ch 11: correlation coefficients Flashcards by Willow Belanger

the square of Pearsons r (r2) is known as…

coefficient of determination

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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

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what is a correlation

a relationship between at least two variables

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when selectin the best correlation test you must ask what question about your variables

what level of meas are they

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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

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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)

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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

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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

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Which correlation test describe the direction and strength of a linear relationship between two variables

spearman and pearsons correlation coefficients

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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

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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

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what is the directionof the relationship

describes either the pos or neg nature of the relationship

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what is the minimum sample size for correlation coefficients

3 for correlation coefficients

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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

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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

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what is The STRENGTH of the RELATIONSHIP or correlation determined by coefficient

the absolute value of the correlation

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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

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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

0. 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% 0. 4 explains 16% med effect size 0. 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