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Hypothesis test
A ___________ is a statistical method that uses sample data to evaluate a hypothesis about a population.
Null hypothesis (H0)
The ______________________ states that in the general population there is no change, no difference, or no relationship. In the context of an experiment, H0 predicts that the independent variable (treatment) has no effect on the dependent variable (scores) for the population.
Alternative hypothesis (H1)
The _____________ states that there is a change, a difference, or a relationship for the general population. In the context of an experiment, H1 predicts that the independent variable (treatment) does have an effect on the dependent variable
1) Sample means that are likely to be obtained if H0 is true; that is, sample means that are close to the null hypothesis
2) Sample means that are very unlikely to be obtained if H0 is true; that is sample means that are very different from the null hypothesis
The distribution of sample means is then divided into two sections, these sections are?
Alpha level, or the level of significance
The______________________, or the_________________ is a probability value that is used to define the concept of "very unlikely" in a hypothesis test.
Critical region
The ______________ is composed of the extreme sample values that are very unlikely (as defined by the alpha level) to be obtained if the null hypothesis is true. The boundaries for the _____________ are determined by the alpha level. If sample data fall in the ______, the null hypothesis is rejected.
False. A larger alpha means that the boundaries for the critical region move closer to the center of the distribution.
If the alpha level is increased from a = 0.01 to a = 0.05, then the boundaries for the critical region move farther away from the center of the distribution. True or false?
1) The sample data are located in the critical region. We conclude that the sample is not consistent with H0 and our decision is to reject the null hypothesis
2) The second possibility is that the sample data are not in the critical region. In this case, the sample mean is reasonably close to the population mean specified in the null hypothesis (in the center of the distribution). Our conclusion is to fail to reject the null hypothesis. This conclusion means that the treatment does not appear to have an effect
In the final step of the hypothesis test, the researcher uses the z-score value obtained in step 3 to make a decision about the null hypothesis according to the criteria established in step 2. There are two possible outcomes:
True. A z-score near zero indicates that the data support the null hypothesis.
A small value (near zero) for the z-score statistic is evidence that the sample data are consistent with the null hypothesis. True or false?
True. A z-score value in the critical region means that the sample is not consistent with the null hypothesis.
A z-score value in the critical region means that you should reject the null hypothesis. True or false?
Type 1 error
A ___________ occurs when a researcher rejects a null hypothesis that is actually true. In a typical research situation, a __________________ means that the researcher concludes that a treatment does have an effect when, in fact, it has no effect
Type 1 errors lead to false reports in the scientific literature. Other researchers may try to build theories or develop other experiments based on the false results.
What are the issues with Type 1 error?
Alpha level
The ______________ for a hypothesis test is the probability that the test will lead to a Type 1 error if the null hypothesis is true. That is, the ________ determines the probability of obtaining sample data in the critical region even though there is no treatment effect.
Type 2 error
Occurs when a researcher fails to reject a null hypothesis that is really false. In a typical research situation, a _________________means that the hypothesis test has failed to detect a real treatment effect
A Type 2 error is likely to occur when the treatment effect is very small. In this case, a research study is more likely to fail to detect the effect.
Under what circumstances is a Type 2 error likely to occur?
False. With a = 0.01, the boundaries for the critical region move farther out into the tails of the distribution. It is possible that a sample mean could be beyond the 0.05 boundary but not beyond the 0.01 boundary
If a sample mean is in the critical region with a = 0.05, it would still (always) be in the critical region if alpha were changed to a =0.01. True or false?
True. With a = 0.01, the boundaries for the critical region are farther out into the tails of the distribution than for a = 0.05. If a sample mean is beyond the 0.01 boundary it is definitely beyond the 0.05 boundary.
If a sample mean is in the critical region with a = 0.01, it would still (always) be in the critical region if alpha were changed to a =0.05. True or false?
Significant or statistically significant
A result is said to be _________________ or _______________, if it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis. Thus, a treatment has a _________ effect if the decision from the hypothesis test is to reject H0.
1) Random sampling
2) Independent observations
3) The value of the standard deviation is unchanged by the treatment
4) Normal sampling distribution
The assumptions for hypothesis tests with z-scores are?
Test statistic
Indicates that the sample data are converted into a single, specific statistic that is used to test the hypotheses
True
In a research report, the term significant is used when the null hypothesis is rejected. True or false?
True. The probability is greater than 0.05, which means there is a reasonable likelihood that the result occurred without any treatment effect.
In a research report, the result of a hypothesis test include the phrase "z = 1.63, p > 0.05." This means that the test failed to reject the null hypothesis. True or false?
True. A larger sample produces a smaller standard error, which leads to a larger z-score.
If other factors are held constant, increasing the size of the sample increases the likelihood of rejecting the null hypothesis. True or false?
Standard deviation = 2. A smaller standard deviation produces a smaller standard error, which leads to a larger z-score
If other scores are held constant, are you more likely to reject the null hypothesis with a standard deviation of 2 or with a standard deviation of 10?
Directional hypothesis test or a one-tailed test
In a ___________________________ or a _______________ the statistical hypotheses (H0 and H1) specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.
No strong directional expectation or when there are two competing predictions
In general, two-tailed tests should be used in research situations when there is?
The directional prediction is made before the research is conducted and there is a strong justification for making the directional prediction
One-tailed tests should be used only in situations in which?
False. Because a two-tailed test requires a larger mean difference, it is possible for a sample to be significant for a one-tailed test but not for a two-tailed test
If a sample is sufficient to reject the null hypothesis for a one-tailed test, then the same sample would also reject H0 for a two-tailed test. True or false?
Effect size
A measure of ____________ is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used.
Cohen's d = mean difference (M treatment - Mu no treatment)/ standard deviation
One of the simplest and most direct methods for measuring effect size is?
Small effect (mean difference around 0.2 standard deviation)
d = 0.2 means what?
Medium effect (mean difference around 0.5 standard deviation)
d = 0.5 means what?
Large effect (mean difference around 0.8 standard deviation)
d = 0.8 means what?
Power
The ________________ of a statistical test is the probability that the test will correctly reject a false null hypothesis. That is, _______ is the probability that the test will identify a treatment effect if one really exists.
