Module 1: Descriptive Statistics & Estimation

Question 1

Define sample.

Answer 1

A sample is a representative portion of a population that makes statistical analysis practical. However, sampling brings uncertainty since it is not a true representation of the entire population.

Question 2

Define statistics.

Answer 2

Statistics is the study of methods for measuring aspects of populations from samples and for quantifying the uncertainty of these measurements.

Question 3

Define estimation.

Answer 3

Estimation is the process of inferring an unknown quantity of a target population using sample data.

Question 4

Define population parameter.

Answer 4

Parameters are quantities that describe some truth about a population, such as averages and proportions. Statistics involves the estimation of these parameters.

Question 5

Define sample statistic.

Answer 5

A sample statistic is any value calculated from a sample.

Question 6

Define statistical population.

Answer 6

A population is the entire collection of individual units of interest.

Question 7

Define sampling unit.

Answer 7

A sampling unit is whatever basic unit the data points of a sample are defined by. This may be actual individuals of 1, or individual groups or selections.

Question 8

Define sampling error.

Answer 8

Sampling error refers to the chance difference between an estimate describing a sample and the corresponding parameter of the whole population.

Question 9

What is the goal of sampling?

Answer 9

Sampling aims to increase the precision and accuracy of estimates and to ensure that it is possible to quantify these outcomes.

Question 10

Define precision.

Answer 10

Precision refers to how consistent estimates are when compared to each other. Larger samples are less affected by chance, therefore allowing for more precise estimates.

Question 11

Define accuracy.

Answer 11

Accuracy refers to how close estimates are to the true population characteristic. If an estimate is unbiased, estimates will be more accurate.

Question 12

Define bias.

Answer 12

Bias is a systematic discrepancy between estimates obtained repeatedly and the true population characteristic.

Question 13

Define random sample.

Answer 13

Random samples contain individuals of a population that have had an equal and independent chance of being selected. The use of random samples minimizes bias and allows the sampling error to be measured.

Question 14

Define independent observation.

Answer 14

Independent observation assumes that no value from a sample can be inferred from any other value.

Question 15

Define sample of convenience.

Answer 15

A sample of convenience is a collection of individuals that are easily available for the researcher, but very likely to be biased and not selected independently. A sample of convenience can be a random sample, but is likely not.

Question 16

Define volunteer bias and provide examples.

Answer 16

Volunteer bias is the systematic differences between volunteer samples and their populations, which occurs when the behaviour of subjects impacts their chance of being sampled.

ex. sicker volunteers for medical studies, liberal volunteers for sex studies, animals willing to be trapped

Question 17

Define variables.

Answer 17

Variables are any characteristics or measurements that differ across a group of individuals. Estimates are technically variables, since they differ across samples.

Question 18

Define descriptive statistics.

Answer 18

Descriptive statistics are quantities that capture important features of frequency distributions, which is done by measuring the location and spread of a given distribution.

Question 19

Define cumulative frequency distribution.

Answer 19

Cumulative frequency distributions show all the quantiles within a sample on a graph.

Question 20

Define standard error.

Answer 20

The standard error of an estimate is the standard deviation of the estimate’s sampling distribution, which means it reflects the precision of an estimate.

Question 21

Define sampling distribution.

Answer 21

A sampling distribution is the probability distribution of all the values for an estimate that could possibly have been obtained.

Question 22

Define probability distribution.

Answer 22

A probability distribution describes the distribution of a variable across an entire population. Since this is almost never known in nature, it is approximated by the normal distribution or bell curve.

Question 23

Define frequency distribution.

Answer 23

A frequency distribution describes how many times each value occurs within a sample.

Question 24

Define confidence interval.

Answer 24

A confidence interval is a range of values surrounding the sample estimate that is likely to contain the population parameter. The values beyond the lower and upper limits are less plausible values for the parameter.

Question 25

What is the difference between explanatory and response variables?

