hypothesis testing with inferential statistics

power can be increased by

1. increasing the a-level 2. increasing the sample size 3. increasing the effect size

questions about parameter estimation means

describing a population in terms of its characteristics

inferential statistics test only the _______ hypothesis

null

Type I error

rejecting the null hypothesis when it is true

typical a-levels

set by researchers = .10, .05, and .01

effect size

the impact made by the independent variable on the dependent variable

β- level (beta level)

the probability of making a Type II error - given a percentage level - ie. in .20, or 20% of the time, - decreases as the power of the study increases

power

the probability that the null hypothesis will be correctly accepted by the test. It is denoted by β

a(alpha)-level

the significance level - Specifies the risk of rejecting the null hypothesis when it is true.

the one-sample z-test is used

to assess whether a sample mean is significantly different from a population mean

point estimation

when an estimation of the population parameter is given as a single member - example: the sample mean, median, variance & standard deviation

Ways to decrease the likelihood of a type II error

- be willing to risk 10/100 rather than just 5/100 that you are wrong - increase sample size - decrease sources of extraneous variation

6 step process for testing hypothesis

1. state the hypothesis (null & alternative 2. define significance level (a-level) for the study, choose the appropriate test statistic, determine the critical region, & state the rejection rule 3. make sure that the data meet the necessary assumptions to compute the test statistic 4. compute the parameters that are being compared by the test statistic (e.g. means & proportions). 5. compute the test statistic, and obtain the p-value of the computed statistic 6. determine whether the result is statistically significant and clearly state a conclusion

power is defined by

1. the a-level 2. the sample size 3. the effect size

hypothesis testing involves

1st constructing a hypothesis about the relationship of 2 or more variables and then testing that hypothesis with the appropriate test

non-directional hypothesis

A specific statement that a difference exists between groups or a relationship exists between variables, with no specification of the direction of the difference or relationship - does not say whether it will be a positive or negative relationship

directional hypothesis

States a relationship between the variables being studied or a difference between experimental treatments that the researcher expects to emerge - states whether it will be a positive or negative relationship

significance level

The highest possible p-value that would reject H0 and declare the results statistically significant.

4 quantities used in statistical inference

a-level power (1 - β) sample size (n) population effect size (y)

________ the null hypothesis means that researchers believe that the variables are not significantly associated

accepting

Type II error

accepting the null hypothesis when it is false

when is the p-value defined

by the researchers - before any statistical tests are conducted

interval estimation

consist of more than one point, consists of a range of values within which the population parameter is thought to be

error of inference

drawing the wrong conclusion related to a study = either a Type I or Type II error

p-value (probability value)

in a statistical hypothesis test, the likelihood of getting the value of the statistic by chance alone - the actual probability of getting the obtained results or results even more extreme - the smaller the p-value the more statistically significant (ie, the less likely the result is due to chance)

construction of a confidence interval (CI) and the upper and lower limits of a range of values, called confidence limits is a common type of

interval estimation

2 forms of parameter estimation

point estimation interval estimation

statistical inference helps to answer 2 types of questions . . . . . . . .

questions about parameter estimation and questions about hypothesis testing

__________ the null hypothesis means that researchers believe that the variables are significantly associated with each other

rejecting

null hypothesis

states there is no difference or relationship btwn the variables of interest

questions about hypothesis testing means

testing relationships btwn 2 or more variables

the one-sample z-test assumes

that the data from the sample are normally distributed and that both the population mean (µ) and the population standard deviation (σ ) are known

power of a study

the ability to detect statistically significant differences 1 - β

alternative hypothesis also known as

the acting or research hypothesis

what test is used instead of the one-sample z-test if the population standard deviation is not known

the one sample t-test

In the broadest sense, the value of a computed statistic is considered significant . . . .

when it is much different from what is expected by chance alone