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ENVS 203 > final > Flashcards

final Flashcards

1
Q

statistics

A

a field of mathematics that develops and studies methods to collect, analyze, interpret, and present empirical evidence

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2
Q

empirical vs anecdotal evidence

A

empirical - information received from the observation or measurements of patterns using experimentation
anecdotal - evidence collected in a casual or informal manner that relies heavily on personal testimony or conclusions (not statistical data collection)

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3
Q

data

A

a collection of numerical facts or information from which conclusions can be drawn

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4
Q

raw data

A

unformatted data (numerical measurements, instrument readings, text) that has not been processed or analyzed

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5
Q

replicates

A

parallel measurements of a phenomenon to estimate variability in your sample (the number of replicates = n)

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6
Q

sampling effort

A

how much data do we need?

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7
Q

precision vs accuracy

A

precision - how fine the divisions on a scale of measurement are
accuracy - how close to the truth our measurement is
(accuracy is the priority)

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8
Q

descriptive statistics

A

quantitative description of observations sampled from a population (mathematically summarizing patterns, data centers, and variability without making conclusions about overall meaning of data)

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9
Q

data distribution (historgram)

A

sampled populations arranged by rank order and graphically presented

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10
Q

normal distribution

A

an arrangement of data in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme

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11
Q

central tendency

A

numeric value describing a central position in a dataset
mean, median, mode are all valid measures

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12
Q

skew

A

positive vs negative
positive - /_
negative - _/\

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13
Q

central limit theorem

A

if a population with finite variants is sufficiently sampled, the mean of all the samples from the population will be approximately equal to the mean of the population, AND the means from the samples will approach a normal distribution

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14
Q

steps of scientific method

A

planning - what are you going to do? learn the system, develop ideas about how the system works (maybe do a pilot study), decide hypothesis, figure out what data you will need
recording - collect and properly accord data, can take many forms, must record extremely carefully
analyzing - interrogate data to test hypothesis, analysis cannot be successful if data gathering was not designed with analysis in mind, should allow you to accept or reject null
reporting - disseminating methods and media will depend on the type of work and audience, statistical results must be reported using proper conventions, graphs must be properly labelled

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15
Q

continuous data

A

data that can take any value (usually measured)

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16
Q

discrete data

A

numerical data that can take a limited number of values (often counted)

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17
Q

ordinal data

A

data in categories that can be placed in order but the magnitude of difference between categories is not fixed

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18
Q

categorical data

A

data in categories that can’t be usefully ordered

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19
Q

null and alternate hypothesis

A

what do we test when we use them
test the null and decide if it is statistically probable

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20
Q

random sampling

A

best choice, random

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21
Q

systematic sampling

A

transects (sampling on a created line)

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22
Q

mixed sampling

A

stratified random sampling

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23
Q

haphazard sampling

A

when you are unable to randomly sample because of practicality

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24
Q

mean, median, mode

A

mean - average
median - less skewed middle
mode - most frequent

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25
Q

quartiles

A

rank data from smallest to largest
smallest is first number, largest is 5th
median is third
middle of first and third is 2nd, middle of fifth and third is 4th

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26
Q

why divide by n-1 when calculating varience

A

penalty for having a small amount of replicates

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27
Q

shapiro-wilk test for normality

A

takes a data distribution and determines whether it is significanyly different to normal
p-value of less than .05 = not normal, reject Ho

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28
Q

SEM (standard error of the mean)

A

=Sx/sqrt n
estimate of how close the sample mean is compared to the true population mean
standard deviation of resampled mean

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29
Q

descriptive projects

A
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30
Q

difference projects

A

is a different to b, bar charts and box and whisker plots, categorical variable and want to know if the response variable differs between categories

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31
Q

correlation/regression projects

A

links between variables, usually quantitative variables are independent and quantitative variables are dependent

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32
Q

association projects

A

similar to correlations but with categorical data

33
Q

how to calculate mean

A

bar x = (E^n i=1 * xi)/n

34
Q

how to calculate median

A

the middle value

35
Q

how to calculate mode

A

the most often

36
Q

how to calculate range

A

rank order observations - highest-lowest

37
Q

how to calculate variance

A

=(E6n i=1(xi-barx)^2/n-1 OR =SS/n-1

38
Q

how calculate standard deviation

A

=sqrt(E^n i=1 (xi-bar x)^2/n-1) OR =sqrt(SS/n-1)

39
Q

how to calculate standard error

A

=Sx/sqrt n

40
Q

outcomes of hypothesis testing

A

test null
p-value is the probability that the null hypothesis is correct from the data gathered

41
Q

what project uses histograms

A

descriptive test

42
Q

what projects use box plots

A

descriptive, difference (side by side)

