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BIOL 300 > vocab definitions > Flashcards

vocab definitions Flashcards

1
Q

sample of convenience

A

a collection of individuals that happen to be available at the time

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2
Q

variable

A

a measured characteristic on individuals from a population under study

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3
Q

data

A

measurements of one or more variables made on a collection of individuals

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4
Q

explanatory variable

A

a variable we use to predict or explain a response vairable

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5
Q

response variable

A

a variable that is predicted or explained from a explanatory variable

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6
Q

populations

A

a group of all individuals or groups that you want to study

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7
Q

sample

A

a subset ideally randomly chosen from a population you wish to study

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8
Q

parameters

A

things we want to know about the population

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9
Q

estimates

A

are calculated from a sample to help understand perameters

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10
Q

bias

A

a systematic discrepancy between estimates and the true population characteristic

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11
Q

volunteer bias

A

volunteers for a study are likely to be different on average from the poulation

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12
Q

sampling error

A

chance difference from the truth

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13
Q

precision

A

the spread of estimates resulting from sampling error
-gives a similar answer repeatedly

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14
Q

accurate or unbiased

A

the average of estimates that are obtained is on the true population value
-accuracy (on average gets the correct answer

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15
Q

random sample

A

in a random sample each member of a population has equal and independent chance of being selected

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16
Q

categorial variables (attribute or qualitative variables)

A

describe membership in a category or group

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17
Q

numerical variable

A

when measurements of individuals are quantitative and have magnitude. numbers

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18
Q

continuous

A

numerical data that can take on any real-number value within some range. Between any two values of a continuous variable, an infinite number of other values are possible.

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19
Q

discrete

A

numerical data that come in indivisible units. Example: number of amino acids in a protein and numerical rating of a statistics professor in a student evaluation are discrete numerical measurements

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20
Q

frequency

A

the number of observations having a particular value of the measurement

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21
Q

frequency distribution

A

shows how often each value of the variable occurs in the sample.
The frequency distribution describes the number of times each value of a variable occurs in a sample

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22
Q

independence

A

two events are independeent if the occurance of on egives no info about whether the second will occrur

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23
Q

multiplication principle

A

if two evens A and B are independent, then Pr[A and B] = Pr[A] xPr[B]

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24
Q

The addition principle

A

If two events A and B are mutually exclusive, then Pr[A or B]= Pr[A] + Pr[B]

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25
Q

Probibility distribution

A

A prob distribution describes the true relative frequency of all possible values of a random vairable

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26
Q

Mutually exclusive

A

if two events are mutually exclusive they cannot both be true
Pr(A and B)= 0

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27
Q

probability

A

The prob of an event is its true relative frequency, the proportion of times the event would occur if we repeat the same process over and over

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28
Q

pseudoreplication

A

the error that occurs when samples are not indepenent, but they are treated as though they are

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29
Q

standard error

A

estimate is the standard deviation of its sampling distribution. predicts the sampling error of the estimate

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30
Q

standard error of an estimate

A

the standard deviation of its sampling distribution
It predicts the sampling error of estimate

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31
Q

conditional probability

A

the conditional probability of an event is the probability of that event occurring given that a condition is met.
Pr[X|Y]

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32
Q

confidence interval

A

the 95% confidence provides a plausible range for a parameter. All values for the parameter lying within the interval are plausible, given the data, whereas those outside are unlikely

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33
Q

The 2SE rule-of thumb

A

the interval from Y-2SEy to Y+2SEy provides a rough estimate of the 95% confidence interval for the mean

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34
Q

what does a x^2 goodness of Fit test do?

A

compares count data to a model of the expected frequencies of a set of categories

-it is an approximation (don’t use when there’s little amount of data)

H0: the data come from a specified probability distribution

x^2= sum of all classes (observed-expected)^2/ expected

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35
Q

Degrees of freedom

A

the number of degrees of freedom of a test specifies which of a family of distributions to use
for x^2 df= number of categories-number of parameters estimated from the data-1

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36
Q

Critical value

A

the value of the test statistic where P= alpha

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37
Q

What are test statistics

A

A test statistic is a number calculated from the data and the null hypothesis that can be compared to a standard distribution to find the P-value of the test

38
Q

What are assumptions of x^2 test

A

=that its a random sample
- No more than 20% of categories have expected <5
- no category with expected = 1

when both these conditions are not met the approximations to make the x^2 test do not work

39
Q

what is a discrete distribution?

A

a porbobility disribution descibing a discrete numerical random variable
example:
number of heads from 10 flips of a coin
number of flowers in a square meter
number of disease outbreaks in a year

40
Q

Poisson distribution

A

a mathematical probability distribution.
- describes the probability that a certain number of events occur in a block of time or space, when those events happen independently of each other and occur with equal probability at every point in time or space

41
Q

x^2 contingency analysis

A

tests the independence of two of more categorical variables

42
Q

Fishers exact test

A

for 2x2 contingency analysis

does not make assumptions about the size of expectations

use when you cant do x^2 contingency analysis

*don’t need to do by hand

43
Q

odds

A

the probability of success divided by the probability of failure

44
Q

Odds ratio

A

the odds of success in one group divided by the odds of success in another group
OR< 1 means odds of bad thing happens lower
OR>1 means odds of bad thing is higher

45
Q

properties of a good sample

A

-independent selection of individuals
-random selection of individuals
-sufficiently large

