A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT) and performance on an anagram task. Anagrams are words with the letters scrambled. Each subject is given a set of 10 anagrams, and the psychologist records how much time is needed to solve all 10 anagrams and correctly unscramble the letters to make all words. The anagram times and each subject’s SAT score are as follows. Note that two subjects failed to complete all 10 anagrams. Use a Spearman correlation to measure and describe the relationship between SAT and anagram performance. Anagram SAT Subject Time Score 1 104 480 2 195 410 3 50 590 4 93 510 5 failed 420 6 170 460 7 failed 380 8 67 570 9 45 640 10 58 600
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT) and performance on an anagram task. Anagrams are words with the letters scrambled. Each subject is given a set of 10 anagrams, and the psychologist records how much time is needed to solve all 10 anagrams and correctly unscramble the letters to make all words. The anagram times and each subject’s SAT score are as follows. Note that two subjects failed to complete all 10 anagrams. Use a Spearman
Anagram SAT
Subject Time Score
1 104 480
2 195 410
3 50 590
4 93 510
5 failed 420
6 170 460
7 failed 380
8 67 570
9 45 640
10 58 600
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