43
Q

what projects use scatterplots

A

correlation and regression

44
Q

what projects use line plots

A

correlation and regression

45
Q

what projects use pie charts

A

association

46
Q

what probability is used as a threshold for hypothesises

A

.05

47
Q

set up for a t-test

A

create hypothesis, collect data, data must be normally distributed, each point must be independent

48
Q

what happens to t when mean, standard deviation, and n

A

when t increases, mean difference increases
when t decreases, standard deviation increases
when t increases, n increases

49
Q

what test is needed to decide if data is appropriate for a t-test

A

find if the data are normal (boxplot and shapiro-wilk test)
greater than .05 = the data is normal and a t-test can be done

50
Q

one tailed vs two tailed t-test

A

one tailed - more power to detect directional effect (greater than or less than)
two tailed - shows evidence that the difference between means is greater than expected

51
Q

paired t-test

A

repeated observations collected for a single variable with 2 levels (differences between sample point 1 and sample point 2 are compered for the same sample unit)

52
Q

how do non-parametric tests work

A

use the rank of data and rank from smallest to largest, compare the ranks
mann - whitney (two sample) and wilcoxon (paired) tests

53
Q

when do we have independent replicates

A

when the replicates are not connected to each other

54
Q

simple pseudoreplication

A

only a single replicate per treatment and subsamples are collected from each area

55
Q

sacrificial pseudoreplication

A

experimental units are replicated

56
Q

temporal pseudoreplication

A

only a single replicate per treatment and subsamples are collected from it repeatedly over time

57
Q

phylogenetic pseudoreplication

A

closely related individuals are the units being sampled (seeds, tadpoles, insect larvae)

58
Q

technical pseudoreplication

A

different observers or instruments are used for different parts of the experiment

59
Q

true positive

A

Ho is true and we fail to reject it

60
Q

true negative

A

Ho is false and we reject it

61
Q

false positive

A

Ho is true and we reject it
type 1

62
Q

false negative

A

Ho is false and we fail to reject it
type 2

63
Q

what is linear regression used for

A

to look for a relationship between quantitative independent and continuous variables

64
Q

linear regression assumptions

A

data are independent and randomly selected
data can be reasonably described by a linear relationship
residuals are normally distributed
residuals have constant variance regardless of x-value
no extreme outliers
(assumptions 3 and 4 are less important)

65
Q

equation for best-fit line (linear regression)

A

y=mx+b
y - dependent variable
m - slope of the line
x - the dependent variable
b - the point that the line crosses the y-axis

66
Q

what is the null hypothesis for linear regression

A

m=0
no relationship between x and y
p-value of more than .05 = no relationship, fail to reject
p-value of less than or equal to .05 = reject

67
Q

p-value meaning for linear regression

A

tells us if there is a significant slope

68
Q

r^2 for linear regression

A

how much of the variation in our dependent variable is explained by the regression
r2=explained variation/total variation
values range between 0 (none of the variation is explained by regression) and 1 (all of the variation is explained by regression)

69
Q

non-parametric linear regression

A

when data do not meet assumptions
Spearman’s Rank
does not give a slope or intercept
tells if the null hypothesis should be rejected
cannot assume the relation is linear

70
Q

anova

A

difference between 3 or more levels of a categorical variable
looks at variance in the dependent variable responses for each group

71
Q

assumptions for anova

A

data are independent and randomly selected
residuals are normally distributed around group means
each within-group residual variance is equal
no extreme outliers

72
Q

hypotheses for anova

A

null - V1=V2=V3=Vt
alternative - V1=V2=V3<Vt
p-value of greater than .05 = fail to reject
p-value of less than or equal to .05 = reject the null hypothesis, at least one group has a different mean –> use Tukey’s HSD test

73
Q

Tukey’s HSD

A

used after getting a significant result for an anova test
looks for pairwise differences
controls the type 1 error rate - gives p-values for all pairwise differences

74
Q

non-parametric anova

A

if assumptions are not met - kruskal-wallis test
based on ranks
p-value of greater than .05 = fail to reject null hypothesis
p-value of less than or equal to .05 = reject the null hypothesis and conclude that one group has a different mean rank to at least one other group

75
Q

chi-squared

A

used to compare two datasets that are categorical
compares the observed data to what would be expected if the values for each variable did not depend on the values for the other

76
Q

chi-squared hypothesis

A

null - no association between the variables
alternative - association between the two variables

77
Q

chi-squared p-value interpretations

A

p-value of greater than .05 = fail to reject
p-value of less than or equal to .05 = reject the null and conclude there is an association between the variables, can look at our observed data to determine where the largest differences are between observed and expected

78
Q
A

ENVS 203 (3 decks)

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