Brief Review of Intro to Statistics (Module 14)

Question 1

What type of data analysis would be appropriate for 1 continuous explanatory variable (x) and 1 continuous response variable (y)?

Answer 1

simple linear regression

Question 2

What type of data analysis would be appropriate for multiple continuous explanatory variables (x1, x2, … x[n]) and 1 continuous response variable (y)?

Answer 2

multiple linear regression

Question 3

What 2 types of data analyses would be appropriate for 1 categorical variable (x) and 1 continuous response variable (y)?

Answer 3

(1) T-test
(2) one-way ANOVA

Question 4

Under what circumstance would we run a T-test rather than a one-way ANOVA?

Answer 4

If the categorical explanatory variable is binary, such as for sex (‘male’, ‘female’) or the main belligerents in the Wars of the Roses (‘House of York’, ‘House of Tudor’), we perform a T-test.

Question 5

Under what circumstance would we run a one-way ANOVA rather than a T-test?

Answer 5

If the categorical explanatory variable has more than two possibilities, such as regions of Italy (‘Tuscany’, ‘Campania’, ‘Sicilia’, etc.), or different types of fruit people commonly pack for lunch (‘Oranges’, ‘Bananas’, ‘Apples’, etc.), we perform a one-way ANOVA.

Question 6

What is the difference between a one-way ANOVA and a two-way ANOVA?

Answer 6

A one-way ANOVA will have only one explanatory variable (x), while a two-way ANOVA will have two explanatory variables (x1, x2).

Question 7

What is an example of a question we might use a two-way ANOVA to answer which concerns people’s preferred fruit (x1), their annual average mileage (y), and the state in the U.S. they live (x2)?

Answer 7

Is the average annual mileage that people drive influenced by their favorite fruit and does that depend on the U.S. state where they live?

Question 8

What does the phrase “n-way ANOVA” mean?

Answer 8

ANOVAs can be performed with as many explanatory variables as one wants - “n” represents the number in the analysis, whether that is two or three or ten, etc.

Question 9

What type of data analysis would be appropriate for 1 categorical explanatory variable (x) and 1 categorical response variable (y)?

Answer 9

Analysis of Contingency Tables

Question 10

In an analysis of contingency tables, if both the explanatory and the response variables are both binary, what term do we use to describe the test we perform?

Answer 10

Analysis of a Two-Way Contingency Table

Question 11

What is it called if one or both of the explanatory or response variables in an Analysis of Contingency Tables has more than two possible entries?

Answer 11

Analysis of a R-by-C (Row-by-Column) Contingency Table

Question 12

What type of analysis would we perform if we have 1 continuous explanatory variable (x) and 1 categorical response variable (y)?

Answer 12

simple logistic regression

Question 13

What type of analysis would we perform if we have more than 1 continuous explanatory variable (x1, x2, … x[n]) and 1 categorical response variable (y)?

Answer 13

multiple logistic regression

Question 14

T-tests, ANOVA, linear regressions and logistic regressions are all part of what family of mathematical concepts?

Answer 14

linear models

Question 15

What is the term and a description for the first assumption of linear models?

Answer 15

LINEARITY - stipulates that there is a linear relationship between the explanatory variable (x) and the response variable (y)

Question 16

What is the term and a description for the second assumption of linear models?

Answer 16

NORMALITY - for any given value of the explanatory variable (x), the values of the response variable (y) have normally distributed errors

Question 17

What is the term and a description for the third assumption of linear models?

Answer 17

HOMOGENEITY OF VARIANCE - the variance in the response variable (y) is constant across a range of explanatory variable (x) outputs

Question 18

What is the term and a description for the fourth assumption of linear models?

Answer 18

INDEPENDENCE - for any given value of the explanatory variable (x), the values from the response variable (y) have independent errors

Question 19

FILL IN THE BLANKS: For linear models, decent method for (1)______________ and a strong (2)____________________ will make it easier to analyze the data than (3)______________ or (4)_______________ it after the fact to better fit the (5)___________________.

Answer 19

(1) sampling
(2) experimental design
(3) transforming
(4) sub-setting
(5) assumptions of linearity

Question 20

What kind of data is able to be analyzed in multiple different ways and may reveal answers to multiple different questions?

Answer 20

data collected in accordance with a sound experimental design

Question 21

What term refers to the ability to detect a pattern when one is present in the data?

Answer 21

statistical power

Question 22

What component of proper experimental design culminates in a good statistical power?

Answer 22

selecting the necessary number of replicates

Question 23

What do we call data for which there are multiple response variables (y1, y2, … y[n]) for each sampling unit or observation?

Answer 23

multivariate data

Question 24

What would be an example of research which collects multivariate data from the hydrological sciences?

Answer 24

The sampling unit is Lake Apopka, from which we collect multiple measurements (y1 = pH, y2 = dissolved oxygen, … y[n-1] = salinity, y[n] = nitrate concentration)

Question 25

What would be an example of research which collects multivariate data from the science of forestry?

