?

We want to be able to shift the data to get a normal distribution

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27

What is the geometric mean (GM)?

The back-transformed mean of a log-transformed variable (Y becomes logY, and then is changed back to Y)

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28

What is a harmonic mean?

  • 1/Y

  • When we take a (highly) skewed distribution and make it normal.

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29

What is the median?

  • M or Y

  • It is the middle value of the distribution

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30

What is mode?

The most frequent value. Can be bimodal or multimodal.

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31

Where are the mode, median, and means in an asymmetric distribution?

  • Mode- Farthest from the tail

  • Median- in between

  • Mean- Closest to the tail

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32

What is the mean deviation?

A measure of the average deviation from the mean

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33

Standard Deviation

  • A measure of the amount of variation from the variables around the mean

  • The square root of the variance

  • σ

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34

Variance

The overall deviation of observations from their mean.

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35

Parameter

The true numerical value of a population.

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36

Sample Statistic

An estimate of a parameter based on a sample.

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37

μ

The population mean or expected value.

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38

ȳ

The unbiased estimate of the population mean.

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39

σ

The standard deviation of a population.

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40

Covariance

A measure of how two numerical variables are related.

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41

Positive Covariance

Indicates that large values of one variable correspond to large values of another.

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42

Negative Covariance

Indicates that large values of one variable correspond to small values of another.

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43

Zero Covariance

Indicates no relationship between two variables.

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44

Standardized Covariance

The correlation coefficient, which scales variance between -1 and 1.

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45

n

The number of possible outcomes in a probability scenario.

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46

s

The number of successful outcomes in a probability scenario.

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47

Probability of Success

The ratio of successful outcomes to total outcomes (s/n).

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48

Simple Event

A single outcome in a sample space.

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49

Event

A set of outcomes that meet a specific criterion.

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50

Intersection

The common elements between two sets (A⋂B).

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51

Union

The combined elements of two sets (A⋃B).

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52

Independence

When the occurrence of one event does not affect the probability of another.

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53

Replacement

A method where the sample space remains unchanged after an event.

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54

Clumped Distribution

A distribution with excess in the tails.

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55

Repulsed Distribution

A distribution with excess in the center.

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56

Skewness

The asymmetry of a distribution.

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57

Kurtosis

The shape and height of a distribution.

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58

Standard Error of the Mean

The standard deviation of the sample mean.

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59

Confidence Interval

The range of values expected to contain the population mean.

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60

Central Limit Theorem

As sample size increases, the sample mean approaches a normal distribution.

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61

Pr

The probability that a certain percentage of data falls within a specified range.

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