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