46
Q

sampling error

A

The difference between the estimate and average value of the estimate

47
Q

larger samples on average will have ____ sampling error

A

smaller

48
Q

best way to graph a numerical variable frequency

A

histogram

49
Q

cumulative frequency distribution

A

The cumulative frequency of a value is the proportion of individuals equal to or less than the value

graphed this goes from 0-1 on y axis, never decreasing

50
Q

best way to show association between two categorical variables

A

contingency table,
grouped bar graph,
mosaic plot,

51
Q

best way to show association between categorical and numerical variable

A

multiple histograms

52
Q

best way to show association between two numerical variables

A

scatter plot

53
Q

how to calculate mean

A

Ybar= sum of Yi/n n=sample size

54
Q

median

A

The median is the middle measurement in a set of ordered data

55
Q

Mode

A

the mode is the most frequent measurment

56
Q

Range

A

the maximum minus the minimum

57
Q

Small samples tend to give ___ estimates of the range than small samples.
So sample range is a _______ of the true range of the population

A

Small samples tend to give _lower__ estimates of the range than small samples.
So sample range is a biased estimator of the true range of the population

58
Q

Variance in a population

A

sigma^2= sum of (Yi- u)^2/N

N is the number of individuals in population
u= true mean of the population

59
Q

Sample variance

A

s^2= sum of(Yi-Ybar)^2/n-1
n=sample size
Ybar= sample mean

60
Q

Standard deviation (SD)

A

positive square root of the variance
sigma is the true standard deviation
s is the sample stand deciation
s= sqare root of s^2= sqrt(sum(Y-Ybar)^2/n-1)

61
Q

coefficient of variation (CV)

A

CV= 100% S/Ybar

62
Q

skew

A

a measurement of asymmetry
refers to the pointy tail of a distribution

63
Q

Standard error of the mean

A

standard error of he mean:
sigma ybar= sigma/ srt(n)

64
Q

Estimate of the standard error of the mean

A

SEYbar= S/ srt(n)
gives us some knowledge of the likely difference b/w our sample mean and the true population mean

65
Q

law of total probability

A

Pr[x]= sum of all values of Y Pr[X|Y] Pr[Y]

66
Q

probability of a positive result using the law of total probability (example if the events are not independent)

A

P[positive result]= Pr(positive result| X)Pr(x) +Pr(positive result| Y) Pr(Y)

67
Q

Bayes theorem

A

Pr[A|B]= Pr[B|A]Pr[A]/ Pr[B]

68
Q

what does hypothesis testing do

A

hypothesis testing asks how unusual it is to get data that differ from the null hypothesis

If the data would be quite unlikely under H0 we reject H0

69
Q

hypothesis are about populations but are tested from? with the assumptin?

A

sapmples with assumption it is random

70
Q

Null hypothesis

A

a specific statement about a population parameter made for the purposes of argument.

usually the simplest statement

71
Q

Alternative hypothesis

A

represent all other possible parameter values except that stated in the null hypothesis

usually the statement of greatest interes

72
Q

A good null hypothesis

A

would be interesting if proven wrong

73
Q

What is P-vale

A

the probability of getting the data or something as or more unusual, if the hypothesis where true

74
Q

How do you find the P-value?

A

Simulation
Parametric tests
Permutation

75
Q

Statistical significance

A

The significance level, alpha, is a probability used as a criterion for rejecting the null hypothesis

If the P-value for a test is less than or equal to alpha then the null hypothesis is rejected

often 0.05

76
Q

A large sample will tend to give and estimate with a ____ confidence interval

A larger sample will give ____ a false null hypothesis

A

A large sample will tend to give and estimate with a smaller confidence interval

A larger sample will give _more power to reject___ a false null hypothesis

77
Q

Type I error

A

Rejecting a true null hypothesis
Probability of Type I error is alpha (the significance level)

78
Q

Type II error

A

Not rejecting a false null hypothesis
The probability of a Type II error is beta
The smaller beta the more power a test has

79
Q

Power

A

The ability of a test to reject a false null hypothesis
Power = 1- beta

80
Q

Most tests are ___ tailed tests which means…

A

most tests are two-tailed tests and this means that a deviation in either direction would reject the null hypothesis
normally alpha is divided into alpha/2 on one side and alpha/2 on the other

81
Q

One-tailed test are

A

are only used when the other tail is nonsensical
example: comparing grades on a multiple choice test to that expected by random guessing

82
Q

Critical value

A

The value of a test statistic beyond which the null hypothesis can be rejected

83
Q

If a hypothesis test rejects a null hypothesis thest (P<0.05) the value proposed by the null hypothesis is

A

outside the 95% confidence interval

84
Q

confounding variable

A

an unmeasured variable that may be the cause of both X and Y

85
Q

a proportion

A

a fraction of individuals having a particular attribute

86
Q

binomial distribution

A

describes the probability of a given number of successes from a fixed number of independent traits

Pr[X]=(n given X)p^X(1-p)^n-X
n trails; p probability of success

87
Q

properties of the binomial distribution

A

mean and variance of number of succusses
u=np
sigma^2= np(1-p)

88
Q

proportion of successes in a sample

A

phat= X/n
the hat (^) shows that this is an estimate of p

89
Q

properties of sample

A

mean: p
variance: p(1-p)/n

90
Q

Agresti-Coull confidence interval

A

(p’-1.96 sqrt(p’(1-p’)/n+4) <= p<= (p’+1.96 sqrt(p’(1-p’)/n+4)

p’= X+2/n+4

91
Q

The binomial test

A

uses data to test whether a population proportion p matches a null expectation for the proportion

example:
H0: dog good is chosen at best 20% of time Ho=0.2
N=18, p0= 0.2, X=2
P-value= 2(Pr[2]+Pr[1]+Pr[0])
example say = 0.543 > 0.05 therefor cannot reject the null hypothesis (It is plausible that people do not prefer pate over dog food)

BIOL 300 (3 decks)

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