ch 11: correlation coefficients Flashcards
the square of Pearsons r (r2) is known as…
coefficient of determination
what is pearsons correlation coefficient
the test used if youre looking for a relationship between two variables that are nomally distrib and are at the interval or ratio level
what is a correlation
a relationship between at least two variables
when selectin the best correlation test you must ask what question about your variables
what level of meas are they
o If in the relationship you want to examine, at least one of the variables is only meas at the nominal level you need what test
chi square test
o If lowest level of data collected for at least one variable is measured at the ordinal level or isn’t normally distrib youll use
the spearman corelation coefficient (p)
can you ever ever use pearsons correlation coefficient w ordinal data
You can sometimes use Pearsons correlation coefficient w ordinal data too but its complicated and the authors said dont worry about it
to use pearsons correlation coefficienct on two variables what char do they need to have
they must be at interval or ratio data level and normally distrib
Which correlation test describe the direction and strength of a linear relationship between two variables
spearman and pearsons correlation coefficients
what is a positive correlation
is the coefficient (p or r) neg or positive
means when both variables move in the same direction together eg one inc the other inc
coefficient is positive
what happens to variables with negative correlation
is the coefficient (p or r) neg or positive
when one inc the other dec
eg smoke more–>dec life expectancy. Here the coefficient, p or r, is negative
what is the directionof the relationship
describes either the pos or neg nature of the relationship
what is the minimum sample size for correlation coefficients
3 for correlation coefficients
if looking for linear relationship between only two measures or subjects of a variable will you find one
yes youll always find one as you can always connect two points with a stright line
for all these tests you need at least __ variables to correlate and min of __ subects in the sample to compute the correlation coefficient
o For all these tests yu need two variables to correlate and min of 3 subjects in the sample; then you can ompute the correlation coefficient
what is The STRENGTH of the RELATIONSHIP or correlation determined by coefficient
the absolute value of the correlation
what is absolute value
eg of -4
or just 4
o ABSOLUTE VALUE is the numeric value of a number without the pos or neg indication ) eg absolute value of -4 is 4 and of +4 it is also 4
what is the range that correlation coefficients must fall between
-1 to +1
a correlation coefficient of what indicates a perfect negative relationship
what about perfect positive
o A correlation coefficient of -1 indicates a perfect neg relationship
o Correlation coeffiecient of 1 indicates a perfect pos relationship
the closer the correlation coefficients relationship is to zero the stronger or weaker its relationship
weaker
at what number (correlation coefficients) are the variables completely independent
o If the correlation is zero=no relationship and the variables are therefore completely independent
at what absolute values of correlation coefficient is the relationshp between variables weak, moderate and strong
<0.3 the relationship bet variables is WEAK
o O.3-0.5=MODERATE relationship between variables
o >0.5=STRONG
what do you use to determine if your correlation coefficient is statistically significant
the p value
if p is less than or greater than alpha is it insignificant
if the p is greater than the alpha
if sample size is very small could you have a large correlation coeffiient that isnt significant
yes
t or f small correlation coeffeficnts cannot be signif when sample is large p
false
Even small correlation coeffeficnts CAN be signif when sample is large p
when selecting tests what are the assumptions you must meet
additional ones for pearsons mentioned soon
Sample subjects should be indep and randomly selected
- Approp level of meas should be met
- o Two variables must be compared and linear relationship must be present
if at least one variable is nominal what test should u use
chi square
if the lowest level of data is ordinal then use
spearmans
if both variables are interval/ratio then use..
pearsons
how can you ensure tha the two variables compared have a linear relationship
can always check a scatterplot
in addition to previous assumptions nec to use correlation coeff what is necessary to use pearsons corr coeff
-both variable should be normally distrib in the pop
and homoscedasticity should be present
what is another name for both variables being normally distrib in the pop
bivariate normal
what is homoscedasticity
when can it be seen
eg of this with inc hrs of work and nursing errors
if the spread of a variable is about the same around all the levels of another variable, this assumption is met)
should be present. HOMOSCEDASTICITYcan be seen visually on scatterplot.
o Eg of HOMOSCEDASTICITY if as each hr of work inc there are 1-2more nursing errors then HOMOSCEDASTICITY is present. But if at 5hrs 0-3 errors are present, at 10hrs of work 0-9 errors are reported and at 15hrs
Questions to answer before you select the best correlation test
• Do you have one indep sample
• Are you looking for linear relationship between two variables in this sample
• Whats the lowest level of meas for each of your variables
o Nominal-chi square
o Ordinal-spearmans
o Interval/ratio-pearsons
When selecting your correlation test ensure the data meets the assumptions. what do you do if it doesnt
o Eg if want to use pearsons correlation coefficieint but sample is only 20 and isn’t normally distrib what do you d
then need to select a test at a lower level
if want to use pearsons correlation coefficieint but sample is only 20 and isn’t normally distrib, you gen need to use spearmans correlation coeff
what is it alled when you square pearons r
it becomes the COEFFICIENT OF DETERMINATION (r2)
what does it tell you when you multiply the coefficient of determination (pearsons r2) by 100
it tells you something called PERENTAGE OF VARIANCE. This is the amount of variance in one variable thats explained by the second variable
This is the amount of variance in one variable thats explained by the second variable
if you had stat signif pearsons correlation coefficent of r=o.7 what would the coefficient of determination be
what do you do to this value (corr ccoeff) to make it the percentage of variance
- 7 x 0.7 = o.49
0. 49 x 100= 49%
once you know what the percentage of variance for one variable is what other info does that give you
eg in a study looking at statistically significant pearsons correlation coefficient between dail caloric intake and total serum cholesterol
eg in above question when given 49% you know that the other 51% is due to other variables
you could say that the differences in total serum cholesterol that were related to factors other than caoric intake by looking at te diference between the % of variance and 100%. So in this study itd be 51%
when you have a value of r >0.3 it is considered clinically important
how much of the variance does this explain
what about when you have pearsons r of 0.4 how much does this explain
and r=0.6
9%
- 4 explains 16% med effect size
- 6 explains 36% a large effect sie
what can you use pearsons correl coeff for in r/t effect size
what is effect size
can use it to det the effect size to use when calculating sample size
The effect size is just an estimate of the relationship/difference you are attempting to find
your data isnt normally distrib can you use pearsons
no must be normally distrib with interval or ratio level variables
