Statistics and Samples

Question 1

statistics (2)

Answer 1

• study of methods to describe and measure aspects of nature from samples
• allows us to determine likely magnitude of a measure’s distance from the truth or to quantify uncertainty

Question 2

estimation

Answer 2

• process of inferring an unknown quantity of a population using sample data

Question 3

parameter

Answer 3

• quantity describing a population

Question 4

estimate/statistic

Answer 4

• approximation of the truth (the true population paramter), subject to error, calculated from a sample

Question 5

population (2)

Answer 5

• entire collection of individual units that a researcher is interested in
• usually too large to directly measure

Question 6

sample

Answer 6

• smaller set of individuals selected from the population of interest

Question 7

sampling error (2)

Answer 7

• the chance difference between an estimate and the population parameter being estimated, caused by sampling
• larger samples, less affected by chance, have lower sampling error

Question 8

bias (2)

Answer 8

• systemic discrepancy between the estimates we obtain from our samples and the true population characteristic
• occurs when the sampling process favours some outcomes over others and systematically under/overestimates the population parameter

Question 9

precision (2)

Answer 9

• the spread of estimates resulting from sampling error

- larger populations are less affected by chance and will have higher precision

Question 10

accurate

Answer 10

• unbiased: the average of all estimates that may be obtained are centred on the true population value

Question 11

precision and sampling error

Answer 11

• the lower the sampling error, the higher the precision

Question 12

random sampling (2)

Answer 12

• each member of the population has an equal and independent chance of being selected
• minimizes bias and makes it possible to measure the amount of sampling error

Question 13

random sampling procedure (4 steps)

Answer 13

1. create a list of every unit, or group of non-independent units, in the population of interest and number them
2. decide on number of units in each sample (n)
3. use a random number generator to generate n random integers in population range
4. sample units whose numbers match those produced by the generator

Question 14

sample of convenience (2)

Answer 14

• collection of individuals that are easily available to the researcher
• researcher must assume sample of convenience is unbiased/independent, but not way to guarantee it

Question 15

volunteer bias

Answer 15

• bias resulting from systematic differences between the pool of volunteers (the volunteer sample) and the population they belong to

Question 16

how might volunteers differ from others (5)

Answer 16

• more health conscious/proactive
• low-income (if volunteers are paid)
• more ill (may die anyway, so willing to take the chance)
• more likely to have free time (retirees, unemployed)
• more angry, less prudish (aren’t afraid to speak up)

Question 17

variables (2)

Answer 17

• characteristics that differ among individuals or other sampling units
• estimates are variables

Question 18

data

Answer 18

• measurements of one or more variables made on a sample of individuals

Question 19

categorical variables (2)

Answer 19

• describe membership in a category or group
• describe qualitative characteristics of individuals that do not correspond to a degree of difference on a numerical scale/magnitude

Question 20

nominal

Answer 20

• describes a categorical variable with categories that have no inherent order

Question 21

ordinal (2)

Answer 21

• describes a categorical variable that can be ordered

- the magnitude of difference between each consecutive value is not known

Question 22

numerical variables

Answer 22

• measurement of individuals are quantitative and have magnitude on a numerical scale
• variables are numbers with measurements that are numerical counts, dimensions, angle, rates, and percentages

Question 23

continuous (3)

Answer 23

• 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
• can be measured (arm length, height, weight)

Question 24

discrete (2)

Answer 24

• numerical data that comes in indivisible units

- can be counted (# of limbs, offspring or petals)

Question 25

explanatory variable

Answer 25

- the variable that predicts or affects the other variable | - the variable that is manipulated during an experiment (treatment variable)

Question 26

response variable (2)

Answer 26

- the variable that is affected by the explanatory variable | - the measured affect of the treatment variable

Question 27

properties of a good sample (3)

Answer 27

- random selection of individuals (each individual has equal probability of being selected) - independent selection of indviduals - sufficiently large

Question 28

population parameters vs estimates

Answer 28

- population parameters: constants | - estimates: random variables that chance from one random sample to the next from the same population

Question 29

bias vs error

Answer 29

- bias is a systematic discrepancy (TENDING toward a certain difference) between an estimate and the true population characteristic - error is a RANDOM difference ( NOT TENDING toward any direction) between an estimate and the true population characteristic

Question 30

reasons why estimates differ from parameters (4)

Answer 30

- measurement bias (property of individuals) - sampling bias (property of sample) - measurement error (property of individuals, results from imprecise measuring) - sampling error (property of sample)

Question 31

frequency (2)

Answer 31

- of a specific measurement in a sample and is the # of observations having a particular value in a measurement - frequency IS NOT a variable, it is not a property of the individuals

Question 32

frequency distribution

Answer 32

- number of times each value of a variable occurs in a sample

Question 33

probability distribution (2)

Answer 33

- distribution of a variable in the whole population - the truth probability distribution of a population in nature is almost never known and is usually theoretically approximated

Question 34

normal distribution (2)

Answer 34

- familiar "bell-curve" shape - a theoretical probability distribution used to approximate the true distribution of a continuous variable in a population

Question 35

experimental studies

Answer 35

- researcher assigns treatments randomly to indviduals

Question 36

observational study

Answer 36

- assignment of treatments if NOT made by the researcher

Question 37

confounding variable

Answer 37

- variable that masks or distorts the causal relationship between measured variables in a study - can limit influence by assigning treatments randomly to subjects