Quant Methods Flashcards
what are we asking when we use statistical inference?
whether the samples were generated or sampled from the same underlying population
what is the measurement of mode?
the value that was recorded the most, so there can be two if two different heights were recorded the same amount of time and they were both the most frequently observed height
how can we compute the probability of observing a specific data point?
by finding the area under the curve can compute the probabilities of certain regions in the distribution and then in turn apply this to a specific point
what is a one way ANOVA? what is our goal ?
analysis of variance.
goal is to measure/compare data from two or more independent groups
what is it called when we have more than two different independent groups?
a between subjects design
what are we examining when we are doing in a between subjects design?
questioning if any of the groups significantly differ from any of the other groups and testing whether all groups were generated from the same distribution?
within group variation occurs by; between group variation occurs by
variation due to random sampling; variation due to random sampling PLUS additional variance due to experimental manipulation
what is the formula for sum of squares ?
SS total = Σ(x - M)^2
for all scores
what are the steps to ANOVA analysis?
get the SS for the total distribution
then get the SS for each individual group (eg, students, ambos and fire fighters groups) and add these values together
then subtract the added individual group scores from the SS total
SSbetween = SStotal - SSwithin
how do you compute variance?
square the SD eg SD of 1.98 squared = 3.95
what is the relationship between the SS and variance?
variance is the average SS that we predict, eg, if we take the SS and divide by number of data points we have in each group (N) that equals the variance
what is the formula to compute SSbetween?
[Σini(mi - M)^2]
when will the variation of the total data when measuring variance between groups be greater?
when the means for each group are different
what does the F ratio tell you?
what the size of the actual ANOVA is
in regards to anova, using words, explain what the p value is telling us?
the probability of observing this f ratio with these degrees of freedom if there is no variation between groups (no effect)
basically, what is the probability of the data under the assumption the null hypothesis is true
what actually is the f ratio ?
the variation between groups compared to ratio of variance within groups
between group variation
f = ———————————-
within group variation
how do you compute the f ratio?
mean square within between groups divided by mean square within groups
MSbetween
F = ——————-
MSwithin
why can’t we use the SS directly to compute the f ratio?
SS is sensitive to our sample size, so we can’t just divide the SSbetween by the SSwithin
how do we correct the SS to compute the F ratio?
by dividing by the degrees of freedom (no. of independent groups, and no. of subjects)
what does N equal?
total data set
what are the 3 df that we can compute?
dftotal
dfbetween
dfwithin
how do we compute df total?
N (no. of total subjects) minus 1
= N-1
what does k equal?
number of conditions
how do we compute df between?
number of conditions (k) minus 1
eg 3 conditions minus 1
= k-1
how do we compute df within?
= N-k
number of participants minus number of groups
eg 3000 participants and 3 groups would mean
3000-3 = 2997
what is the mean square within groups?
how is it calculated?
the measure of within groups variation that has been corrected for sample size
- SSwithin divided by dfwithin
what is the mean square between?
the measure of between groups variation corrected for sample size ‘
- SSbetween divided by df between
when do we have evidence that the difference is real when using f ratio?
when the f ratio is sufficiently large
as when F is large, it is very unlikely to achieve this score if the differences were due to chance alone
how do you determine whether an f ratio is extreme or not?
it is assessed against the F distribution
what do we require to tell us what the shape of the f distribution is?
dfwithin and dfbetween
F ratio will always be a positive number? T or F?
True
how do we compute the probability of observing an f ratio with a specific value?
by finding the area under the curve
if the f ratio is greater than the value that represents the 95% cutoff, what do we do?
we conclude that the differences between the means of our groups is actually significant
what does the p value tell us?
the probability of your f ratio assuming the null hypothesis is true?
what is the null hypothesis?
is that there is no difference between the groups - that all groups were generated from the same population
when is the p value less than 0.5 when using ANOVA?
when the f ratio is larger than that 95% cut off
T or F? ANOVA tells us if there is a sig. difference, but also tells us how big the difference is (effect size)
False, does not tell how big the diff. is
what are the 2 things anova does not tell us?
how big the difference is, and where the difference is coming from
when would you use a two/three way ANOVA; a repeated measures ANOVA?
you have more than one factor which differs between groups; you have a within subjects design