Answer 25

The sampling unit is the German Schwarzwald, from which we collect multiple measurements (y1= canopy height, y2 = canopy cover, … y[n-1] = snag density, y[n] = trunk diameter)

Question 26

Multivariate analysis always involves multiple response variables (y1, y2, … y[n]), but we can have (1)______________________, referred to as (2)____; or (3)________________________, referred to as (4)__________________; or even (5)______________________.

Answer 26

(1) one explanatory variable
(2) x
(3) multiple explanatory variables
(4) x1, x2, … x[n]
(5) no explanatory variables

Question 27

The linear models studied in this class have only focused on explanatory variables which have been chosen ahead of time (i.e., the treatment groups). What are these referred to as?

Answer 27

fixed effects

Question 28

What do the fixed effects influence?

Answer 28

the mean of the response variable

Question 29

What is the difference between a Fixed Effects Model (FEM), Random Effects Model (REM), and a Mixed Effects Model (MEM)?

Answer 29

FEMs only contain parameters which are fixed or non-random quantities

REMs only contain parameters which are random quantities

MEMs contain both fixed effects and random effects

Question 30

What is the definition of a random effect?

Answer 30

A variable which is represented by a random sample of all the possible levels of said variable

Question 31

What do random effects influence?

Answer 31

the variance of the response variable

Question 32

What type of effects represent unobserved variables?

Answer 32

random effects represent unobserved variables

Question 33

Are you interested in the size of the effect? If you are, it is most likely a (1)_______________. If you are not interested, it is most likely a (2)_______________.

Answer 33

(1) fixed effect
(2) random effect

Question 34

Is it reasonable to think that the factor levels arise from a population of levels? If it is, the variable likely has (1)________________. If it is not reasonable to assume that, the variable likely has (2)_________________.

Answer 34

(1) random effects
(2) fixed effects

Question 35

Are there sufficient levels of the factor in the data frame that an estimate of the variance of the population effects can be based? If yes, the factor likely has (1)________________. If no, the factor likely has (2)___________________.

Answer 35

(1) random effects
(2) fixed effects

Question 36

Are the factor levels of the explanatory variable informative? If they are, we are likely dealing with ____________________.

Answer 36

fixed effects

Question 37

Are the levels of a variable just numeric labels? If they are, the variable probably has _____________________.

Answer 37

random effects

Question 38

Consider the four variables below:

(1) sex assigned at birth (M/F)
(2) the colors on a rose (red/white)
(3) possible Summer temperatures to the nearest whole degree Celsius (integer values, 78 =< x =< 111)
(4) one strain of ‘B. bassiana’ versus another possible strain (ANT-03 vs. GHA)

Would we expect fixed effects or random effects from these variables?

Answer 38

fixed effects would be expected

Question 39

Consider the four variables below:

(1) day selected at which to perform a certain collection of data given the demands of the researcher’s schedule
(2) site selected at which to collect data
(3) responses from different members of the same household
(4) the nesting attempts by the same bird

Would we expect fixed effects or random effects from these variables?

Answer 39

random effects from these variables would be expected

Question 40

What do we call flexible linear models which allow for non-normal error terms to be applied to response variables?

Answer 40

generalized linear models (GLMs)

Question 41

What are the four possible types of distribution seen in generalized linear models?

Answer 41

normal
binomial
Poisson
gamma

Question 42

What makes GLMs more useful in some respects than simpler linear models, even if it also makes them more conceptually challenging?

Answer 42

GLMs can unify several types of data analysis into the same model framework

Question 43

Most of the statistics we have learned in “Intro to Stats” is referred to typically as what?

Answer 43

frequentist statistics

Question 44

What is another name for frequentist statistics, albeit one which is slightly less descriptive?

Answer 44

classical statistics

Question 45

The main idea of frequentist statistics can be summarized how?

Answer 45

consideration of uncertainty in terms of the expected outcome to the statistic under repeated sampling iterations

Question 46

What is the desired culmination of the repeated sampling iteration one performs under frequentist statistics?

Answer 46

obtaining the P-value for the desired confidence interval

Question 47

What is the most common P-value, which is a direct reflection of the most common desired confidence interval?

Answer 47

the most common P-value (alpha-level) is 0.05, which describes a 95% confidence interval

Question 48

What development has allowed Bayesian statistics to become more popular in the 21st century than it was in the early 20th century and beforehand?

Answer 48

advent of cheap computing technologies

Question 49

What is it called if we run a linear model in which we know the errors are not normally distributed but we assume that we have lots of data that can compensate for that short-coming?

Answer 49

asymptotic theory

Question 50

What is the main advantage that Bayesian statistics has over other linear models?

Answer 50

Bayesian statistics frees the researcher to devise a model which best matches the problem at hand, rather than one which forces the data into one of the premade statistical models like ANOVA or T-tests, with all of the assumptions that need to be required therein

Question 51

What is the primary disadvantage of using Bayesian models?

Answer 51

Bayesian statistics comes with the knowledge barrier of needing to know how to write computer code and the material barriers of needing to have strong computers