Vocab - Unit 4

Sampling Distribution Model

The distribution that shows the behavior of a statistic (value from a sample) with its sampling variability over all possible samples of the same sample size n

Central Limit Theorem

The sampling distribution model of means/proportions is approximately Normal for “large enough” sample size n as long as the observations are independent

Law of Diminishing Returns

The standard deviation of a sampling distribution model decreases by the square root of the sample size… e.g. quadruple the sample size → standard deviation cut in half

Large Enough Sample Condition

A “large enough” sample size is necessary to ensure the CLT “kicks in” (Success/Failure Condition for proportions; n ≥ 30 often sufficient for means if data is not severely skewed

Standard Error of Proportions

An estimate of the unknown standard deviation for sigma sub p-hat for a sampling distribution of proportions using a sample statistic

Confidence Interval

An interval of values found from a sample that has a statistical probability of capturing the true population parameter (which is unknown)

Critical Value

The number of standard errors to move away from the sample statistic in order to determine a confidence interval, denoted as z\* for Normal models and t\* for t-models

Margin of Error

The extent of a confidence interval on either side of the sample statistic (± of a poll, for example)

Hypothesis Test

A statistical procedure that involves comparing a sample statistic to a proposed model in order to infer about the associated population parameter

Null Hypothesis

A baseline hypothesis (H0) that is originally assumed to be true about a population

Alternative Hypothesis

A hypothesis (HA) about a population that a test is trying to provide evidence for in order to reject the null hypothesis

One-Tailed Hypothesis Test

A hypothesis test that is interested in deviations on only one side of the null hypothesis value; involves the sign > or <

Two-Tailed Hypothesis Test

A hypothesis test that is interested in deviations on either side of the null hypothesis value; involved the sign ≠

*p*-Value

The probability that the observed statistic (or a more extreme one) could occur, by chance, if the null hypothesis was true

Significance/Alpha Level

The cutoff *P*-value that determines when to reject the null hypothesis, denoted by the Greek letter alpha (α); the most common levels are 0.10, 0.05, and 0.01

Statistically Significant

If the *P*-value falls below the significance/alpha level, then the test is said to be statistically significant at that level, meaning that there is sufficient evidence to reject the null because the observed difference is too large to believe that it was likely to have occurred naturally

Student’s *t* Model

A family of distributions whose shapes are roughly “bell-shaped” and unimodal/symmetric, but are shorter and wider with fatter tails than Normal models… used when the true population standard deviation for a sampling distribution of means is unknown

Degrees of Freedom

Found by subtracting 1 from the sample size (*df* = *n*-1); defines the specific *t*-distribution to be used as a model, affecting the spread of the curve…. approaches Normal as *df* increases

Standard Error of Means

An estimate of the unknown standard deviation sigma sub x-bar for a sampling distribution of means using a sample statistic s sub x

*t-*Score

Standardized value that identifies how many standard errors a value is from the sampling distribution mean

Paired Data

Observations that are collected in pairs or for which one group is naturally related to the other group, such as before/after treatment

Paired Data Condition

The condition of relationship between the two groups of data that must be met for the use of a paired *t*-test… groups should NOT be independent of each other

Type I Error

Rejecting the null hypothesis when it is in fact true, which has the probability of α (false positive)

Type II Error

Failing to reject the null hypothesis when it is in fact false, which has the probability of β

Power

The probability that a hypothesis test will correctly reject a false null hypothesis; 1-β

Effect Size

The difference between the null hypothesis value (*p*0 or µ0) and the true value (*p* or µ)… how far off from what’s actually true is the null hypothesis? As effect size increases, the likelihood of seeing sufficient evidence to reject the null hypothesis increases; thus, power increases