descriptive statistics
- stats that simply describe statistics
- screen data and observe trends
inferential statistics
- Use samples to infer something about a population.
- Allow us to test hypotheses and make decisions.
unimodal
scores that vary around one point.
modality
the number of central clusters that a distribution possesses
bimodal
varies around two central points
positive skew
tail points to right
negative skew
tail points to left
normal
- unimodal
- moderate peakness
- symmetric tails
sum of squares
tell us about the total variability in the data set but does not characterise the degree by which each participant varies around the mean.
SS= sum of (X-M)^2
variance
o^2= SS/(n-1)
standard deviation
o= sqrt(SS/(n-1)).
essentially the average amount of variability around the mean.
stat value
= estimate of effect size/estimate of error
compare the stat value against the appropriate probability distribution.
if it is far into the tails it is significantly different from the means.
= 0.05 or 0.001
Z score
Z= (X-M)/SD
tells how many SDs away from the mean a particular score is.
sample Z tests
for a population mean=100, SD=10, sample mean =104.75, n=20
Z= (M-u (pop))/Sm (SD/sqrt(n)).
t tests
used where the pop mean is known but the SD is not.
t= (M-u)/(s(sqrt(SS/n-1)/ sqrt(n)).
t
t distribution changes according to the size of the degrees of freedom.
this is because, the larger the sample, the more accurate our sample statistics estimate the population parameters.
- gets closer to normal as sample increases.
-slightly more error in t tests than z tests because the population variance is estimated and thus there is more distribution in the tails.
df
= n-1
repeated measures t test
identical to single sample but calculated from difference scores and u=0
Ho= no difference
independent t test
two means from two different populations
t= (M1-M2)/Sdiff
sdiff= sqrt(s^2M1+S^2M2).
single sample t test
comparing one set of data to the population
t test assumptions
- all observations are independent (ensure no participant’s performance is affected by or affects anothers).
- distributions are normal (check histograms for skewness and kurtosis, samples over 30 - sample dist. is less important as theoretical distribution of the difference between the means will be normal).
- homogeneity of variance
- variance of one group is not too much larger than the other.
- breaches to homogeneity can inflate type 1 error.
