Descriptive Statistics (B)

Question 1

what is the difference between bar graphs and histograms?

Answer 1

• bar graphs are good when data is in categories

- histograms deal with continuous data

Question 2

what is continuous data/

Answer 2

• can be measured
• has an infinite scale
• e.g. temperature
• opposite of discrete data

Question 3

what is a histogram

Answer 3

displays the frequency density of X-values occurring in each class interval of a frequency table

as a series of rectangular bars

Question 4

what is/how do you work out frequency density?

Answer 4

• measures of how many observations there are per unit of X
• width of a bar is proportional to the width of class interval and the height (area) of the bar is proportional to the density (frequency)

Question 5

what do you normally use standard deviation for?

Answer 5

• in comparative terms, e.g. one data set is more variable than another, hard to see whether one is high or low
• make claims about the proportion of data values we expect to find within a certain number of standard deviations from the mean

Question 6

what is the empirical rule?

Answer 6

also known as the 68,95,99.7 rule

68 refers to 68%, amount of data you’ll find will fall within this area

95 wil fall between two standard deviation

99.7 will fall between three standard deviations

creates bell shaped frequency distribution

Question 7

when can you use the empirical rule?

Answer 7

only the you have normal distribution

Question 8

what is the coefficient of variation?

Answer 8

with larger means there is normally larger standard deviations, which is hard to compare

it is the ratio of the mean to standard deviation

measure of relative variability

it is independent of units of measurement

the higher the variation the greater level of dispersion around mean

Question 9

when is the coffeictent of variation useful?

Answer 9

• when you want to compare results from two surveys in which use two measures, e..g tests with different scoring systems
• same variable over time
• international comparisons

Question 10

how do you work out the coefficient of variation?

Answer 10

standard deviation / mean

Question 11

what is skewness?

Answer 11

measures the degree of symmetry of a distribution

degree of distortion around the symmetrical bell curve

histogram is useful graphical display for plotting frequency of values against a numerical scale

Question 12

which way does positive skew go?

Answer 12

left

Question 13

which way does a negative skew?

Answer 13

right

Question 14

what is the relative position of mean and median when distribution is symmetrical?

Answer 14

mean = median

Question 15

what is the relative position of mean and median when data is positively skewed?

Answer 15

mean is greater than the median

Question 16

what is the relative position of mean and median when data is negatively skewed?

Answer 16

mean is less than the median

Question 17

what are the ways in which you measure skewness?

Answer 17

1) persons coffectient of skewness (PCS)

2) Bowleys coefficient of skewness (BCS)

Question 18

what is PCS?

Answer 18

Pearsons coefficient of skewness

work out if the skewness is positive or negative

Question 19

how do you work out PCS?

Answer 19

= 3(mean-median) /SD

Question 20

what are the results of PCS?

Answer 20

ranges from -3 to +3
0 = symmetrical (normal)

values outside -1 to +1 can be regarded as highly skewed

Question 21

when can you not use PCS?

Answer 21

you you don’t know anything in formula

only know quartile, if you have extreme outliers

Question 22

what is BCS?

Answer 22

more robust that PCS
use when know quartiles or have outliers

focuses on middle 50% of data

Question 23

what is the equation for BCS?

Answer 23

[(Q3-median) - (median - Q10] / (Q3-Q1)

Question 24

what are the results for BCS?

Answer 24

if the upper quartile is further from the median than lower then positive skew

0> p
<0 n

Question 25

what is a scatter plot?

Answer 25

displays the relationship between two continuous variables

Question 26

why are scatter plots useful?

Answer 26

useful in the early stage of analysis when exploring data and determining whether a linear regression analysis is appropriate

may show outliers

Question 27

what are the measures of association?

Answer 27

• scatter plot

- correlation coefficient

Question 28

what does measure of associations show?

Answer 28

analysis of relationships between to variables..

form the next logical step beyond decretive data analysis

Question 29

what are the measures of correlation?

Answer 29

• pearsons correlation coefficient

- spearmans rank

Question 30

what does Pearsons correlation show?

Answer 30

measure of how slowly the point on a scatter plot lie on a straight line (range -1 to +1)

association between two numbers

if two numbers move in the same direction = positive correlation

if one moves up and one down = negative correlation

useful for comparative purposes

unit free

Question 31

what is the calculation for persons correlation coefficient?

Answer 31

covariance (X,Y) / SD(X) x SD(Y)

Question 32

what is covariance?

Answer 32

shows how two variable X and Y change with eahcothwr (move together)

Question 33

how do you work out covariance?

Answer 33

sigma

(X-mean of X) (Y-Mean of Y) / n-1

Question 34

how can you interpret Pearsons correlation?

Answer 34

theoretical / textbook perspective

(-) 0.7 = strong
(-) 0.5) = moderate
(-) = weak

Cohens effect sizes

0.1 = small
0.3 = medium
>0.5 = large