Chapter 6: Correlation and Predicted Variance Flashcards Preview

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Flashcards in Chapter 6: Correlation and Predicted Variance Deck (30):

Relationships in statistics are looked at for what three reasons?

- comparison of different distributions - determining causality - psychometric properties of questionnaires


Correlations? (4)

- 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!


Curve relationship?

- 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 no unit score issue...


What is the raw score Pearson r Formula?? What does each part represent? 


Variability of Y can be explained by? 

- X 


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?

- X 

-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   

is what??

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 _____. 

-decreases, increases 


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...

r                  r2

0.10       1 

.20        4

0.30       9 

0.40        16 

0.50       25 

0.60     36 

0.70      49 

0.80     64

0.90       81 

1.00     100 

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 ! 

Pearson r 

Biserial  rb 

Spearman rank order rho

Phi ro 


- 2 interval/ or ratio 

-one interval/ratio and one dichotomous 

-1 or both = ordinal 

- 2 dichotomous 


Phi coefficient?? 




 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