Linear Stats Flashcards
primarily concerned with finding out whether a relationship exists
Correlation
Correlation determines the _______ and ______
magnitude and direction
are attempts to find the extent to which two or more variables are related.
correlational studies
TRUE OR FALSE: in a correlational study, no variables are manipulated as in an experiment
True
TRUE OR FALSE: the researcher measures NATURALLY occurring events, behaviors, or personality characteristics
TRUE
The simplest correlational study involves?
obtaining a pair of observations or measures on two different variables from a number of individuals
Possible outcomes for correlation?
Perfect Positive, Zero, Perfect Negative
How would you describe the shape or the pattern of the data points
linear pattern
When one variable moves a certain direction, the other tends to move in the same or opposite direction.
COVARIANCE
Positive or Negative Correlation: people who do more revisions get higher exam results
Positive correlation
Positive or Negative Correlation: When more jabs are given, the number of peple with flu falls
Negative correlation
is one of a family of statistical measures used to analyse the linear relationship between two variables
Covariance
provides the DIRECTION (positive, negative, near zero) of the linear relationship between two variables
Covariance
provides DIRECTION and STRENGTH
Correlation
result has no upper or lower bound and its size is dependent on the scale of the variables
Covariance
is always between -1 and +1 and its scale is independent of the scale of the variables themselves.
Correlation
Example of why covariance is not standardized:
we can measure the covariance of two variables that are measured in meters, however, if we convert the same values to centimetres, we get the same relationship but with a completely different covariance value.
Which is standardized? Covariance or Correlation?
Correlation
What is the standardised covariance used?
Pearson’s correlation coefficient (or “r/R”)
Range of Pearson R?
-1.0 to + 1.0
What do the values Zero, Greater than zero, and less than zero indicate?
❏ A value of 0 indicates that there is no association between the two variables
❏ A value greater than 0 indicates a positive association; that is,
as the value of one variable increases, so does the value of the other variable.
❏ A value less than 0 indicates a negative association; that is, as
the value of one variable increases, the value of the other variable decreases (inverse correlation)
The ______ the association of the two variables, the _______ the Pearson correlation coefficient, r, will be to either +1 or -1 depending on whether the relationship is positive or negative, respectively.
Stronger ; closer
Achieving a value of +1 or -1 means that all your data points are included on the line of ______ _____ – there are no data points that show any variation away from this line.
Best fit
How can we determine the strength of association based on the Pearson
correlation coefficient?
❏ Values for r between +1 and -1 (for example, r = 0.8 or -0.4) indicate that there is variation around the line of best fit
❏ The closer the value of r to 0 the greater the variation around the line of best fit.
Before going crazy computing correlations look at a ________ of your data. What pattern (if any) does it exhibit?
Scatterplot
TRUE OR FALSE: Correlation is NOT causation
TRUE
TRUE OR FALSE: Correlation is only applicable to LINEAR relationships.
TRUE
TRUE OR FALSE: Correlation strength necessarily means that the correlation is statistically significant; related to sample size.
FALSE
Non-Parametric test used:
Spearman rank order correlation coefficient (r rho)
employed with interval or ratio scaled variables
Pearson product moment correlation coefficient ( r )
employed with ordered or ranked data.
Spearman rank order correlation coefficient (r rho)
Two sets of measurements are obtained on the same individuals or on pairs of individuals who are matched on some basis
Correlation
The values of the correlation coefficients vary between +1.00 and –1.00. Both of these extremes represent ________ relationships between the variables, and 0.00 represents the _______ of a relationship.
Perfect ; Absence
means that individuals obtaining high scores on one variable tend to obtain high scores on a second variable. The converse is also true, i.e., individuals scoring low on one variable tend to score low on a second variable.
Positive Relationship
means that individuals scoring low on one variable tend to score high on a second variable. Conversely, individuals scoring high on one variable tend to score low on a second variable.
Negative Relationship
Assumptions:
1.) there must be related pairs of scores that come from one subject
2.) RS between 2 variables must be linear
3.) Variables should be measured at least at the interval ( x and y are scale/continuous )
4.) variability of scores on the Y variable should remain
constant at all values of the X variable. This assumption is called homoscedasticity.
There is gradual spreading and has unequal variability
Heteroskedasticity
How do I report the output of a Pearson product-moment correlation?
how to solve df
Minus 2
How do I report the output of a Pearson product-moment correlation?
“A Pearson product-moment correlation was run to determine the relationship between height and distance jumped in a long jump. There was a strong, positive correlation between height and distance jumped, which was statistically significant (r = .706, n = 14, p = .005).”
“A Pearson correlation coefficient was computed to assess the linear relationship between hours studied and exam score. There was a positive correlation between the two variables, r(38) = .48, p = .002.”
If you take the correlation cofficient r and square it you get the_______ __ _______ (__). This is a statistical measure of the proportion of variance in one variable that is explained by the other variable
coefficient of determination (R2 )
OR
R2 = Explained variation / Total variation
In the example above r = 0.984, so R2 = 0.968. This suggests that
jump height accounts for 96.8% of the variance in explosive leg power.
