shapes of distrib: transformations Flashcards
what is the distribution shape
the curve enclosing the histogram
why do many people assume normal distribution
otherwise would have to examine and collect every member of pop data; impossible
makes easier for statistics
what does normal distribution look like
bell shaped; symmetrical
what is normal distribution
50% values on either side of mean
mean=median=mode
skewness and kurtosis= 0
what is asymmetrical data
skewed data
ranges from +∞ to -∞
what does it mean if a skew is greater than +-2
data is substantially skewed
what does it mean if the data has a standard error of skewness greater than 1.96
data is substantially skewed
what do measures of central tendency look like in a positive skew
mean>median>mode
what do measures of central tendency look like in a negative skew
mean
what is kurtosis
altitude of distribution
relative conc of scores in centre, upper and lower tails and shoulders
what is the range of kurtosis
-2 to +∞
what does -2 kurtosis mean for the figure of the grraph
flat
what does +∞ mean for the figure of the graph
peaked
what are the 3 types of kurtosis
mesokurtic
platykurtic
leptokurtic
what does mesokurtic mean
neutral degree; normal curve
what does platykurtic mean
flat; thick in shoulders
what does leptokurtic mean
peaked; thick in centre and tails
how can you tell that the distribution of data is significantly different from mesokurtic
if kurtosis divided by standard error of kurtosis is greater than 1.96
define modality
number of peaks
what are the 3 types of modality
unimodal
bimodal
multimodal
what does multimodal mean
more than 1 peak
what does transforming data enable us to do
meet assumptions
give an example of a transformation
take each score and multiply by itself
which values are transformed in nonlinear transformations
all values for a particular variable
what are the 3 nonlinear transformations to positively and negatively skewed data
square root
log
reciprocal
what is the difference in nonlinear transformations between positively and negatively skewed data
at the beginning of neg skew transformation; must reflect the distribution then add constant so lowest value is 1.0
then at end reflect back so order of values is identical to original data
what transformation do you apply to a moderate skew
square root each value
what transformation do you apply to a substantial skew
logarithm each value
what transformation do you apply to a severe skew
reciprocal transformation for each value of 1/x¡
how do you retain order with reciprocal transformation
1/(xhighest - x¡)
how do you avoid 0 with reciprocal transformations
1/(xhighest - x¡)
is it cheating to transform data
no
does nonlinear transformation change the shape of distribution of scores
yes
does linear transformation change the shape of distribution of scores or effect stat anal; why
no because a constant is always
what does linear transformation allow
expression of data in diff units and distrib shape stays same
give examples of linear transformations
add sub a constant
mult div by a constant
what does tabling the distribution mean we can do
give estimates of probability
what is there a link between in data distribution
data distrib and prob of obtaining particular value in distribution
what is the standard normal distribution for normal distribution
mean= 0 SD= 1
what does subtracting a constant from each score do to the mean of distrib
Reduce it by that constant
what does dividing all values by a constant do to the SD
Divides SD by that constant
what happens if you subtract the mean from all values in th distribution
gives mean of 0
what happesn if divide all values in distrib by value of SD
gives SD of 1
what does a Z score tell us
how many SD units a score is from mean
what is the range of scores for z scores and where are most scores concentrated
-∞ to +∞
between -2 to +2
what does the Z score magnitude tell us
how far the score is from the mean
what is the Z score magnitude also known as
absolute value
what Z score does the mean have in the standard normal distribution
0
what does a positive Z score tell us
observation is more than mean
what does a negative Z score tell us
observation is less than mean
