Lecture 9 Flashcards
A Scattergram plots each participants score on the
Independent variable against the dependent variable
In a Scattergram the dependent variable goes on which axis?
Y
There are 3 types of relationships found in scattergrams
Linear
Curvilinear
None
Correlation and linear regression can only be used for this type of Scattergram relationship
Linear or straight line relationship
Pearson correlation will only tell you if you have a ……type of relationship
Linear
If you have no linear relationship looking at a Scattergram what can’t you do?
Pearsons correlation
Linear regression
What’s the next step afte funding a linear relationship in your Scattergram?
You superimpose a line of best fit also called the regression line
Regression line best represents the
Relationship between the 2 varables
Regression line tells you if
Y can be predicted on X
Independent variable always goes on which axis?
X
Where can the effect size be found in a Scattergram in SPSS??
Top right corner where it says R2 linear = ……
Effect size is the….
Correlation of the two variables squared
In a Scattergram you’re looking for a line of best fit that is….
On an angle
If line of best fit is on an angle it means….
There is a relationship!!!
What does the Scattergram look like if there is no relationship??
Flatline/horizontal
Relationship is not strong when points are
Scattered all around Scattergram
5 points to think about with a Scattergram…
Type of relationship Direction Cluster Gaps Outliers
The easiest way to work out if two variables are related is by plotting them on a
Scattergram
What does direction of relationship refer to on a Scattergram?
Positive or negative
Type of relationship in a Scattergram refers to
Linear etc?
A line that goes up towards the right on a Scattergram is what type of relationship?
Positive - as one variable increases so does the other…
If the line goes up to the left of the Scattergram the relationship between variables is
Negative - as one variable increases the other decreases
Y stands for which variable?
Dependent
X is what variable?
Independent
Gaps in the data suggest the existence of
Sub samples in the data
An R2 of 0 or similar on a Scattergram means that there
Is no linear relationship between the varables
What is covariance?
How two variables vary together
If we want to see if there is a relationship between 2 variables we are actually interested in whether
Changes in one variable are met with changes in another variable
In covariance…When one variable deviates from it’s mean we would expect
The other variable to deviate from it’s mean in a similar way
To calculate the exact similarity between the pattern of differences in covariance we calculate the…
Cross-product deviations
When calculating variance essentially what you’re looking at is how
Each score deviates from it’s mean
To get an average of the combined differences for the two variables you need to:
Sum the cross products
Divide by the number of cases minus 1
Covariance formula:
CPF = (X - M2) (Y - M2)
Covariance mean of two different variables formula:
CovXY = Sum of [(X - Mx) (Y - My)] / N -1
Degrees of freedom (N -1) give you
An unbiased estimate
Covariance problem is that it depends on
The scales of measurement you’re using - it’s not a standardised measure
Need to convert covariance into a set of standard set units to be able to
Compare it
Covariance is converted to standard units by computing the
Pearsons r
Pearsons r is most common in measuring
Association between two variables
What type of scale do you need at least to use pearsons r?
Interval scale
Interval scale means
Equal differences (1-2-3-4-5) with no true 0
Ordinal scale is
Rank order - has no 0. Goes from smallest - biggest
Nominal data is
Grouping data, data in categories. Numbers mean group names etc
Pearsons r is the
Standardised covariance between two variables
Pearson r formulae is
r = covXY / SxSy
Pearsons r will only tell you about what sort of relationship?
Linear!!!
Pearsons r can range from
-1 (strong neg) to +1 (strong pos)
What is a weak pearsons r (correlation only!!)
0-0.29
A moderate pearsons r is (correlation only!!)
0.30-0.59
A strong pearsons r is (correlation only!!)
0.60-1.00
Pearsons r does not reveal
Causality
Pearsons r sig (effect size)
At .05
Usually R2 converted to a
%
Weak effect size
r = .10 R2 = .01
Medium effect size
r = .3 R2 = .09
Strong effect
r = .5 R2 = .25
3 factors that influence the size of Pearson correlation
Sample size
Restriction of range or variability
Use of heterogeneous sub samples
There are 2 mathematical assumptions for pearsons r
Interval scale data
Normality
What is particularly bad for correlation and regression?
Outliers!
A partial correlation is where there is
Overlapping variance - or how much variance is commonly shared by all variables
A partial correlation will Allow you examine the relationship between
2 variables when the 3 has been removed
Two types of partial correlation
Semi partial
Partial
Semi partial correlation will only remove the effect of the 3rd variable
Only from the independent variable
Partial correlation will remove the effect of the 3rd variable from
Both other variables
Partial correlations give us a more
Accurate reflection of the relationship between two variables
Partial correlations also tell us what variables
Shouldn’t go in the model together
Why is partial correlation important?
We want to account for as much variance as possible!
Doing a partial correlation helps you work out if you have
Multicollinearity between your variables
Multicollinearity is where the overlap
Between variances is considerable
You know if you have multicollinearity with 2 things
Pearsons r correlations exceed absolute value if .6
Or .8 with Field
What correlation techniques do you use if your variables aren’t interval scale but categorical?
Chi squared
Phi
Cramer’s V
Cohens kappa
What correlation techniques do you use if your variables aren’t interval scale but ranked or ordinal data?
Spearman rank
Kendalls W
What correlation techniques do you use if your variables aren’t interval scale but categorical and interval data
Eta
Point biserial
Is chi square non parametric or parametric?
Non-parametric
Chi squares used in 2 situations…
To compare groups on one nominal/categorical variable
To determine if there is a relationship between 2 variables that are both nominal/categorical
Pearson called the chi square test a
Goodness of fit
Chi square called goodness of fit because it determines if there is a good fit between
The data (observed frequencies) What would be expected from theory (expected freq)
df - in a 2x2 table, df would =
(2 - 1) (2 - 1) = 1*1 = 1
Chi square can be used when nominal/categoric variables have been measured on how many levels?
2 or more
Chi square does not indicate
Strength OR relationship between variables
Phi used for a
2x2 contingency tables
2 methods to determine effect size in chi square analysis
Cramers v (most common) Odds ratio
Cramers v measure of effect size for weak, mod, strong are
.1
.3
.5
Chi square has 2 mathematical assumptions:
Independence of observations (diff ppl in each of your groups and only tested once)
Expected cell frequencies must exceed 5
