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PSYC300A - test #2 Cheat Sheet (DRAFT) by

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This is a draft cheat sheet. It is a work in progress and is not finished yet.

Equations!

Deviation score:
(x-x̄)
Squared deviation score:
(x-x̄)2
Sum of squares:
SS= Σ(x-x̄)2
Variance:
SD2 = SS÷N
Standard deviation:
√variance or √SD2
Covariance
cov = SP÷N
Pearson correl­ation:
r = cov. ÷ (SDx)(SDy)
Slope:
by = r(SDy÷SDx)
intercept:
ay = ȳ - by(x̄)
Total variab­ility:
SST = Σ(Y-ȳ)2
explained variab­ility:
SSR = Σ(Y’-ȳ)2
unexpl­ained variab­ility
SSE = Σ(Y-Y’)2
Standard error of predic­tion:
SDy-y' = SDy√1-r2
Predicting X':
X’ = ax + bxY
Predicting Y':
Y’ = ay + byX

General guidelines for test reliab­ility

>.85
very desirable
.70 to .85
desirable aka moderately acceptable
<.70
not desirable aka poor reliab­ility

describe relati­onship between two variables?

1.) Direction of the relati­onship:
Positive (+) or negative (-)
Positive correl­ation = As the values of x increase or decrease, so do the values of y
No relati­onship = no consistent relati­onship between variables
Negative correl­ation = As the values of x increases, the value of y decreases, and vice versa
2.) shape of the relati­onship
Linear relati­onship = straight line relati­onships
– All dots clustered around straight line
Curvil­inear relati­onship = consis­tent, predic­table relati­onship, but not linear
– As the values of x increase, the values of y increases but at some point the pattern reverses
3.) Strength of the relati­onship
Subjective measure of relati­onship between two scores (e.g., weak, moderate, strong, no relati­onship)
how closely the data points cluster together
The more spread out they are from a line of some sort, the weaker the correl­ation between variables
4.) Magnitude of the relati­onship
Objective measure of relati­onship based on computed r value: ranges from -1 to 1

biserial correl­ation

 
When to use it:
– when one of the variables is nominal (with only two groups) and the other variable is interv­al/­ratio
How to calculate:
– use the same formula as pearson r
 

Curvil­inear relati­ons­hips:

Linear: Y’ = a + bX
Quadratic: Y’ = a +bX + cX2
Cubic: Y’ = a + bX + cX2 + dX3
Quartic: Y’ = a + bX + cX2 + dX3 + eX4

Comparing SDy-y’ and SDy

When R does not equal Zero, SDy-y’ will be smaller than SDy
When R=0 (no correl­ati­on/­rel­ati­ons­hip), SDy-y’ = SDy
When R=+/- 1 (perfect correl­ation), SDy-y’=0

How do we describe our data?

1.) Shape
plotting a scatter plot, linearity, strength, direction, magnitude
2.) Central tendency
defining the regression line (mean of bivariate data)
3.) Variab­ility
standard error or estimates (SDY-Y’)

Factors affecting R

1.) Relati­onship is real and strong or weak
contri­butes to a bigger­/sm­aller r
2.) Sampling error
Sampling error = naturally occurring discre­pancy, or error, that exists between a sample statistic and the corres­ponding parameter
3.) Unmeasured third variable
contri­butes to a bigger­/sm­aller r,Corr­elation tells us if a relati­onship between two variables exists but does not tell us about causation
4.) Hetero­geneous sample
Data in which the sample of observ­ations could be subdivided into two distinct sets on the basis of some other variable
5.) Sampling from a restricted (trunc­ated) range
The correl­ation coeffi­cient will be affected by the range of score in the data
6.) Non-li­nea­rity: relati­onship is curvil­inear
Reminder: r undere­sti­mates a curvil­inear relati­onship, contri­butes to a smaller r
7.) Hetero­sce­das­ticity in the data
contri­butes to a smaller r

PHI

When to use it:
– when both variables are nominal (with only two groups per variable, i.e., dichot­omous)
Calcul­ating Phi:
– use the same formula as pearson r
 

How to calculate Pearson r:

1.) Plot the data (scatt­erplot)
2.) Compute bivariate statistics
(e.g., deviation scores, SP, COV)
3.) Compute correl­ation coeffi­cient r
(number beyond +/-1 means you did it wrong)

Interp­reting Pearson Correl­ation

< |.10|
no relati­onship
|.10| to |.30|
weak relati­onship
> |.30| to |.50|
moderate relati­onship
> |.50|
strong relati­onship

Reporting in APA format

1.) describes relati­onship in statis­tical terms
Give variables, R = ?, Mean = ?, Standard deviation = ?, Give sample size, Mention strength and if its positive for negative
2.) Results in plain language

extra stuff

Homosc­eda­sticity (a good thing):
Variab­ility in Y scores remains constant across increasing values of X
Hetero­sce­das­ticity (not a good thing):
variab­ility in y scores changes across increasing values of x, Caused by a skew in one or both variables
SST = SSy
SSe = SSy-y' (error)
SSr = SSt - SSe
Σ(Y-Y’) = 0
For Y’: if r=0, by=0 (i.e., regression line is parallel to the x-axis), and ay=ȳ
For X’: if r=0, bx=0 (i.e., regression line is parallel to the x-axis), and ax=x̄
As correl­ation (r) increases, the numerical value for b increases
Total variab­ility = differ­ences between observed data (Y) and the mean value of Y
– Y-ȳ
Unexpl­ained variab­ility (i.e., residuals) = difference between the observed value for Y and the predicted value for Y(Y’)
– Y - Y'
Explained variab­ility = the difference between total and unexpl­ained variab­ility
– Y’- ȳ
Standa­rdized test = interval

Spearman rho

When to use it:
– one or both variables are on an ordinal scale of measur­ement
– there is a weak curvil­inear relati­onship in interv­al/­ratio data
– there is hetero­sce­das­ticity in interv­al/­ratio data
How to calculate:
Convert all scores into ranks
Lower scores get lower ranks
High scores get higher ranks
Use the pearson correl­ation formula to find how consis­tently increases in one variable are associated with increases in another variable