Statistics Terms to Know
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Questions and Answers

What is a variable in the context of a study?

  • A method for choosing individuals for a sample
  • A characteristic of an individual (correct)
  • An explanation for a response
  • A numerical summary of a population

A parameter is a summary of values for a sample.

False (B)

What is the difference between a retrospective study and a prospective study?

A retrospective study looks back at past events, while a prospective study follows subjects into the future.

A __________ sample is chosen using a probability method.

<p>probability</p> Signup and view all the answers

Match the sampling methods with their descriptions:

<p>Simple random sample = Each individual has an equal chance of selection Stratified random sample = Dividing the population into strata and sampling from each Cluster random sample = Selecting whole clusters and pooling individuals from them Convenience sample = Drawing from those who are easily available</p> Signup and view all the answers

What is a confounding variable?

<p>A variable that influences the relationship between studied variables (A)</p> Signup and view all the answers

Response bias occurs when individuals provide incorrect answers due to poorly worded questions.

<p>True (A)</p> Signup and view all the answers

Define sampling bias.

<p>Sampling bias occurs when there is a systematic tendency to exclude one type of individual from a study.</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Statistic = A numerical summary of values based on a sample Parameter = A numerical summary of values for the entire population Variable = A characteristic of an individual Sample = A subset of the study populations made of individuals</p> Signup and view all the answers

Match the following types of studies with their characteristics:

<p>Prospective Study = Follows subjects into the future Retrospective Study = Looks backward in time to past events Comparative Study = Establishes cause and effect relationships Observational Study = Values of variables are observed without testing</p> Signup and view all the answers

Match the following sampling methods with their descriptions:

<p>Probability Sample = Chosen using a probability method Convenience Sample = Not chosen using a probability method Simple Random Sample = Each possible sample has the same chance of selection Stratified Random Sample = Divides population into groups and samples from each</p> Signup and view all the answers

Match the following biases with their descriptions:

<p>Sampling Bias = Systematic tendency to exclude certain individuals Nonresponse Bias = Occurs when a person chooses not to respond Response Bias = Occurs when a person responds incorrectly Measurement Bias = Inaccuracy in the process of measuring outcomes</p> Signup and view all the answers

Match the following variables with their explanations:

<p>Response Variable = Measures an outcome or result of interest Explanatory Variable = Helps explain changes in a response variable Lurking Variable = Influences relationships among variables but is not measured Confounding Variable = Effects on a response variable cannot be distinguished from each other</p> Signup and view all the answers

Match the following concepts with their focus:

<p>Sampling Procedure = Method for choosing individuals for a sample Cluster Random Sample = Divides population into clusters for sampling Stratified Random Sample = Samples from defined strata of a population Simple Random Sample = Ensures every individual has equal chance of selection</p> Signup and view all the answers

Match the following terms with their relevance to experimental design:

<p>Experiment = Subjects assigned to certain conditions to assess causal links Randomization = Process to eliminate bias in sample selection Control Group = Group that does not receive treatment for comparison Treatment Group = Group that receives the experimental intervention</p> Signup and view all the answers

Match the following statements with the type of variable they describe:

<p>Explanatory Variable = Expected to explain changes in a response Response Variable = Outcome that is measured in a study Confounding Variable = Complicates the interpretation of results Lurking Variable = Hidden factor that may influence the observed variables</p> Signup and view all the answers

Flashcards

Capital of France (example flashcard)

Paris

individual

sampling unit evaluated in a study

population

set of all individuals of interest

sample

a subset of the study populations made of individuals

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variable

a characteristic of an individual. Different individuals will have different values of the characteristic of interest

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statistic

a numerical summary of values based on a sample (mean, median, ect)

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parameter

a numerical summary of values for the entire population (usually not known)

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experiment

subjects are assigned to certain experimental conditions (treatments/interventions) to determine a causal link between assigned treatments and measured responses.

