Stats: Overview of Inferential Stats

hypothetico-deductive method

positivist research design based on the development and systematic testing of hypotheses

grounded theory

an inductive method of generating theory from already collected data by creating categories in which to place data and then looking for relationships among categories

population mean

μ

sample mean

x̅ or M

population standard deviation

σ

sample standard deviation

SD

population variance

σ²

sample variance

s²

sampling distribution

a distribution of statistics obtained by selecting all the possible samples of a specific size from a population

Central Limit Theorem

The theory that, as sample size increases, the distribution of sample means approaches a normal distribution.

standard error of the mean

the standard deviation of a sampling distribution. the error in samples' means compared to population mean

population standard deviation (σ)/ square root of sample size (n)

what is the formula to calculate standard error of the mean?

pooled error

type of standard error (of mean) used when there is homogeneity of variance (variance is equal)

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

reject, retain

if your data shows differences you __ the null and __ the alternative hypothesis

one-tailed alternative hypothesis

a type of alternative hypothesis in which only one direction of an effect or relationship is predicted

two-tailed alternative hypothesis

a type of alternative hypothesis in which it is predicted that the two groups being compared will differ, but does not predict the direction of that difference

rejection region

area of a sampling distribution that corresponds to test statistic values that lead to rejection of the null hypothesis. determined by the alpha

retention region

area of the sampling distribution that lies in central portion and consists of the values that are likely to occur as a consequence of sampling error only

rejection region, retention region

if the alpha is 0.05 then 5% of the sampling distribution represents the... and 95% of the sampling distribution represents the...

alpha

level of significance

statistically significant

if the sample value lies in the rejection region, the results are said to be...

signifiance

shows if an effect exists

split in half

when a two-tailed test is used, the percent of the sampling distribution in the rejection region (determined by alpha) is ___

p value

The probability level which forms basis for deciding if results are statistically significant (not due to chance). if this value ≤ α: The result is statistically significant, and the null hypothesis is rejected.

type I error

Rejecting null hypothesis when it is true (false positive)

type II error

failing to reject a false null hypothesis (false negative)

alpha

the probability of type I error is...

beta

the probability of type II error is...

power

likelihood of detecting the effect (most directly associated with the chance of finding significance)

inverse (as probability of one increases, the other decreases)

there is a ___ relationship between type I and type II errors

statistical power

when a statistical test enables you to reject a false null hypothesis, the test has ___.

1 - beta

Power =

increase alpha, increase sample size, use one-tailed test, use a parametric test, minimize random error

how do you increase power?
increase __ and __
use a ___ and a ____
minimize ___

1-alpha

type II error, beta

type I error, alpha

power, 1-beta

true accept:

false accept:

false reject:

true reject:

sample size

using a small ___ makes it easy to find significant differences (that aren't there)

statistical nonsignificance, low power

it is least informative to have ___ significance under ___ power