Module 1

Question 1

Biostatistics

Answer 1

A branch of statistics that applies statistical theories and methodologies to the collection, review, and analysis of data arising from biological, agricultural, medical, and public-health-related contexts

Question 2

Population

Answer 2

In statistics, a population referes to the entire group or collection of items, individuals, or elements that share a common characteristic and are of interest for the purpose of analysis or study. It encompasses every possible member of a group under consideration

For example - public health researchers conducted a comprehensive survey to assess the vaccination rates against the flu virus among the population of elderly individuals living in nursing homes

Question 3

Sample

Answer 3

A sample is a smaller subset of the population selected to study or analyze the characteristics of the entire population. Samples are used to make inferences and draw conclusions about the larger population without having to examine every single individual within it. The goal is to ensure that the sample is representative of the population to obtain accurate and meaningful results.

Example: public health officials collected a random sample of 500 households in the urban area to study the prevalence of air population-related respiratory illnesses among residents

Question 4

Variable

Answer 4

Any characteristic, number of quantity that can be measured or counted. It varies or changes from one observation to another, hence the name. Variables can be classified into different types such as categorical

Exmaple: in a public health study examining the relationship between dietary habits and the onset of diabetes, the amount to daily sugar intake could be considered a variable.

Question 5

What are the three main components of statistics as a discipline?

Answer 5

Design - how we collect data
Description -describing data in a sample
Inference - using data from a sample to make generalizations about a population

Question 6

When is it appropriate to use absolute frequency vs relative frequency

Answer 6

Absolute frequency - when you want to convey the actual number of cases of occurrences. Relative when you want to provide a sense of proportion or rate

Question 7

What are the advantages and disadvantages of transforming a continuous variable into an ordinal variable?

Answer 7

Advantages: simplicity - making it easier for non-experts to understand
Applicability - interventions can be tailored to high, medium, and low risk for example

Disadvantages
Loss of information
Arbitrary boundaries

Question 8

What are the types of data?

Answer 8

Nominal - qualitative and used to name or label variables without assigning any quantitative value or order. Categories are mutually exclusive and cannot be ranked or measured. Examples: Gender, nationality, types of transportation

Ordinal - Ordinal data is categorical data where variables have a natural, ordered sequence, but the intervals between categories are not necessarily equal or known. You can rank the values, but you cannot quantify the difference between them. Examples: Survey ratings (e.g., poor, fair, good, excellent), letter grades, socioeconomic status

Discrete - Discrete data is quantitative and consists of countable, indivisible values. Each data point is a distinct, separate value, often representing “the number of” something. Discrete data cannot take on every possible value within a range, only specific, separate values. Examples: Number of students in a class, number of cars in a parking lot.

Continuous - Continuous data is quantitative and can take on any value within a given range, including fractions and decimals. It represents measurements and can be infinitely subdivided. Continuous data is often obtained through precise measurement tools. Examples: Height, weight, temperature, time spent on a website

Question 9

What are the primary measures of location

Answer 9

Percentile - the p-th percentile is the value that p% of observations lie below

Median - the 50th percentile value (the middle value)

Mean - the average value

Question 10

How do median and mean interact when data is unimodal

Answer 10

Symetric: Median = Mean
Left Skewed: Mean < Median
Right Skewed: Median < Mean

Question 11

What is dispersion

Answer 11

How spread out from the center are typical observations
Range - distance between the smallest and largest
IQ Range- distance between 25% and 75%

Question 12

What is Variance

Answer 12

Average squared distance

Question 13

What is standard deviation

Answer 13

The square root of the variance puts it into the same units as the original data

Question 14

What is anecdotal evidence

Answer 14

Refers to unusual observations that are easily recalled because of their striking characteristics. While it cannot be used as a basis for a conclusion, it can inspire the design of a more systematic study

Question 15

Simple Random Sample

Answer 15

Each member of a population has the same chance of being sampled. Each case is sampled independently of theother cases

Question 16

What can happen with non-response

Answer 16

A non-response bias can skew the results and lead to incorrect conclusions about a population

Question 17

What is stratified sampling

Answer 17

The population is divided into strata before cases are selected within each stratum. The strata are chosen such that similar cases are grouped together.

This is especially useful when the cases are similar with respect to the outcome of interest, but the cases between strata are different

Question 18

What is a cluster sample

Answer 18

The population is divided into cluster,s then a fixed number of clusters is sampled and all observations from those clusters are included

Useful when high case-to-case variability, but clusters are similar

Question 19

What is multistage sampling

Answer 19

Similar to cluster sampling, but instead of keeping all observations in each cluster, a random sample is collected within each cluster

Useful when high case-to-case variability, but clusters are similar

Question 20

What are the three principles on which experimental design is based? is based

Answer 20

Control - control for extraneous variables and choose a sample that is representative of the population of interest

Randomization - ensures balance and protects against bias. Allows differences in outcomes to be reasonably attributed to a treatment rather than inherent variability between patients

Replication - results from a large study are more likely to be reliable than those from small samples

Question 21

What is a confounding variable

Answer 21

A variable associated with both the explanatory and response variables

Question 22

What is the difference between a population and a sample

Answer 22

A population is the collection of individuals about whom you want to make inferences. A sample is a subset of the population on whom data is collected.

