61 terms

TheMathHawkTEACHER

Symmetric

data on which both sides are fairly the same shape and size. "Bell Curve"

Parameter

value of a population (typically unknown)

Statistic

a calculated value about a population from a sample(s).

Median

the middle point of the data (50th percentile) when the data is in numerical order.

Variability

allows statisticians to distinguish between usual and unusual occurrences.

Standard Deviation

measures the typical or average deviation of observations from the mean

Skewed Right

mean is a larger value than the median.

Z-score/T-score

is a standardized score. This tells you how many standard deviations from the mean an observation is.

Normal Model

is a bell shaped and symmetrical curve.

As σ increases the curve flattens.

As σ decreases the curve thins.

As σ increases the curve flattens.

As σ decreases the curve thins.

Mutually Exclusive

A and B have no intersection. They cannot happen at the same time.

Independent

if knowing one event does not change the outcome of another.

Law of Large Numbers

as an experiment is repeated the experimental probability gets closer and closer to the true (theoretical) probability.

Correlation Coefficient (r)

is a quantitative assessment of the strength and direction of a linear relationship.

Least Squares Regression Line (LSRL)

is a line of mathematical best fit. Minimizes the deviations

(residuals) from the line. Used with bivariate data.

(residuals) from the line. Used with bivariate data.

Residual (error)

is vertical difference of a point from the LSRL. They should all add to zero. Is the difference between the observed and expected value.

Coefficient of Determination (r-squared)

gives the proportion of variation in y (response) that is explained by the relationship of (x, y).

Extrapolation

LRSL cannot be used to find values outside of the range of the original data.

Influential Points

are points that if removed significantly change the LSRL.

Census

a complete count of the population. Disadvantages of this: Not accurate, Expensive, Impossible to do

Simple Random Sample

one chooses so that each unit has an equal chance and every set of units has an equal chance of being selected.

Stratified Sampling

divide the population into homogeneous groups then SRS from every group. [Observational studies]

Cluster Sampling

Usually can be based on location. Select a random location and sample ALL at that location. Divide the population into heterogeneous groups and SRS a certain amount of groups. Take all members/things in that group.

Bias

favors a certain outcome, has to do with center of sampling distributions - if centered over true parameter then considered unbiased

Voluntary Response Bias

people choose themselves to participate.

Convenience Sampling

ask people who are easy, friendly, or comfortable asking.

Undercoverage

some group(s) are left out of the selection process.

Nonresponse Bias

someone cannot or does not want to be contacted or participate.

Control Group

a group used to compare the factor to for effectiveness - does NOT have to be placebo

Single Blind

a method used so that the subjects are unaware of the treatment (who gets a placebo or the real treatment).

Double Blind

neither the subjects nor the evaluators know which treatment is being given.

Replication

A MUST for EVERY experimental design. Uses many subjects to quantify the natural variation in the response.

Completely Randomized Design

all units are allocated to all of the treatments randomly [Experiment]

Randomized Block

units are separated based on a KNOWN factor. Then randomly assign treatments in each group -reduces variation

Matched-Pair Design

Once a pair receives a certain treatment, then the other pair automatically receives the second treatment.

OR individuals do both treatments in random order (before/after or pretest/post-test)

Assignment is dependent

OR individuals do both treatments in random order (before/after or pretest/post-test)

Assignment is dependent

Confounding Variables

are where the effect of the variable on the response cannot be separated from the effects of the factor being tested - happens in observational studies - when you use random assignment to treatments you do NOT have this!

Randomization

reduces bias by spreading extraneous variables to all groups in the experiment. MUST have in EVERY experiment

Binomial Probability

Trials have two outcomes; Trials are independent; and most importantly, the number of trials are fixed!

Geometric Probability

two mutually exclusive outcomes, each trial is independent, probability (p) of success is the same for all trials. (NOT a fixed number of trials)

Sampling Distribution

is the distribution of all possible values of all possible samples. Use normalcdf to calculate probabilities

Standard Error (SE)

estimate of the standard deviation of the statistic

Central Limit Theorem

when n is sufficiently large (n > 30) the sampLING distribution is approximately normal even if the population distribution is not normal.

Confidence Interval

used to estimate the unknown population parameter by providing a range of possible parameters

Hypothesis Test

tells us if a value occurs by random chance or not. If it is unlikely to occur by random chance then it is statistically significant.

P-Value

assuming the null is true, the probability of obtaining the observed result or more extreme

Level of Significance

is the amount of evidence necessary before rejecting the null hypothesis. [Alpha - Chances of Type I error occurring]

Type I Error

is when one rejects H0 when H0 is actually true.

Type II Error

is when you fail to reject H0, and H0 is actually false.

Power (of the test)

is the probability that the test will reject the null hypothesis when the null hypothesis is false assuming the null is true. [The chances you make the right decision!]

Chi-Square

is used to test counts of categorical data.

T-Test

is used when your test involves sample means/averages

Z-Test

is used when your test involves proportions/percents. (3 out of 100)

Goodness of Fit

is for univariate categorical data from a single sample. Does the observed count "fit" what we expect. Must use list to perform

Confidence level

In repeated sampling, ______% of all the possible intervals that can be constructed by this method will give us a correct estimate.

Low P-Value

Conclusion "reject the null" and "there is enough evidence to support the HA"

High P-Value

Conclusion "fail to reject"

Lurking Variable

is a variable that is not included as an explanatory or response variable in the analysis but can affect the interpretation of relationships between variables. It can falsely identify a strong relationship between variables or it can hide the true relationship.

Systematic Sampling

Use random number generator to select the first person. Then select every "third" or "fourth" or "fifth" etc...after that

Simulation

is a way to model random events, such that simulated outcomes closely match real-world outcomes

Placebo effect

A remarkable phenomenon in which a fake treatment, can sometimes improve a patient's condition simply because the person has the expectation that it will be helpful

Factors

is an explanatory variable manipulated by the experimenter. Combinations of these help create the number of treatments

Histogram

A graphical display that represents a frequency distribution by means of rectangles whose widths represent class intervals or "bins"