shapes of distrib: transformations

Question 1

what is the distribution shape

Answer 1

the curve enclosing the histogram

Question 2

why do many people assume normal distribution

Answer 2

otherwise would have to examine and collect every member of pop data; impossible
makes easier for statistics

Question 3

what does normal distribution look like

Answer 3

bell shaped; symmetrical

Question 4

what is normal distribution

Answer 4

50% values on either side of mean
mean=median=mode
skewness and kurtosis= 0

Question 5

what is asymmetrical data

Answer 5

skewed data

ranges from +∞ to -∞

Question 6

what does it mean if a skew is greater than +-2

Answer 6

data is substantially skewed

Question 7

what does it mean if the data has a standard error of skewness greater than 1.96

Answer 7

data is substantially skewed

Question 8

what do measures of central tendency look like in a positive skew

Answer 8

mean>median>mode

Question 9

what do measures of central tendency look like in a negative skew

Answer 9

mean

Question 10

what is kurtosis

Answer 10

altitude of distribution

relative conc of scores in centre, upper and lower tails and shoulders

Question 11

what is the range of kurtosis

Answer 11

-2 to +∞

Question 12

what does -2 kurtosis mean for the figure of the grraph

Answer 12

flat

Question 13

what does +∞ mean for the figure of the graph

Answer 13

peaked

Question 14

what are the 3 types of kurtosis

Answer 14

mesokurtic
platykurtic
leptokurtic

Question 15

what does mesokurtic mean

Answer 15

neutral degree; normal curve

Question 16

what does platykurtic mean

Answer 16

flat; thick in shoulders

Question 17

what does leptokurtic mean

Answer 17

peaked; thick in centre and tails

Question 18

how can you tell that the distribution of data is significantly different from mesokurtic

Answer 18

if kurtosis divided by standard error of kurtosis is greater than 1.96

Question 19

define modality

Answer 19

number of peaks

Question 20

what are the 3 types of modality

Answer 20

unimodal
bimodal
multimodal

Question 21

what does multimodal mean

Answer 21

more than 1 peak

Question 22

what does transforming data enable us to do

Answer 22

meet assumptions

Question 23

give an example of a transformation

Answer 23

take each score and multiply by itself

Question 24

which values are transformed in nonlinear transformations

Answer 24

all values for a particular variable

Question 25

what are the 3 nonlinear transformations to positively and negatively skewed data

Answer 25

square root log reciprocal

Question 26

what is the difference in nonlinear transformations between positively and negatively skewed data

Answer 26

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

Question 27

what transformation do you apply to a moderate skew

Answer 27

square root each value

Question 28

what transformation do you apply to a substantial skew

Answer 28

logarithm each value

Question 29

what transformation do you apply to a severe skew

Answer 29

reciprocal transformation for each value of 1/x¡

Question 30

how do you retain order with reciprocal transformation

Answer 30

1/(xhighest - x¡)

Question 31

how do you avoid 0 with reciprocal transformations

Answer 31

1/(xhighest - x¡)

Question 32

is it cheating to transform data

Answer 32

no

Question 33

does nonlinear transformation change the shape of distribution of scores

Answer 33

yes

Question 34

does linear transformation change the shape of distribution of scores or effect stat anal; why

Answer 34

no because a constant is always

Question 35

what does linear transformation allow

Answer 35

expression of data in diff units and distrib shape stays same

Question 36

give examples of linear transformations

Answer 36

add sub a constant | mult div by a constant

Question 37

what does tabling the distribution mean we can do

Answer 37

give estimates of probability

Question 38

what is there a link between in data distribution

Answer 38

data distrib and prob of obtaining particular value in distribution

Question 39

what is the standard normal distribution for normal distribution

Answer 39

``` mean= 0 SD= 1 ```

Question 40

what does subtracting a constant from each score do to the mean of distrib

Answer 40

Reduce it by that constant

Question 41

what does dividing all values by a constant do to the SD

Answer 41

Divides SD by that constant

Question 42

what happens if you subtract the mean from all values in th distribution

Answer 42

gives mean of 0

Question 43

what happesn if divide all values in distrib by value of SD

Answer 43

gives SD of 1

Question 44

what does a Z score tell us

Answer 44

how many SD units a score is from mean

Question 45

what is the range of scores for z scores and where are most scores concentrated

Answer 45

-∞ to +∞ | between -2 to +2

Question 46

what does the Z score magnitude tell us

Answer 46

how far the score is from the mean

Question 47

what is the Z score magnitude also known as

Answer 47

absolute value

Question 48

what Z score does the mean have in the standard normal distribution

Answer 48

0

Question 49

what does a positive Z score tell us

Answer 49

observation is more than mean

Question 50

what does a negative Z score tell us

Answer 50

observation is less than mean