### The Spearman & Pearson Correlation Study, Two Tailed Test – Statistic Quiz

The key terms in these Statistic chapter include Correlation Study, Height And Weight, The Spearman Correlation, Pearson Correlation, Two Tailed Test – Statistic Quiz.

Which of the following values represents a perfect correlation?

**-1,1**

The population of a bacteria colony is measured at 3:00, 3:15, and 3:30. The corresponding population values are 40, 80, and 160. Explain why this does or does not have a linear correlation.

**This does not have a linear form because the population does not increase by the same amount every fifteen minutes.**

A set of n = 25 pairs of X and Y values has a Pearson correlation of r = 0.24. If each of the X values were multiplied by -3, and each Y value is increased by 2, then what is the correlation for the resulting data?

**-24**

Which of the following is not measured and described by a correlation?

**The mean difference of a relationship**

The relationship between age and height in trees is most likely a _____________ correlation.

**positive**

Which of the following is an application of correlations?

**PredictionValidityReliability**

The scatter plot for a set of X and Y values shows the data points clustered in a nearly perfect circle. For these data, what is the most likely value for the Pearon correlation?

**either positive or negative near 0**

What is indicated by a positive value for a correlation?

**increases in X tend to accompanied by increases in Y**

Which of the following are accurate considerations of correlations?

**The value of a correlation can be affected greatly by the range of scores represented in the data.One or two extreme data points can have a dramatic effect on the value of a correlation.**

Which of the following values represents a perfect correlation?

**-1,1**

The population of a bacteria colony is measured at 3:00, 3:15, and 3:30. The corresponding population values are 40, 80, and 160. Explain why this does or does not have a linear correlation.

**This does not have a linear form because the population does not increase by the same amount every fifteen minutes.**

A set of n = 25 pairs of X and Y values has a Pearson correlation of r = 0.24. If each of the X values were multiplied by -3, and each Y value is increased by 2, then what is the correlation for the resulting data?

**-24**

Which of the following is not measured and described by a correlation?

**The mean difference of a relationship**

The relationship between age and height in trees is most likely a _____________ correlation.

**positive**

Suppose the correlation between age and number of hours of sleep per night for adults is -0.70. What proportion (or percent) of the variability in nightly hours of sleep can be explained by the relationship with age?

**49%**

In a correlation study, X = the age of the participant, Y = the average driving speed on the highway, and Z = the average number of accidents per year. What does represent?

**The correlation between age and average speed with yearly accidents held constant**

A researcher is using a regular, two-tailed test with α = .05 to determine whether a non-zero correlation exists in the population. A sample of n = 25 individuals is obtained and produces a correlation of r = 0.21. The null hypothesis states that there is no correlation in the population. What is the t statistic, and what is the conclusion about the null hypothesis?

**The correlation is significant with α = .05 but not with α = .01.**

A researcher evaluating the significance of a Pearson correlation obtains r = 0.78 and is able to conclude that t = 1.34. Unfortunately, the researcher discovered an error in the original calculation. The actual r should have been -0.78. Once this is fixed, what is the actual t statistic?

**T=-1.34**

What can be used to conduct the hypothesis test for the Pearson correlation?

**T-Statistic and F-Ratio**

What is the difference between the Pearson correlation and the Spearman correlation?

**The Spearman correlation is the same as the Pearson correlation, but it is used on data from an ordinal scale.**

What would the scatter plot show for data that produce a Pearson correlation of r = +0.88?

**points clustered close to a line that slopes up to the right**

Which of the following Pearson correlations shows the greatest strength or consistency of relationship?

**-0.90**

Which of the following situations is an example of a dichotomous variable and would therefore suggest the possible use of a point-biserial correlation.

**Whether a computer is running the latest version of an operating system or an earlier version**

Which situation would be appropriate for obtaining a phi-coefficient with a Pearson test?

**Comparing gender with whether or not someone has a PhD**

For a group of graduating college seniors, a researcher records each student’s rank in his/her high school graduating class and the student’s rank in the college graduating class. Which correlation should be used to measure the relationship between these two variables?

**Spearman correlation**

Suppose that the correlation between height and weight for adults is +0.40. What proportion (or percent) of the variability in weight can be explained by the relationship with height (as indicated by r2)?

**16%**

Under what circumstances is the point-biserial correlation used?

**when X consists of regular, numerical scores but Y is dichotomous**

A set of n = 5 pairs of X and Y scores has ΣX = 15, ΣY = 5, and ΣXY = 10. For these data, the value of SP is ____.

**-5**

A college professor reports that students who finish exams early tend to get better grades than students who hold on to exams until the last possible moment. The correlation between exam score and amount of time spent on the exam is an example of a ____.

**negative correlation**

The Spearman & Pearson Correlation Study

The Pearson and the Spearman correlations are both computed for the same set of data. If the Pearson correlation is r = +1.00, then what can you conclude about the Spearman correlation?

**It will be positive and have a value of 1.00**

If the Pearson correlation is calculated for a sample of n = 20 individuals, what value for df should be used to determine whether or not the correlation is significant?

**18**

The effect size for the data from an independent-measures t test can be measured by r2. Which of the following also produces the value for r2?

**Taking the square root of the Pearson correlation**

A set of n = 15 pairs of scores (X and Y values) produces a correlation of r = 0.40. If each of the X values is multiplied by 2 and the correlation is computed for the new scores, what value will be obtained for the new correlation?

**r = 0.40**

A researcher measures IQ and weight for a group of college students. What kind of correlation is likely to be obtained for these two variables?

**a correlation near zero**