data on which both sides are fairly the same shape and size. "Bell Curve"
value of a population (typically unknown)
a calculated value about a population from a sample(s).
the middle point of the data (50th percentile) when the data is in numerical order.
allows statisticians to distinguish between usual and unusual occurrences.
measures the typical or average deviation of observations from the mean
mean is a larger value than the median.
is a standardized score. This tells you how many standard deviations from the mean an observation is.
is a bell shaped and symmetrical curve. As σ increases the curve flattens. As σ decreases the curve thins.
A and B have no intersection. They cannot happen at the same time.
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.
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).
LRSL cannot be used to find values outside of the range of the original data.
are points that if removed significantly change the LSRL.
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.
divide the population into homogeneous groups then SRS from every group. [Observational studies]
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.
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.
ask people who are easy, friendly, or comfortable asking.
some group(s) are left out of the selection process.
someone cannot or does not want to be contacted or participate.
a group used to compare the factor to for effectiveness - does NOT have to be placebo
a method used so that the subjects are unaware of the treatment (who gets a placebo or the real treatment).
neither the subjects nor the evaluators know which treatment is being given.
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]
units are separated based on a KNOWN factor. Then randomly assign treatments in each group -reduces variation
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
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!
reduces bias by spreading extraneous variables to all groups in the experiment. MUST have in EVERY experiment
Trials have two outcomes; Trials are independent; and most importantly, the number of trials are fixed!
two mutually exclusive outcomes, each trial is independent, probability (p) of success is the same for all trials. (NOT a fixed number of trials)
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.
used to estimate the unknown population parameter by providing a range of possible parameters
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.
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!]
is used to test counts of categorical data.
is used when your test involves sample means/averages
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
In repeated sampling, ______% of all the possible intervals that can be constructed by this method will give us a correct estimate.
Conclusion "reject the null" and "there is enough evidence to support the HA"
Conclusion "fail to reject"
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.
Use random number generator to select the first person. Then select every "third" or "fourth" or "fifth" etc...after that
is a way to model random events, such that simulated outcomes closely match real-world outcomes
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
is an explanatory variable manipulated by the experimenter. Combinations of these help create the number of treatments
A graphical display that represents a frequency distribution by means of rectangles whose widths represent class intervals or "bins"