Stats test 3

*in directional, two-tailed tests:

(H1: >) or(H1: <) -alternative hypothesis is stated as > or < null -interested in specific alternative from null --Upper-tail critical test (H1>H0), level of significance placed in upper tail of distribution --Lower-tail critical test (H1<H0), level of significance placed in lower tail of distribution

*a statistical procedure used to describe the strength and direction of the linear relationship between two factors

correlation

a cutoff value that defines the boundaries beyond which less than 5% of the sample mean can be obtained if the null hypothesis is true*

critical value (appendix B)

*hypothesis tests where the aternative hypothesis is stated as greater than > or less than < a value stated in the null hypothesis

directional tests or one-tailed tests

statistical measure 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

effect size (246)*

when the null hypothesis is retained, we ___

fail to reach significance

*a negative value of r that indicates that the values of the two factors change in different directions, meaning that as the values of one factor increase, values of the second factor decrease

negative correlation -1.0≤r<0

we can compare the value of the z-statistic called the ___ to the ___*

obtained value to the critical values we determined in step 2

the best fitting straight line to a set of data points. a best fitting line is the line that minimizes the distance of all data points that fall from it.

regression line

the z-statistic formula is:*

the sample mean minus the population mean stated in the null hypothesis divided by the standard error of the mean (238)

What type of error do we directly control?

type I error*

What type of error is associated with the decision to reject the null?

type I errors*

___ is the probability of retaining a null hypothesis that is actually false*

type II error or beta (β) error (incorrect decision to retain the null hypothesis

What type of error is associated with the decision to retain the null?

type II errors*

1 vs 2 tailed test: which eliminates possibility of type III error?

2

the test statistic in step 3:

converts the sampling distribution we observe into a standard normal distribution, thereby allowing us to make a decision in step 4

*used to measure the strength and direction of the linear relationship or correlation between two facotrs

correlation coefficient (r) the value of r ranges from -1.0 to +1.0

The likelihood that we reject the null _(increases or decreases)_ the closer the value of a sample mean is to the value stated by the null hypothesis

decreases

increase in sample size ___

decreases standard error, thereby increases power*

a correlation can be used to:

describe the pattern of change in the values (data points) of two factors and determine whether the pattern observed in a sample is also present in the population from which the sample was selected

what influences power which will allow you to reject null*

directionality sample size effect size

___ measures the size of an effect in a population, whereas ___ measures whether an effect exists in a population

effect size (effect in)* hypothesis or significance testing (effect exists)

effect size-size of an effect in a population is ___. it's the ___ that can be explained by a given variable. Most meaningfully reported with ---

effect size-size of an effect in a population is how far scores have shifted in the population. Percent of variance that can be explained by a given variable. Most meaningfully reported with significant effects (decision to reject null)*

in step four we:

make a decision- Use the value of the test statistic to make a decision about the null hypothesis

*hypothesis tests where the alternative hypothesis is stated as not equal to

non directional tests or two-tailed tests

which is more powerful directional or non

non-directional

__ is the value of a test statistic. this value is compared to the critical value(s) of a hypothesis test to make a decision*

obtained value

1 vs 2 tailed test: which is easier to detect and reject H0?

one-tailed but difficult to justify

alpha level is compared to

p value

___ is the probability of obtaining a sample outcome, given that the value stated in the null hypothesis is true.*

p value (range between 0 and 1) (never -)

*a positive value of r that indicates that the values of two factors change in the same direction: as the values of one factor increase, values of the second factor also increase; as the values of one factor decrease, values of the second factor also decrease

positive correlation 0<r≤+1.0 (pg 474)

the ___ in hypothesis testing is 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

power

as effect size increases, ___

power increases*

when the null hypothesis is rejected, we ___*

reach significance

___ describes a decision made concerning a value stated in the null.*

significance or statistical significance

the null hypothesis is a __. We will: ___*

starting point. We will: test whether the value stated in the null is likely to be true

then compute the z-statistic by:

subsituting the values of the sample mean, M; the population mean stated by the null hypothesis, μ; and the standard error (previous slide), σM

___ is a mathematical formula that allows researchers to determine the likelihood of obtaining sample outcomes if the null were true. Used to make a decision regarding the null hypothesis*

test statistic (230)

the p value for obtaining a sample outcome is compared to ___*

the level of significance

in step two, we state:

the level of significance for a test

the likelihood of detecting an effect, called ___, is critical in behavioral research because it _______

the likelihood of detecting an effect, called power, is critical in behavioral research because it lets the researcher know the probability that a random selected sample will lead to a decision to reject the null, if it's false*

when ___, we decide to reject the null hypothesis; otherwise we retain the null

the obtained value exceeds a critical value

to calculate the z-statistic, first compute:

the standard error (σM)which is the denominator for the statistic standard error is equal to SD divided by the square root of the sample size (238)

goal of hypothesis testing:

to determine the likelihood that a population parameter, such as a mean, is likely to be true

to report results of a z test, report ____. Don't state that we reject or retain the null. Instead, report ___. Not required to report ___, but is recommended

to report results of a z test, report the test statistic, p value, and effect size. Don't state that we reject or retain the null. Instead, report whether a result is significant or insignificant. Not required to report exact p value, but is recommended*

*in non-directional, two-tailed tests

H1:≠ -alternative hypothesis is stated as not equal to the null -interested in any alternative form null hypothesis

The likelihood that we reject the null _(increases or decreases)_ the further the value of a sample mean is to the value stated by the null hypothesis

