Stats Vocabulary

Aleatory Uncertanty

depends on random chance (ex. coin flips, poker hands, etc.)

Epistemic Uncertainty

Results from lack of knowledge (Ex. sea rise due to climate change)

data

evidence; information gathered from observations

Index

the total number of data

Mean

the average of a data set

Median

the middle score in a distribution; half the scores are above it and half are below it

Mode

The value that occurs most frequently in a given data set.

Expected Value

the probability-weighted average of all possible values in a random variable

Variance

the square of the standard deviation

Standard Deviation

a measure of variability that describes an average distance of every score from the mean

Coefficient of Varriance

- known as relative standard deviation, is a statistical metric that measures the relative dispersion of data points around their mean - (Mean/SD)*100

Probability

- The classic definition of probability is based on frequency

• Probability that A will occur where A is an event that can happen

k ways out of a total of n possible, equally likely ways

• Limitations: Both k and n must be finite, Both k and n must be countable

P(a)=k/n

Conditional Probability

the probability that one event happens given that another event is already known to have happened

Discrete Random Variable

- a variable that takes on a finite or countably infinite number of distinct, separate numerical values as the result of a chance process

- things you can count

continous random variable

- Has an infinite number of possible values that can be represented by an interval on the number line

- things that can take any value in a range

Measure of Skewness

- how skewed to the left or right something is from the normal distribution

Kurtosis

Measure of the fatness of the tails of a probability distribution relative to that of a normal distribution. Indicates likelihood of extreme outcomes.

Population

the complete set of all individuals, items, events, or data points that share a common characteristic

Sample

a subset of the population

Level of Significance

the proportion in the tails of the distribution that is outside the confidence interval

p-value

a number that measures how likely you are to get your observed results if the null hypothesis is true (p must be less than alpha)

Type 1 Error

Rejecting null hypothesis when it is true

Type 2 Error

failing to reject a false null hypothesis

Standard Error of the Mean

measures how far a sample mean is likely to be from the true population mean

First Step of Hypothesis Testing

State the null hypothesis

Second Step of Hypothesis Testing

state the alternative hypothesis

Third Step of Hypothesis Testing

choose the level of significance

Fourth Step of Hypothesis Testing

choose the sample size

Fifth Step of Hypothesis Testing

determine the appropriate statistical technique and corresponding test statistic to use

(T-test if n = 30 or less)

Sixth Step of Hypothesis Testing

set up the critical values that divide the rejection and nonrejection regions

Seventh Step of Hypothesis Testing

collects the data and compute that sample value of the appropriate test statistic

Eighth Step of Hypothesis Testing

determine whether the test statistic has fallen into the rejection region or the nonrejection region

Ninth Step of Hypothesis Testing

make the statistical decision (reject or dont reject null)

Tenth Step of Hypothesis Testing

express the statistical decision in words

Null Hypothesis

the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

Alternative Hypothesis

The hypothesis that states there is a difference between two or more sets of data.

Test Statistic

a statistic whose value helps determine whether a null hypothesis should be rejected

Critical Statistic

The standard score associated with a given degree of confidence or level of significance