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observational study

values of variables of interest are observed, nothing is being tested and used when experimenting is unethical

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prospective study

a study that follows its subjects into the future

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retrospective study

a study that looks backward in time to events that happened in the past

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response variable

measures an outcome or result of interest in a study

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explanatory variable

what we think will help explain changes in a response variable

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comparative study

comparing variables and experimental conditions given to individuals establish a cause and effect relationship

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sampling procedure

method for choosing individuals for a sample

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sampling bias

occurs when there is a systematic tendency to exclude one or another type of individual

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nonresponse bias

occurs when a person chooses not to respond to a question or doesn’t respond at all (often due to disinterest in the subject or insecurity)

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response bias

occurs when a person responds incorrectly to one or more questions (often affected by insecurity, poorly worded questions, or order of questions)

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probability sample

a sample chosen using a probability method (based on randomization)

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convenience sample

a sample not chosen using a probability method (drawing from a population close at hand for convenience)

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simple random sample

a sample created from a population in which each possible sample of that size has the same chance of being selected

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stratified random sample

population is divided into groups (called strata/stratum), a simple random sample of individuals is then drawn from each stratum, and the individuals are pooled to form the sample

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cluster random sample

a population is divided into groups called clusters, and a simple random sample of clusters is selected, and the individuals in the chosen clusters are pooled to form the sample

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lurking variable

one that influences the relationships among the variables in a study but is not included in the variables studied, either intentionally or by mistake

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confounding variable

two variables are said to be confounded if their effects on a response variable cannot be distinguished from each other (either among the explanatory variables studies or the lurking variables).

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randomized comparative experiment

an experiment that compares the effects of two or more treatments while randomly assigning subjects to different treatments

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Features of randomized comparative experiments

Control the effects of lurking variable on the response by using comparison Reduce potential bias in treatment assignment

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treatment group

the individuals chosen to receive the proposed treatment or intervention

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control group

the individuals chosen to receive a standard treatment or no treatment at all

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blind experiment

subject in a randomized comparative experiment does not know how they were assigned (treatment vs control group)

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double blind experiment

subject and doctor/nurse are blind to the subject’s treatment assignment, and only the researchers know

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categorical variable

places an individual into one of several categories or classes

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quantitative variable

produces numerical data

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categorical variables can be characterized by ....

nominal or ordinal

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nominal

when the categorical variable categories are unordered

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ordinal

when the categorical variable categories have a natural ordering

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dichotomous or binary categorical variables

when the categorical variable has exactly two categories

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quantitative variables can be characterized by...

discrete or continuous

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discrete categorical variable

values form a finite sequence of numbers

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continuous quantitative variable

values have infinite possibilities

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frequency distribution

raw values are counted

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relative frequency

percentage of the total raw count

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back-to-back-stem plot

stem is leading digit(s), leaves on the left represent values from one data set, and the leaves on the right side represent the values from the other data set.

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height (density) histogram

divide the relative frequency by length of class interval

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class interval

interval on histogram

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what does a density histogram represent

the proportion of data points that fall within a specific range on the x-axis, essentially showing how concentrated the data is within that range, with a higher density indicating a greater concentration of data points in that bin compared to others; the total area under the density histogram will always sum to 1, signifying the total probability distribution across all data points.

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interquartile range

q3-q1

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what do you include in a box and whisker plot

median, q1, q3, calculated whisker endpoints (within the whisker interval), outliers

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Q1 whisker endpoint

q1-1.5(IQR)

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q3 whisker endpoint

q3+1.5(IQR)

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how to get the standard deviation

mean, xi-mean, (xi-mean)^2/n-1, square root

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Sv^2

Variance: ((x1-mean)^2 + (x2-mean)^2...)/n-1

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Sx

Standard deviation: square root of Sv^2

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standard z-score

measures how many standard deviations a data point is from the mean in a distribution. helps to compare a value relative to the mean

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Zxi= (xi-mean)/Sx

divide xi-mean by the standard deviation of that data set. each x has a z score

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sample correlation (r)

number between -1 and 1 that indicates strong neg/pos association (close to -1 or 1) or weak neg/pos association (closer to 0 than -1 or 1) between an x and y variable

