Relationships in statistics are looked at for what three reasons?
- comparison of different distributions - determining causality - psychometric properties of questionnaires
- interested in relationship not magnitude of one over the other.. - one variable carries information about another variable - easy first step in determining causality but there has to be a correlation - Correlations do not = CAUSATION. ever.
When constructing a scatter what is being graphed?
X and Y data points....
Linear relationships? What the heck are they?
- straight line...what we are interested in!
- not interested in this - BAD.....they are bias..
Describe a positive relationship?
- each variable is increasing together - correlation is evident - direct
Describe a negative relationship?
- one variable is increasing while the other is decreasing... -inverse
Describe a perfect relationship ? Are they common?
- all data points fall exactly on the line - not very common
Describe an imperfect relationship? Are they common?
- all data points do not fall on the line - still linear -very common -line of best fit/ regression line L> basically a mean....points around it = variance...
Correlation part 2 yo
- family of statistical tests that quantify the relationship between the variables....
Correlation coefficient what the heck is that?
single # that summarizes the relationship of two variables.. ranges from +1.00 to - 1.00 L> signs only indicate direction....both are equally as strong correlations
Characteristics of Correlation coefficient? most common correlation coefficient values?
- zero = very weak/ no relationship - + correlation = with every one unit increase there is a proportional increase in another variable..and vise versa - -0.5- + 0.5
Describe the Pearson r Correlation Coefficient.. how does it get around the issue of varying units?
- extent that paired scores occupy the same or opposite positions within their distributions.... - convert data into z score...so no unit score issue...
What is the raw score Pearson r Formula?? What does each part represent?
Variability of Y can be explained by?
When r= 0 the best predictor of Y is the _____ of the y scores.. What are the erros associated with this?
- mean, imperfection in prediction...
When r does not equal 0 the best predictor of Y is ____. Prediction errors?
-when x is a predictor the error goes down significantly
The total deviation of score is divisible into two parts..what are they?
1. the distance from the regression line to the mean line = deviation accounted for by X (A)
2.The distance from the regression line to the point in question....prediction error (B)
A+B= deviation of score
The deviation of Yi
prediction error + deviation of Yi accounted for by X
The total variablilty of Y ?
Variability of prediction errors + variability of Y accounted for by x
When correlation goes up the variability of prediction errors goes _____, variability of Y accounted for by Y _____.
When r= 0 the variability of P.errors = ________. Variability of Y accounted for x =___?
-min variable, none
When r= 1.00 Variability of P.errors = _____ and the variability of Y accounted for by x ____.
The greater x is = ___ proportion of Y is accounted for
- none, maximum
Explained variance? Explain it ! (4)
- r= correlation coefficient
L> magnitude and direction of relationship
- r = coefficient of determination
L>proportion of total variability in Y accounted for by x...
Describe the Explained Variance table...
1, 9 and 16 are the most common in the behavioural sciences
25, 36 are large correlations
49, approx 1/2 variance
64, 81 and 100 are rarely seen ever...more so in psychometrics..
Issues with a curve shaped graph?? GO
r values cancel each other out
magnitude of correlation is severly reduced....
ex: performance in anxiety
Describe the following coefficients !
Spearman rank order rho
- 2 interval/ or ratio
-one interval/ratio and one dichotomous
-1 or both = ordinal
- 2 dichotomous
AD-BC/ >/ (A+B)(C+D)(A+C)(B+D)
>/ = square root
With the phi coefficient everything is related to ____
What are the three issues with correlations?
- restricted ranges : reduces magnitude of correlation...reducing variability
-outliers: increases magnitude
-correlation does not equal causation