Question 23

What is Simpson’s Paradox

Answer 23

An extreme example of confounding where associations observed in several groups disappear of change direction when the groups are combined

Question 24

What are the three principal points where data analysis could go wrong

Answer 24

Collection - when gathering data
Processing - when analyzing the data and its implications
Presentation - when sharing your findings with others

Question 25

Points to a good graph

Answer 25

To have reliable results, any sample size quantitative analysis should include at least 200 people. Data is from a neutral source Questions should not imply or provoke a specific response Be wary of misleading averages Tracking information for each year provides a truer picture of the general trends. Avoiding biased samples Looking for truncating on an axis Percentages can hide small sample sizes Using different bases Data fishing - data dreging - the analysis of large data with the goal of findings an association that is implied as coorelation

Question 26

What are some important characteristics of good graphs?

Answer 26

Should convey the general patterns in a set of observations at a single glance. Should be simple, self-explanatory, clearly labeled

Question 27

What are Descriptive Statistics

Answer 27

means of organizing and summarizing observations

Question 28

What is Nominal Data

Answer 28

Values fall into unordered categories or classes (sex, blood type) Proportion measurements can be used

Question 29

What is ordinal data

Answer 29

When order becomes important, a natural order exists, but we still aren't concerned with the magnitude (pain scale)

Question 30

What is ranked data

Answer 30

Data is arranged from highest to lowest and then assigned a rank (possible causes of death) - disregard magnitude and only care about relative position

Question 31

What is Discrete Data

Answer 31

Order and magnitude are important - numbers represent actual quantities (unlike ranks) and can only take on specific values (e.g., the number of car accidents in MA in a month). These will be integers. Arithmetic can be applied

Question 32

What is continuous data

Answer 32

Data that represents specific quantities but is not restricted to specific values (like integers). Eg. Time) The only limiting factor with continuous data is the degree of accuracy with which it can be measured

Question 33

Frequency Distribution

Answer 33

Nominal and Ordinal data: consists of a set of classes/categories and the numerical counts Discrete or Continuous Data: 1. Breakdown into a series of non-overlapping intervals. 2. count

Question 34

Relative frequency

Answer 34

the proportion of the total number of observations that appears in that interval. Useful for comparing sets of data that contain unequal numbers of observations

Question 35

Cumulative relative frequency

Answer 35

The cumulative relative frequency is calculated by summing the relative frequencies for the specified interval and all previous ones

Question 36

Stochastically ordered

Answer 36

Two random variables are stochastically ordered if one is more likely to take on larger values than the other, as formalized by the comparison of their probability distributions or cumulative distribution functions

Question 37

Bar Charts

Answer 37

Pictorial representation of frequency distribution for nominal and ordinal data

Question 38

Histogram

Answer 38

Frequency distribution for discrete or continuous data. The total area = 1 or 100%; frequency is associated with the area, not the height of the bar. RElative frequency and absolute frequency histograms will have the same shape

Question 39

Frequency Polygon

Answer 39

Superior to histograms for comparing two sets of data A cumulative frequency polygon

Question 40

One Way Scatterplots

Answer 40

A one-way scatter plot uses a single horizontal axis to display the relative position of each data point in the group No observations are lost, but they can be difficult to read

Question 41

Box Plots

Answer 41

similar to one-way scatter plots in that they require a single axis; instead of plotting every observation, however, they display only a summary of the data Adjacent values are the most extreme observations that are not more than 1.5X the interquartile range

Question 42

Two-way scatterplots

Answer 42

used to depict the relationship between two different continuous measurements.

Question 43

Mean

Answer 43

The most frequently used measurement of central tendency - also called the average Not appropriate for nominal or ordinal data The mean is extremely sensitive to unusual values

Question 44

Median

Answer 44

Can be used for ordinal, discrete and continuous data. It is the 50th percentile of all measurements Odd number of observations: [(n + 1)/2] - even takes the average of the two middle numbers. Only take ordering into account and is not as sensitive to unusual values (robust)

Question 45

Mode

Answer 45

It can be used for all types of data. It is the set of values that occurs most frequently.

Question 46

Measures of central tendency by shape of data

Answer 46

Unimodal, evenly distributed: mean, median, and mode are about the same Bimodal, recently shaped: mean, median, and mode are about the same (but the measurement would be extremely unlikely to occur) Asymmetric data - median is often the best measure

Question 47

Range

Answer 47

difference between the largest observation and the smallest. Highly sensitive to exceptionality

Question 48

Interquartile range

Answer 48

Not as easily impacted by extremes Calculated by subtracting the 25th percentile of the data from the 75th percentile; consequently, it encompasses the middle 50% of the observations.

Question 49

Variance

Answer 49

quantifies the amount of variability, or spread, around the mean of the measurement

Question 50

Variance Con't

Answer 50

variance is calculated by subtracting the mean of a set of values from each of the observations, squaring these deviations, adding them up, and dividing by 1 less than the number of observations in the data set.

Question 51

Standard Deviation

Answer 51

positive square root of the variance. In a comparison of two groups of data, the group with the smaller standard deviation has the more homogeneous observations; the group with the larger standard deviation exhibits a greater amount of variability.

Question 52

Coefficient of Variation

Answer 52

relates the standard deviation of a set of values to its mean. Most useful for comparing two ormore data sets

Question 53

What is the benefit of calculating a grouped mean?

Answer 53

this procedure can be applied to data that have been summarized in the form of a frequency distribution. Data that is organized in this way is often referred to as grouped data. Can also be interpreted as a weighted average

Question 54

Chebychev's inequality

Answer 54

can be used to summarize the distribution of values instead. Chebychev's inequality is less specific than the empirical rule, but it is true for any set of observations, no matter what its shape