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Statistics

the science of data

Data

Observations (measurements, survey responces, etc.) that have been collected.

Population

a complete collection of all elements to be studied. It is the group of individuals that we want information about

Sample

a subcollection of elements drown from a population. It is the part of the population that we actually examine in order to gather information

Census

collection of data from EVERY element in a population

Parameter

numerical measurement describing some characteristic of a POPULATION

Statistic

a numerical measurement describing some characteristic of a SAMPLE

categorical variable

records which of several groups or categories an individual belongs.

Categorical value aka

qualitative variable

quantitative variable

takes numerical values for which hit makes sense to do arithmetic operations like adding and averaging

Lurking variable

a variable that affects the variables being studied but is not included in the study. It hided, if you will, in the background and has the potential to ruin the results

Discrete data

data results that are due to when the number of possible values is either a finite number or a countable number (i.e. the number of possible values is infinite but you can assign the natural numbers (1,2,3...) to each value present. ex. binomial distribution

continuous data

__________ data result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps. ex. the normal distribution

Nominal level of measurement

_______________ level of measurement is characterized by data that consists of names, labels or categories only. Data can't be arranged in an ordering scheme, such as low to high

Ordinal level of measurement

the _______________ level of measurement is characterized by date that can be arranged in some order, but aritmetic differeces( aka subtraction) are meaningless

football rankings are an example of....

____________ is an example of ordinal level of measurement

Interval level of measurement

_______________ level of measurement is like the ordinal level with the additional property that the difference between any two data values is meaningful. Quotients though are meaningless and there is no natural zero (where none of the quantity is present) EX temerature, IQ

Ratio level of measurement

____________ level of measurement is characterized by data that have a natural zero starting point. Both arithmetic differences and quotients are meaningful. EX. height, miles

Random sample

in a _________________ sample, members of the population are selected in such a way that each has an equal chance of being selected.

Simple Random Sample

a _____________ ______________ sample of size n subjects is chosen in such a way that every possible sample of size n has the same chance of being the sample actually selected.

Systematic Sampling

In ____________ sampling we select some starting point and then select every k-th element in the population. Mod arithmetic is useful for this type of sampling.

Stratified sampling

with ___________ sampling we subdivide the population into at least tow different subgroups (or strata) that share the same characteristics (such as gender or age bracket) then we draw a sample (most often an SRS) from each stratum and combine these to form the full sample.

cluster sampling

in ______________ sampling we divide the population into sections or clusters. Then we randomly select some of those clusters and choose all of the members from each cluster selected.

multistage sampling

with multistage sampling, some combination of the various methods of random sampling is used to form the sample.

sampling error

the difference between a sample result and the true population result, such an error results form chance sample fluctuations.

non-sampling error

when the sample data are incorrectly collected, recorded or analyzed (such as selecting a biased sample, using a defective measurement instrument, or copying the data incorrectly)

bias

systematic error which favors certain outcomes

Undercoverage

occurs when some groups of the population are left out of the process of choosing a sample.

observational study

we observe and measure specific characteristics but we don't attempt to modify the subjects being studied.

experiment

we deliberately impose some treatment and then proceed to observe its effects on the subjects.

blinding

a technique in which the subject doesn't know whether he or she is receiving a treatment or placebo

range

x max - x min

IQR

inter-quartile range. Q3-Q1

Standard deviation

A statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.

histogram

bar graph