Question : Four research participants take a test of manual dexterity (high scores mean
better dexterity) and an anxiety test (high scores mean more anxiety). The
scores are as follows.
Person Dexterity Anxiety
1 1 10
2 1 8
3 2 4
4 4 2
the correlation coefficient; and figure whether the correlation is statistically significant
(use the .05 significance level, two-tailed);
thank you fo..
Answer : Here are the answers and then the following will be notes about the correlation and the
the correlation coefficient r = -0.9036961
because of the very small sample size I used the Spearmans's Rank Correlation Rho to test whether or not r is statistically significant.
S = 19.4868, p-value = 0.05132
alternative hypothesis: true rho is not equal to 0
since the p-value is greater than the significance level we fail to reject the null hypothesis and conclude that the correlation is not statistically significant.
vv==== NOTES ====vv
The correlation coefficient, r, is a measure of the linear relationship between two variables. If the data is non-linear then the correlation coefficient is meaningless.
r takes on values between -1 and 1. negative values indicate the relationship between the variables is indirect, i.e., on a scatter plot the data tends to have a negative slope. Positive values for r indicate the data ten..
Question : What is correlation? Does correlation prove causation? Why or why not? Can you explain and provide some examples so I can understand this concept?
Answer : Correlation is the degree to which two variables are related. Mathematically it is represented by 'r' -- Pearson's correlation coefficient. It is a number that ranges from -1 to +1, where -1 is a perfect negative correlation (one rises as the other falls), 0 is no correlation, and +1 is a perfect positive correlation (both rise and fall together).
Correlation does NOT prove causation. Assuming one (at least partially) causes the other, the math simply provide no way to know. Either variable can be calculated from the other. For example, there is a correlation between education and income. Does increased education result in increased salaries (most people would say yes). However, do people with more money buy more education? That is almost certainly true as well.
There can be very good correlations where neither cause the other. It may be that both are caused by some third variable. For example, there is a correlation between the price of Irish Whiskey and Catholic Priests' salara..
Question : So I have two variables, but they're arranged in a 2D array. How do I calculate the correlation coefficient for them?
The array is 4x7. It's obvious that there's correlation, but I can only figure it out if I isolate a single column vs. single row.
Answer : Simply perform a multiple correlation analysis:
It's the multivariate equivalent of a regular correlation.
Be advised: regardless of which is your data (4 variables, 7 samples or 7 variables, 4 samples), you have a small sample. Your data may not be reliable, depending on what you are measuring.