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 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?

- 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 Y_{i }

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

-greater

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 r^{2}

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??

|A|B|

|C|D|

formula?

AD-BC/ >/ (A+B)(C+D)(A+C)(B+D)

>/ = square root

With the phi coefficient everything is related to ____

A

What are the three issues with correlations?

- restricted ranges : reduces magnitude of correlation...reducing variability

-outliers: increases magnitude

-correlation does not equal causation