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what is the equation for the sample correlation (r)

r= ((Zx1 Zy1) + (Zx2 Zy2)+ (Zx3 Zy3)...)/n-1

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symmetric data

mean and median are roughly the same, mean and standard deviation are good measures of center and spread

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skewed right

mean is greater than the median, median and IQR are better measures of center and spread

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skewed left

median is greater than mean, median and IQR are better measures of center and spread

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effect of outliers on mean

mean changes a lot

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effect of outliers on median

median does not change much

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(two-way) scatter plot

displays the relationship between two quantitative variables measured on the same individuals (ordered pairs of x and y)

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approximate linear relationship

when the data pairs between x and y variable make a roughly straight trend line. Use sample correlation (r) to measure the strength of this linear relationship

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what is density (histogram)

relative frequency/length of class interval (base)

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least square regression line

y=bx+a b is slope and a is y-intercept Usethisequation to make a prediction about where a point will be relative to the data set (point must be within data set range)

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how to calculate slope (b)

sample correlation (r) times the standard deviation of Y over the standard deviation of X b=r(Sy/Sx)

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how to calculate y-intercept (a)

the y-intercpt is the mean of y minus b times the mean of x a=ymean-b(xmean)

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cluster random sample

divide the population into groups and then randomly select one or multiple groups to be part of your sample

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stratified random sample

divide the population into groups, then randomly select a number of people from each group, pooling them together to form your sample

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Study Notes

Study Notes on Statistical Methods

  • Individual: A single unit evaluated in a study.
  • Population: All individuals of interest in a study.
  • Sample: A subset of the population, made of individuals from the population of interest.
  • Variable: A characteristic of individuals. Different individuals may have different values.
  • Statistic: A numerical summary of values from a sample. Examples include mean, median.
  • Parameter: A numerical summary of values for the entire population. Usually unknown and estimated from a sample.
  • Experiment: Subjects are assigned to different conditions/treatments (interventions) to find causal links.
  • Observational Study: Values of variables are observed to determine relationships without manipulation. Used when experiments are unethical or impractical.
  • Prospective Study: Follows subjects into the future to observe how variables change.
  • Retrospective Study: Looks back in time to observe variables and how they were related in the past.
  • Response Variable: Measures outcome or result of interest.
  • Explanatory Variable: A variable thought to explain changes in the response variable.
  • Comparative Study: Compares variables and conditions to determine cause and effect relationships.
  • Sampling Procedure: Method for selecting individuals for a sample.
  • Sampling Bias: Systematic tendency to exclude certain types of individuals.
  • Nonresponse Bias: Occurs when individuals chosen for a sample do not respond, often due to disinterest or insecurity.
  • Response Bias: Occurs when individuals respond inaccurately or falsely to questions, potentially due to insecurity, poorly worded questions, or question order.
  • Probability Sample: Selected using probability methods, ensuring each individual has a known chance of selection.
  • Convenience Sample: Selected for convenience, not based on a probability method.
  • Simple Random Sample: Each possible sample of the chosen size has the same probability of being selected.
  • Stratified Random Sample: Population divided into groups (strata), then a random sample from each stratum.
  • Cluster Random Sample: Population divided into groups (clusters), then a random sample of clusters, and all individuals in the selected clusters are included.
  • Lurking Variable: A variable influencing the relationship between variables in a study but not studied directly.
  • Confounding Variable: Effects of two variables on a response cannot be distinguished, among explanatory or lurking variables.
  • Randomized Comparative Experiment: An experiment that compares effects of treatments with random assignment of subjects to treatments. This reduces potential bias in treatment assignment.
  • Treatment Group: Individuals receiving the treatment.
  • Control Group: Individuals receiving a standard treatment or no treatment.
  • Blinding: Method where subjects do not know group assignment (single-blind) or subjects and researchers do not know assignment (double-blind).

Randomized Comparative Experiments: Features

  • Controls the effects of lurking variables through comparison.
  • Reduces bias in treatment assignment through randomization.

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