Statistical Inference Terms: Chapter 23 Definitions

inferential statistics

involve a decision-making process that allow us to estimate population characteristics from a sample; two concepts that form the basis for the assumption that the sample represents the population - probability and sampling error

probability

the likelihood that any one event will occur, given all the possible outcomes; signified by "p"; we are assuming no bias and the outcomes are choice-dependent; predictive for what should happen over the long run, not for any one event or trial

sampling error

the tendency for sample values to differ from population values; difference in the sample mean from the population mean; unpredictable and occurs due to chance/randomness; an attempt to estimate the population SD from sample data

increases

As samples size INCREASES/DECREASES, samples become more representative of the population.

decreases

The sample mean approximates the population mean, thus the standard error of the mean INCREASES/DECREASES.

point estimate

a single value obtained by direct calculation from sample data (such as a sample mean) to reflect the population data (such as the population mean)

interval estimate

an interval (range) of sample values within which we believe (or are confident) that the actual population parameter of interest lies

confidence intervals

a range of scores within specific boundaries which should contain the population mean; boundaries are based on the sample mean and its standard error; degree of confidence expressed as a percentage (usually 95%)

sample mean + (1.96)(standard error of mean)

What is the equation used to construct a confidence interval?

true

T/F: Interpretation of confidence intervals - we are 95% confident that the population mean will fall within the +/- CI boundaries.

true

T/F: Interpretation of confidence intervals - 95 of 100 random samples of that size would contain the population mean, and 5 would not.

false

T/F: Interpretation of confidence intervals - 95% of all single events/observation will fall within the +/- CI boundaries.

false

T/F: Interpretation of confidence intervals - we are 95% confident that a single event/observation will fall within the +/- CI boundaries.

false

T/F: Interpretation of confidence intervals - 95% of the time the sample mean will be the population mean.

null hypothesis

hypothesis testing; observed difference occurred by chance and the means are not significantly different; due to the nature of change differences, even in the absence of a real effect, we will most likely NOT have equal means; we can never actually "prove" this; we can "reject" this hypothesis

alternative hypothesis

hypothesis testing; the observed difference occurred due to a real effect; the observed difference is too large to likely be the result of chance; we can "accept" this hypothesis

directional hypothesis

hypothesis testing; under the umbrella of alternative hypothesis; we expect one mean to be larger/smaller than the other

non-directional hypothesis

hypothesis testing; under the umbrella of directional hypothesis; we do not state the expectation that one mean will be larger/smaller than the other

type I error

type of error; mistakenly finding a difference - shows an effect; occurs when we reject the null hypothesis when the null hypothesis is true

type II error

type of error; mistakenly finding no difference - shows no effect; occur when we do not reject the null hypothesis when it is actually false

alpha

For type I error, we set the risk level for this error by setting the level of significance, denoted as?

5% (0.05)

What is the alpha value arbitrarily set to (%)?

p-value

What will we eventually compare to the alpha after the statistical test?

p-value

the probability that are the observed difference occurred due to change; probability of finding a difference (effect) at least as large as the one you observed if the null hypothesis is true; NOT measures of the magnitude of the effect

beta

For type II error, we set the risk level for this error by setting the level of significance, denoted as?

0.20

By convention, beta is often set to?

power

complement of beta --> "1-beta"; the probability that is a test will lead to rejection of the null hypothesis (by attaining statistical significance) if actual differences exist

alpha, variance, sample size, effect size

List the four determinants of statistical power.

alpha

four determinants of statistical power; if you choose to lower this value, the probability of committing type I error goes down but the probability of committing type II error goes up; making the standard to reject the null more rigorous, we make it harder for sample results to meet this standard

variance

four determinants of statistical power; more of this in data leads to reduced power; less increases power

sample size

four determinants of statistical power; as this increases, power does too

effect size

four determinants of statistical power; the stronger the real magnitude of difference, the greater the power

power analysis

purposes: (1) to estimate the sample size in recruiting during the planning of the study, and (2) to determine the probability of type II error (or observed power) with actual (usually non-significant) results

larger

power analysis; the smaller the effect, the SMALLER/LARGER the sample needed.

one-tailed test

critical region/directional tests; to reject the null... - we are only interested in reporting one direction of difference; alpha region all at one side

two-tailed test

critical region/directional tests; to reject the null... - we are interested in reporting either direction; split the alpha magnitude, with have on each end; PREFERRED!!