The following bivariate data set contains an outlier. x y 62.1 -2396.1 74.2 1036.9 71.5 48.4 58 -1102.2 73.3 -1245.4 64.3 786.6 47.7 1545.7 85.2 -1397 72.4 884 90.2 -197.3 64.3 1609.4 92.4 -436.4 59.8 -72.8 67.2 307.9 226.5 -713.1 What is the correlation coefficient with the outlier? rw = What is the correlation coefficient without the outlier? rwo = Would inclusion of the outlier change the evidence for or against a significant linear correlation? Yes. Including the outlier changes the evidence regarding a linear correlation. No. Including the outlier does not change the evidence regarding a linear correlation. Question for thought: Would you always draw the same conclusion with the addition of an outlier?
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.
The following bivariate data set contains an outlier.
| x | y |
|---|---|
| 62.1 | -2396.1 |
| 74.2 | 1036.9 |
| 71.5 | 48.4 |
| 58 | -1102.2 |
| 73.3 | -1245.4 |
| 64.3 | 786.6 |
| 47.7 | 1545.7 |
| 85.2 | -1397 |
| 72.4 | 884 |
| 90.2 | -197.3 |
| 64.3 | 1609.4 |
| 92.4 | -436.4 |
| 59.8 | -72.8 |
| 67.2 | 307.9 |
| 226.5 | -713.1 |
What is the
rw =
What is the correlation coefficient without the outlier?
rwo =
Would inclusion of the outlier change the evidence for or against a significant
- Yes. Including the outlier changes the evidence regarding a linear correlation.
- No. Including the outlier does not change the evidence regarding a linear correlation.
Question for thought: Would you always draw the same conclusion with the addition of an outlier?
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