Statistics Chapter 7
increasing
________________ the sample size decreases standard error thereby increasing power
decreasing
___________________ beta error increases power
level of significance
a criterion of judgment upon which a decision is made regarding the value stated in a null hypothesis. the criterion is based on the probability of obtaining a statistic measured in a sample if the value stated in the null hypothesis was true.
critical value
a cutoff value that defined the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true.
value
a hypothesis is often a statement about the _______________ for a parameter in a population
test statistic
a mathematical formula that identifies how far or how many standard deviations a sample outcome is from the value states in a null hypothesis. it allows researchers to determine the likelihood of obtaining sample outcomes if the null hypothesis were true
Cohen's d
a measure of effect size in terms of the number of standard deviations that mean scores shifted above or below the population mean stated by the null hypothesis
hypothesis testing
a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample
null hypothesis
a statement about a population parameter such as the population mean that is assumed to be true
hypothesis
a statement or proposed explanation for an observation, a phenomenon, or a scientific problem that can be tested using the research method
alternative hypothesis
a statement that directly contradicts a null hypothesis by stating the actual value of a population parameter is than, greater than, or not equal to the value stated in the null hypothesis
effect size
a statistical measure of the size of an effect in a population, which allows researchers to describe how far scores shifted in the population, or the percent of variance that can be explained by a given variable
one sample z test
a statistical procedure used to test hypotheses concerning the mean in a single population with a known variance
type III error
a type of error possible with one-tailed tests in which a decision would have been to reject the null hypothesis, but the researcher decides to retain the null hypothesis because the rejection region was located at the wrong tail
z statistic
an inferential statistic used to determine the number of standard deviations in a standard normal distribution that a sample mean deviates from the population mean stated in the null hypothesis
increases
as effect size ________________ power increases
reject
effect size is only calculated when we _____________ the null hypothesis
stating level of significance
how do researchers control for type I error?
one tailed test
hypothesis tests in which the alternative hypothesis is stated as greater than or less than a value stated in the null hypothesis
two-tailed tests
hypothesis tests in which the alternative hypothesis is stated as not equal to a value stated in the null hypothesis. the researcher is interested in any alternative to the null hypothesis
0.8
in a large effect size d is greater than __________
0.2, 0.8
in a medium effect size d is greater than _________ but less than __________
0.2
in a small effect size d is less than __________
control
researchers directly ___________ for the probability of committing a type I error
beyond
sample means obtained _____________ the critical value will result in a decision to reject the null hypothesis
Cohen's effect size conventions
standard rules for identifying small, medium, and large effects based on typical findings in behavioral research
larger
the _____________ the value of the d the larger the effect in the population
larger
the ______________ the difference of discrepancy between the sample mean and population mean, the less likely it will be that the value of the population mean we hypothesized is correct
larger
the _______________ the rejection region, the greater the likelihood of rejecting the null hypothesis, and the greater power will be
null result
the correct decision to retain a true null hypothesis
effect
the difference between a sample mean and a population mean stated in the null hypothesis
1 minus alpha
the formula for retaining a true null hypothesis
wrong
the key reason we are testing the null hypothesis is because we think it is _____________
likely
the level of significance in hypothesis testing is the criterion we use to decide whether the value stated in the null hypothesis is ___________ to be true
alpha level
the level of significance of criterion for a hypothesis test. it is the largest probability of committing a type I error that we will allow and still decide to reject the null hypothesis
possibilities
the null and alternative hypotheses must encompass all ___________________ of the population mean
power
the one tailed test is associated with greater _______________; it makes it easier to reject the null hypothesis
level of significance
the p value is compared to the ____________________
p value
the probability of obtaining a sample outcome, given that the value stated in the null hypothesis is true
power
the probability of rejecting a false null hypothesis. specifically, it is the probability that a randomly selected sample will show that the null hypothesis is false when the null hypothesis is indeed false
type I error
the probability of rejecting a null hypothesis that is actually true
type II error
the probability of retaining a null hypothesis that is actually false
rejection region
the region beyond a critical value in a hypothesis test
retain the null
the sample mean is associated with a high probability of occurrence when the null hypothesis is true
reject the null
the sample mean is associated with a low probability of occurrence when the null hypothesis is true
conservative
the two tailed test is more ______________; it makes it difficult to reject the null hypothesis
obtained value
the value of a test statistic. this value is compared to the critical values of a hypothesis test to make a decision
less than 5%
we can state an alternative hypothesis to locate the probability of obtaining sample means with __________ chance of being selected if the value stated in the null hypothesis is true
equal
we expect that if the null hypothesis is true then a random sample selected from a given population will have a sample mean ___________ to the value stated in the null hypothesis
decision
we use the test statistic to make a _____________ regarding the null hypothesis
5%
what is the criterion usually used in behavioral statistics?
.80
what is the typical standard power?
exceeds
when an obtained value _____________ a critical value, we decide to reject the null hypothesis
reach
when the null hypothesis is rejected we __________ significance
fail
when the null hypothesis is retained we ___________ to reach significance
reject
when the probability of obtaining a sample mean would be less than 5% if the null hypothesis were true, then we _____________ the null hypothesis
zero
Cohen's d is _____________ when there is no difference between 2 means
significance
describes a decision made concerning a value in the null hypothesis