18 terms

Significance Test

A formal procedure for using observed data to decide between two competing claimes

Null Hypothessis

Claim we weigh evidence against in a significance test

Alternative Hypthesis

The claim that we are trying to find evidence for in a significance test

One-Sided

It states that a parameter is larger than the null hypothesis value or states that the parameter is smaller than the null value

Two-Sided

It states that the parameter is different from the null hypothesis value (it could be either larger or smaller)

P-Values

The probability, computed assuming the null hypothesis is true, that the statistic would take a value as extreme as or more extreme than the one actually observed, in the direction specified by the alternative hypothesis

Reject Null Hypthesis

If the observed result is too unlikely to occur just by chance when the null hypothesis is true, we can reject the null hypothesis and say that there is convincing evidence for alternative hypthesis

Fail to Reject Null Hypothesis

If the observed result is not very unlikely to occur when the null hypothesis is true, we should fail to reject the null hypothesis and say that we do not have convincing evidence for the alternative hypothesis

Statistically Significant at the Level (alpha)

If the p-value is smaller than alpha, we say that the results of a study are ... . In that case, we reject the null hypothesis and conclude that there is convincing evidence in favor of the alternative hypothesis

Type I Error

If we reject the null hypothesis when the null hypothesis is true

Type II Error

If we fail to reject the null hypothesis when the alternative hypothesis is true

Test Statistic

Measures how far a sample statistic diverges from what we would expect if the null hypothesis were true, in standardized units. That is

test statistic = statistic - parameter/standard deviation of statistic

test statistic = statistic - parameter/standard deviation of statistic

Significance Test - four step process

STATE: what hypotheses do you want to test, and at what significance level?

PLAN: choose the appropriate inference method. Check conditions.

DO: if the conditions are met, perform calculations

-compute the test statistic

-find the p-value

CONCLUDE: make a decision about the hypotheses in the context of the problem

PLAN: choose the appropriate inference method. Check conditions.

DO: if the conditions are met, perform calculations

-compute the test statistic

-find the p-value

CONCLUDE: make a decision about the hypotheses in the context of the problem

One-sample z test for a proportion

Suppose the conditions are met. To test the hypothesis null hypothesis:P=Po, compute the z statistic (see image for formula)

Find the p-value by calculating the probability of getting a z statistic this large or larger in the direction specified by the alternative hypothesis Ha:

Ha:p>p0

Ha:p<p0

Ha:p cannot equal p0

Find the p-value by calculating the probability of getting a z statistic this large or larger in the direction specified by the alternative hypothesis Ha:

Ha:p>p0

Ha:p<p0

Ha:p cannot equal p0

Power

The _________________ of a test against a specific alternative is the probability that the test will reject the null hypothesis at a chosen significance level alpha when the specified alternative value of the parameter is true

One-sample t test

Suppose that the random 10%, and normal/large sample conditions are met. To test the hypothesis null hypothesis = mean(0), compute the ...(use formula in image) Find the p-value by calculating the probability of getting a t statistic this large or larger in the direction specified by the alternative hypothesis in a t distribution with df=n-1

Paired Data

Study designs that involve making two observations on the same individual or one observation on each of two similar individuals result in ...

Paired t procedures

When paired data result from measuring the same quantitative variable twice, we can make comparisons by analyzing the differences in each pair. If the conditions for inference are met, we can use one-sample t procedures to perform inference about the mean difference mean(d). These methods are sometimes called pared t procedures