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Biometrics 340 > Exam 1 > Flashcards

Exam 1 Flashcards

1
Q

Y

A

Data

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2
Q

Yi

A

An observation of the data

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3
Q

Y bar

A

Mean of the data

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4
Q

s2

A

Variance of the data

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5
Q

s

A

Standard deviation of the data

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6
Q

µ

A

Mean

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7
Q

σ2

A

Variance

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8
Q

σ

A

Standard deviation

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9
Q
A

Arithmetic Mean

The average

Most common

Unbiased estimate of µ if assumptions on the earlier slide are met

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10
Q

Geometric Mean

A

Used when the values are multiplied

Used in population ecology

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11
Q

Harmonic Mean

A
  • Greater weight to extreme small values

Used for rates, and in population genetics to estimate effective population size

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12
Q

Symmetrical Distributions

A

If the distributions are perfectly symmetrical then the arithmetic mean, median, and mode are equal.

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13
Q

Variance

A

The variance of the population (σ2) can be estimated from data

Remember that variance is in units2

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14
Q

Standard Deviation

A

The square root of the variance

On average, s does not change when you increase sample size

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15
Q

Standard Error of the Mean

A

The standard deviation of the estimated population mean

Decreases when you increase sample size

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16
Q

Coefficient of Variation

A
  • The sample standard deviation divided by the sample mean

Often multiplied by 100 to represent a percent

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17
Q

Classical definition

A

P=0, outcome will never happen

P=1, event will always happen

Note: typically cannot measure

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18
Q

Frequentist definition

A

P=0, outcome didn’t occur in any trial

P=1, outcome occurred in every trial

Note: can measure

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19
Q

Experiment

A

¡A set of trials

¡E.g. all the crocodiles in a nest

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20
Q

Trial

A

¡Each replicate event

¡E.g. a particular crocodile

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21
Q

Sample space { }

A

¡The set of all possible outcomes

¡E.g. hatched and didn’t hatch

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22
Q

Outcome ( )

A

¡A possible result of a event

¡E.g. hatched

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23
Q

Event

A

¡A process with a beginning and end

¡E.g. hatching of an crocodile

24
Q

Defining Sample Space

A

nOutcomes are mutually exclusive

nOutcomes are exhaustive

25
Q

Axiom 1

A

The sum of all the probabilities of outcomes within a single sample space = 1.

26
Q

nComplex events

A

¡Composites of simple events in the sample space

¡

¡Rolling 3 OR rolling 4

¡First crocodile hatching OR the second crocodile hatching

27
Q

nShared events

A

¡Multiple simultaneous occurrences of simple events in the sample space

¡Rolling 1 on the first roll AND 1 on the second roll

¡First AND second crocodile hatch

28
Q

Axiom 2

A

The probability of a complex event equals the sum of the probabilities of the outcomes that make up that subset.

29
Q

Conditional Probabilities

A

Used to calculate probabilities when you know that an outcome has occurred or will occur

Probability of a given b

30
Q

Bayes’ Theorem

A

The conditional probability rewritten in terms of the inverse conditional probability.

31
Q

Frequency Distribution

A

nBased on number of observations within a given range

¡Non-negative integers

32
Q

Probability Distributions

A

nBased on probabilities and often represented by the density

¡Density is calculated using the area of each bar

¡Thus, densities can be greater than 1

33
Q

Discrete

A

nTake on finite numbers

nE.g., integers

34
Q

Continuous

A

nTake on any value within a range

nE.g., diameter of your head

35
Q

Discrete Distributions

A

nBernoulli

¡Uncommon because of simplicity

nBinomial

¡Common in biological data

nPoisson

¡More appropriate when a successful outcome is rare

36
Q

Bernoulli Distribution

A

nA single event

nOnly two outcomes

¡E.g., 0 and 1

nP(1)=p and P(0)=1-p

37
Q

Binomial Distribution

A

nMultiple Bernoulli trials

nProbability of successful outcomes

¡E.g. 5 of 10 eggs hatch

nNeed to know

¡Probability of success (p)

¡Number of trials (n)

¡Number of successful trials (X)

38
Q

Poisson Distributions

A

nUsed when

¡Number of trials is unclear

¡p is very small

¡Sampling fixed area of space or time interval

nNeed to know

¡Number of observed occurrences (x)

¡Rate parameter (λ)

39
Q

Rate Parameter

A

Estimated from experiments or prior data

Represents the average of the Poisson Distribution, and also the variance

40
Q

Expected Value of the Distribution

A

Is the mean or average

41
Q

Variance of the Distribution

A

The spread of the data

Calculated as the squared deviations from the mean

42
Q

Continuous Distributions

A

Uniform Distributions

Used to represent truly random events

Normal Distributions

Extremely common and important in biology (as well as many other fields)

There are lots of other continuous distributions

F, t, Beta, Gamma, Log-normal, exponential, chi-squared, etc.

43
Q

Problem with Continuous Distributions

A

Probability for any given value is zero

There are an infinite number of different possibilities

44
Q

Solution

A

Calculus and axioms

Axiom 1 state the sum of all probabilities must equal 1.0

So, using integral calculus, we can find the function that satisfies axiom 1

45
Q

Parameters

Min (a) and max (b)

A

Uniform Distribution

46
Q

Probability Density Function (PDF)

A

Is the function that gives the probability for x

47
Q

Cumulative Density Function (CDF)

A

Is a function that gives the area under the curve (i.e. the cumulative probability)

48
Q
A
49
Q

Parameters

Mean (µ) and Standard deviation (σ)

A

Normal Distribution

50
Q

Works for any type of distribution

Sum or average random samples from a distribution

Result is a distribution that is normal!

A

Central Limit Theorem

51
Q
A
52
Q

Lambda and Max of x axis

A

Poisson Dist.

53
Q

of trials and probability of success

A

Binomial Dist

54
Q

Min and Max

A

Uniform Dist.

55
Q
A

Biometrics 340 (1 decks)

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