Increases

in a correlation we treat each factor like:

a dependent variable and measure the relationship between the pair

the probability of obtaining a z-obtained score is given as:

a p value (appendix B)

we can state one of 3alternative hypotheses:

a population mean (μ) is greater than (>), less than (<), or not equal to (≠) the value stated in a null hypothesis

for a single sample, an effect is the difference between:

a simple mean and the population mean stated in the null*

to locate the probability of obtaining a sample mean in a sampling distribution, we must know:*

(1) the population mean and (2) the standard error of the mean. each value is entered in the test statistic formula computed in step 3, thereby allowing us to make a decision in step 4

State the two correct decisions that a researcher can make

-retain a true null -reject a false null

1 vs 2 tailed test: which has greater power

1 tailed

the two decisions a researcher can make:

1. reject the null hypothesis. Sample mean is associated with low probability of occurrence when the null hypothesis is true 2. retain the null hypothesis. Sample mean is associated with a high probability of occurrence when the null hypothesis is true

4 steps of hypothesis testing*

1. state the hypothesis- ID the hypothesis which should be tested 2. set the criteria for a decision- select a criterion upon which we decide the claim being tested is true or not. 3. compute the test scores- select a random sample from the population and measure the sample mean. 4. make a decision- compare what we observe in the sample to what we expect to observe if the claim we are testing is true.

1 vs 2 tailed test: which is more difficult to reject null hypothesis

2

1 vs 2 tailed test: which is more difficult to reject null hypothesis?

2

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

Cohen's d*

we can describe how far scores shifted in the population using a measure of effect size called___ which measures the number of sd an effect shifted above or below the population mean stated by the null hypothesis

Cohen's d*

___ is the level of significance or 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*

alpha (α) level usually α=.05

the ___ establishes where to place the level of significance

alternative hypothesis

___ is a statement that directly contradicts a null hypothesis by stating that the actual value of a population parameter is less than, greater than, or not equal to the value stated in the null hypothesis*

alternative hypothesis (H1)

*In non directional tests or two-tailed tests, the researcher is interested in ___

any alternative from the null hypothesis

the z-statistic converts __ into __. The solution of the formula gives the ___

any sampling distribution into a standard normal distribution. Solution gives the number of SD, z-scores, that a sampe mean falls above or below the population mean stated in the null hypothesis

*used to measure the proportion of variance in one factor that can be explained by known values of a second factor

coefficient of determination (r to the 2nd power)

step 4: to make a decision, we:*

compare the obtained value to the critical value. We reject the null if the obtained value exceeds a critical value.

in step three we:

compute the test statistic

in hypothesis testing, we test some hypothesis by:

determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true

a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample

hypothesis testing

other ways to increase power:

increase effect size, sample size, and alpha level decrease beta, population sd and population standard error*

in hypothesis testing, an effect is insignificant when ___; an effect is significant when ___

insignificant when we retain the null hypothesis; an effect is significant when we reject the null*

___ refers to a criterion of judgement 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 were true*

level of significance (229) usually 5%

*__ stated as ___ is a statement about a population parameter, such as the population mean, that is assumed to be true

null hypothesis (H0) stated as the null

a statistical procedure used to test hypothesis concerning the mean in a single population with a known variance

one-independent sample z-test

the SD of a sampling distribution of sample means*

standard error of the mean (σM)

1 vs 2 tailed test: which is more conservative

two-tailed

in behavioral science, the criterion or level of significance is typically set at ___. When probability of obtaining a sample mean is less than that number if the null hypothesis were true, then we reject the value stated in the null

5%

*a measure used to determine the direction and strength of the linear relationship of two dichotomus factors on a nominal scale of measurement

phi correlation coefficient (r weird circle with sward)

if the null hypothesis is true the __ will equal __

sample mean will equal the population mean on average if the null is true. All other possible values of the sample mean are normally distributed (central limit theorem). The empirical rule tells us that at least 95% of all sample means fall within about 2 SD of the population mean, meaning that there is less than a 5% probability of obtaining a sample mean that is beyond 2 SD from the population mean

standard error of the mean (σM) is the:*

standard error or distance that the sample mean values deviate from the value of the population mean; also stated as the standard error

four decision alternatives regarding the truth and falsity of the decision we make about a null hypothesis

the decision to retain the null hypothesis could be correct the decision to retain the null hypothesis could be incorrect the decision to reject the null hypothesis could be correct the decision to reject the null hypothesis could be incorrect

to locate the probability of obtaining a sample mean from a given population, we use:*

the standard normal distribution. We will locate the z scores in a SND that are the cutoffs or critical values for the sample mean values with less than a 5% probability of occurrence if the value stated in the null hypothesis is true

the test statistic we use depends largely on ___. When we know __ in a single population, we can use the ___

the test statistic we use depends largely on what we know about the population. when we know the mean and sd in a single population, we can use the one-independent sample z-test

most studies in behavioral research are:

two-tailed tests

___ is the probability of rejecting a null hypothesis that is actually true. Researchers directly control the probability of committing this type of error*

type I error

type of error for one-tailed tests. Occurs when we retain null hypothesis because rejection region was located in the wrong tail*

type III errors

*in a nondirectional two tailed test:

we divide the alpha value in half so that an equal proportion of area is placed in the upper and lower tail.

the alternative hypothesis states:*

what we think is wrong about the null hypothesis, which is needed for step 2

__ is an inferential statistic used to determine the number of sd in a SND that a sample mean deviates from the population mean stated in the null hypothesis*

z-statistic

the test statistic for a one-independent sample z-test is called the ___

z-statistic