Answer 25

Explanatory (independent) variables predict or affect response (dependent) variables. In experiments, the explanatory variable is manipulated to measure the effect on the response variable. There may be more than one of each variable in more complex experiments.

Question 26

What is the difference between experimental and observational studies?

Answer 26

Experimental studies involve the manipulation of variables by the researcher (ex. clinical trial), which allows cause-and-effect relationships to be determined. Observational studies can only point to associations, since the researcher has no control over different treatment groups.

Question 27

What are the properties of good samples?

Question 28

How are random samples obtained?

Answer 28

Every individual within a population is assigned a number, then a computer is used to randomly generate which of these individuals will be sampled (n).

Question 29

How are types of data classified?

Answer 29

Data may be categorical (qualitative) or numerical (quantitative). If data is categorical, it may be nominal (no inherent organization) or ordinal (consecutive). If data is numerical, it may be discrete (indivisible, finite values) or continuous (range of infinite values).

Question 30

How can you distinguish between frequency, probability, and sampling distributions?

Question 31

How do you calculate variance?

Answer 31

Variance (s²) is measured by squaring the sum of each deviation from the mean (∑(Y-Ybar)²), then dividing this by n-1.

Question 32

How do you calculate residual deviation?

Question 33

How do you calculate sums of squares?

Answer 33

The sum of squares of Y is calculated by adding each value’s deviation from the mean.

Question 34

How do you calculate standard deviation?

Answer 34

Standard deviation (s) measures how far observations are from the mean. It is calculated by taking the square root of variance.

Question 35

How do you calculate arithmetic sample mean?

Answer 35

The sample mean (Ybar) is the average of the measurements in the sample. It is calculated by dividing the sum of all individual values (∑Y) by the number of individuals (n).

Question 36

How do you calculate coefficient of variation?

Answer 36

The coefficient of variation is the standard deviation expressed as a percentage of the mean. To calculate CV, divide standard deviation (s) by the mean (Ybar) and multiply by 100%. This allows different values to be compared even if they do not have the same units or relativity.

Question 37

How do you calculate interquartile range?

Answer 37

Interquartile range refers to the span of the middle half of the data, from the first quartile to the third quartile. It is the result of subtracting the first quartile from the third quartile. To obtain these values: multiply n by the target quartile (ex. 0.25) to determine whether j is an integer. If it is an integer, then the quartile is the average of that integer and the next one up. If it is not, then the quartile is the rounded up version of the number.

Question 38

How do you calculate median?

Answer 38

The median is the middle observation in a set of data. It is equivalent to whatever value is at either (n+1)/2 (if n is odd) or [(n/2)+(n/2+1)] (if n is even).

Question 39

How do you calculate percentiles?

Answer 39

The percentile of a measurement specifies the percentage of observations less than or equal to it.

Question 40

How do you calculate quantiles?

Answer 40

Quantiles are the same measurement as percentiles, just displayed as decimals instead of percentages. To calculate a quantile, multiply n by the target quantile (ex. 0.25) to determine whether j is an integer. If it is an integer, then the quantile is the average of that integer and the next one up. If it is not, then the quantile is the rounded up version of the number.

Question 41

How do you calculate standard error of the mean?

Answer 41

Standard error of the mean is equal to the sample standard deviation (σ) divided by the square root of n.

Question 42

How are residuals, sums of squares, variances, and standard deviations related to one another?

Question 43

What are the advantages and disadvantages of residuals?

Question 44

What are the advantages and disadvantages of sums of squares?

Question 45

What are the advantages and disadvantages of variances?

Question 46

What are the advantages and disadvantages of standard deviations?

Question 47

How are Greek and Roman letters used to distinguish between population parameters and sample statistics?

Answer 47

Sample statistics are written in Roman letters, whereas population parameters are denoted by Greek letters.

Question 48

What happens to the precision of the sampling distribution as the sample size increases?

Answer 48

Increasing sample size reduces the spread of the sampling distribution, which means precision increases.