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Example of a Correlation Test
Consider a study investigating the correlation between people's calorie estimates and their weight. Since there is no expectation about the direction of the relationship, a two-tailed test is conducted. For a sample of students, Pearson's is computed to be . Using statistical software, the -value is found to be . Because the -value is greater than , the null hypothesis is retained, concluding that there is no statistically significant relationship between the variables. Alternatively, computing the test by hand involves finding the critical value. For degrees of freedom, the critical value is . Since the absolute value of the sample correlation coefficient () is less extreme than the critical value (), this confirms that the -value is greater than , leading to the same conclusion to retain the null hypothesis.
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Research Methods in Psychology - 4th American Edition @ KPU
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Correlation Coefficient as a Test Statistic
What does a hypothesis test of the correlation coefficient specifically assess when evaluating the relationship between quantitative variables using Pearson's r?
Match each term related to a hypothesis test of the correlation coefficient with its specific role in the research process.
A psychologist finds a correlation of r = +.65 between 'number of friends' and 'happiness' in a sample. If the hypothesis test of the correlation coefficient results in a p-value of .07 and the alpha level is set at .05, the psychologist must fail to reject the null hypothesis, even though there is a strong correlation in their sample.
A researcher has calculated a Pearson's in a sample and needs to evaluate if this relationship reflects a true, non-zero correlation in the broader population. Arrange the following steps in the correct logical sequence to justify a conclusion about the population.
When evaluating the relationship between two quantitative variables using Pearson's r, what does the associated hypothesis test specifically assess?
A researcher investigating the link between 'workplace stress' and 'sleep quality' calculates a Pearson’s of -0.40, but the resulting hypothesis test is not statistically significant. Arrange the logical steps in the correct order to analyze why this result prevents a general conclusion about the population.
A researcher conducts a study on 80 students and finds a Pearson's of +0.32 between 'hours of sleep' and 'exam performance.' They perform a hypothesis test to see if this relationship is significant. Match each element of this scenario to its correct role in the hypothesis testing process.
When conducting a hypothesis test of the correlation coefficient, the primary goal is to assess whether a true, non-zero correlation exists within the broader population.
Null Hypothesis for a Correlation Test
Example of a Correlation Test
A researcher finds a Pearson's of in a sample of 15 people but the result is not statistically significant (). The researcher correctly concludes that they cannot claim the variables are related in the broader population because the study lacks sufficient evidence to reject the null hypothesis that the population correlation is _____.
A researcher finds that a Pearson's r of .20 results in a p-value of .02 in one study, but the exact same r of .20 results in a p-value of .45 in a different study. By analyzing the mathematical components of the hypothesis test for the correlation coefficient, it becomes clear that these two studies must have differed in their _____.
Based on the provided text, what is the specific statistical procedure used to evaluate the relationship between quantitative variables using Pearson's , and what does this procedure specifically assess?
Explain how the researcher should proceed using a hypothesis test of the correlation coefficient. What does this test assess regarding the population, and how does its underlying logic connect to other null hypothesis tests?
A psychology student is analyzing the correlation between self-esteem and academic performance (both quantitative variables) in a sample of students using Pearson's . To determine if they can generalize their finding to all students at their university, what specific test must they apply, and what is the null hypothesis testing question they are testing?
Learn After
In the correlation study examining calorie estimates and weight (), what p-value did the statistical software report for Pearson's ?
In the calorie-estimate and weight correlation study, a two-tailed test was chosen because the researcher predicted that weight would be positively associated with calorie estimates.
Match each element from the calorie-estimate and weight correlation hypothesis test to its correct description or role in the statistical decision-making process.
In the calorie-estimate and weight study, analyzing the hand-calculated test results shows that the null hypothesis must be retained because the absolute value of the sample correlation coefficient () is _____ than the critical value ().
Order the steps taken to evaluate the correlation coefficient by hand and determine whether to reject or retain the null hypothesis.
According to the calorie-estimate and weight study, what is the critical value for the hand-calculated correlation test with degrees of freedom?
In the context of the study investigating the correlation between calorie estimates and weight, explain the statistical logic behind why a researcher can use either the software-provided -value or a hand-calculated critical value comparison to make a decision about the null hypothesis. Describe how the sample values from this study are evaluated under both methods.
Based on this new research design, calculate the degrees of freedom for the correlation test. Then, identify whether the psychologist should use a one-tailed or two-tailed test, and state the mathematical decision rule she would use if she conducts the test by hand with a critical value.
In the calorie-estimate and weight study (), Pearson's was calculated as . Analyze why the researcher compared the absolute value of the correlation coefficient () rather than the raw value () to the critical value () when determining significance.