Chapter 14
Blank 1: larger, bigger, or greater
For most tests if the calculated value is than the critical value, we reject the null hypothesis.
Hypothesis
Formulated for testing (substantiation).
Blank 1: parameter Blank 2: statistics
Hypothesis testing is used to test for a difference between a population and the sample being compared to it.
F
When the data are measured on an interval-ratio scale and we can meet the necessary assumptions, analysis of variance and the test are used.
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When the k related samples have been measured on a nominal scale, the
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When there are k independent samples for which nominal data have been collected, the
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With one-sample tests, we might encounter the question is there a difference between
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With one-sample tests, we might encounter the question: is it reasonable to conclude that a sample is drawn from a population with some specified
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With one-sample tests, we might encounter the question: is there a difference between
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With one-sample tests, we might encounter the question: is there a significant difference between some measures of central tendency and its
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With one-way ANOVA, how do we determine which pairs are not equal? We could calculate a series of t-tests, but they would not be of each other and the resulting Type I error would substantially.
n1-1S12+n2-1S22n1+n2-2
With small sample sizes, normally distributed populations, and the assumption of equal population variances, the pooled variance estimate is calculated as...
Blank 1: significant
With two-way ANOVA, main effects are considered separately only if the interaction is not
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You can also change the Type 1 error and the regions of acceptance by changing the size of the
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value is the criterion that defines the region of rejection from the region of acceptance of the null hypothesis.
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Following a classical statistics approach, we or a hypothesis on the basis of data collected from the sample alone.
Sum of squares betweendegrees of freedombetween
For an ANOVA for k-independent-samples, mean square between is calculated as... Multiple choice question. Sum of squareswithindegrees of freedombetween
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Comparisons after the results are compared require
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A difference has significance if there is good reason to believe the difference does not represent random sampling fluctuations only.
The same participant is measured more than once The grouping factor has more than two levels The data are at least interval Observations or subjects are matched
A k-related-samples test is required when?
Two-tailed test
A nondirectional test.
Type I error
A true null hypothesis is rejected.
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A two-tailed test has rejection region(s).
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ANOVA model, the levels of the factor are established in advance, and the results cannot be generalized to other levels of treatment.
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ANOVA uses a single-factor, fixed-effects model to compare the effects of one treatment or factor on a continuous dependent variable.
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Alpha is the probability of making a Type error.
Hypothesis
An unsubstantiated assumption about the relationship between concepts and constructs.
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Beta is the probability of making a Type
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Beyond a sample size of , the t and standard normal distributions are virtually identical.
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By changing the probability of a Type I error, you move critical values either closer to or farther away from the
Nominal - McNemar Ordinal- Sign test Interval and Ratio - t-test for paired samples
Categorize these test types by their data requirements.
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If a manager judges that this variation has no real importance, then it is of little significance.
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If the measurement scale is nominal, it is possible to use the
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If the null hypothesis is false, the ratio should be
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If the p value is less than the significance level, the null hypothesis is
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If we a null hypothesis, then we are the alternative hypothesis.
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If we decided in advance that a comparison of specific populations was important, a special class of tests known as could be used after the null was rejected with the F ratio.
Is the measurement scale nominal, ordinal, interval, or ratio? Does the test involve one sample, two samples, or k>2 samples? If two or more samples are involved, are the individual cases independent or related?
In attempting to choose a particular significance test, what questions should the researcher consider initially?
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In testing these hypotheses, researchers adopt this decision rule: Take no corrective action if the analysis shows that one the null hypothesis.
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It is also common for an study to require comparison of more than two independent sample means.
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It is often necessary to measure subjects several times. These repeated measurements are called
1-β
Power of the hypothesis test.
a
Symbol for a Typer I error.
Ha
Symbol used for the alternative hypothesis.
Ho
Symbol used for the null hypothesis.
McNemar
The Cochran Q test extends the
Blank 1: correction Blank 2: continuity
The McNemar test uses a transformation of the χ2 test: χ2=(||A−D||−1)2A+DA-D-12A+D The "minus 1" in the equation is a
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The Z test or t-test is used to determine the statistical significance between a sample distribution mean and a
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The binomial test is appropriate when the population is viewed as only
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The binomial test is particularly useful when the size of the sample is
∑i=1kOi-Ei2Ei
The formula by which the chi-square test is calculated is...
∑Dn
The formula for DD for two-relates-samples is...
∑D2-∑D2nn-1
The formula for SDSD for two-related-samples is...
X1-X2-μ1-μ2 S12n1+s22n2
The formula for the Z test with two-independent-samples is...
DSp/n
The formula for the t-test for two-relates-samples is...
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The p value represents the probability of a Type error that must be assumed if the null hypothesis is rejected.
The true value of the parameter The sample standard deviation The α level Whether a one- or two-tailed test was chosen The sample size
The probability of committing a Type II error depends on which factors?
Hypothesis testing
The process of proving that an assumption about the relationship between two variables is valid.
Blank 1: F
When the data are measured on an interval-ratio scale and we can meet the necessary assumptions, analysis of variance and the test are used.
Blank 1: inappropriate, incorrect, or wrong
The t-test for independent samples would be for a two-related-samples test.
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The two-related-samples tests are used when cases (persons, objects, or events) are closely or the phenomena are measured
2
There are outcomes possible with statistical testing.
Seek to improve both α and β errors simultaneously Accept a bigger α Increase the sample size
There are several ways to reduce a Type II error. Which of the following are one of those ways?
Parametric tests
These are the tests of choice if their assumptions are met.
Parametric tests
These tests have greater efficiency when their use is appropriate.
Inferential statistics
This includes two topics: estimation of population values and testing statistical hypotheses.
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We evaluate the importance of a statistically significant difference by weighing the
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We often use k-independent-samples tests in research when or more samples are involved.
The t distribution has more tail area
What is the difference between the standard normal and t distributions?
Can test two variable interactions jointly
What is the distinct advantage of the two-way ANOVA model?
Two-tailed test
What type of test is shown below? H0: μ=75 H1: μ≠75
One-tailed test
What type of test is shown below? H0: μ≤75 H1: μ>75
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When the data are at least ordinal, the two-way analysis of variance is appropriate.
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determines the size of ratio necessary to reject the null hypothesis for a particular sample
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k>2 related samples using the interval and ratio measurement scales would use the - ANOVA statistical technique.
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n an ANOVA model, each group has its own
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offers another approach to choosing appropriate statistics.
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test is appropriate for data that are collected on an ordinal scale or for interval data that do not meet F-test assumptions, that cannot be transformed, or that for another reason prove to be unsuitable for a parametric test.
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test may be used with either nominal or ordinal data and is especially useful with before-after measurement of the same subjects.e4
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tests are applicable to two-related-samples tests.
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tests are the only ones usable with nominal data.
Nonparametric
tests have fewer and less stringent assumptions.
