Week 9 Kuracloud: Measuring and Summarising Data

Question 1

Statistics

=

(Kirkwood & Sterne. Essential Medical Statistics, 2nd ed., 2010)

Answer 1

= “the science of collecting, summarising, presenting and interpreting data, and of using them to estimate the magnitude of associations and test hypotheses”

(Kirkwood & Sterne. Essential Medical Statistics, 2nd ed., 2010)

Question 2

Descriptive Statistics

Answer 2

= describes features of data sample
“summarising, presenting and interpreting data”

Question 3

Inferential Statistics

Answer 3

= infer findings of sample to target population
“estimate the magnitude of associations and test hypotheses”

Question 4

Data

=

Answer 4

= “a set of values of subjects with respect to qualitative or quantitative variables”

Question 5

Raw Data

=

Answer 5

= observations

Question 6

Data set

=

Answer 6

= collection of information regarding a group of people or other items

Question 7

Variables

=, 2

Answer 7

= characteristics that you can measure or observe and may take any one of a specified set of values
- Numerical (quantitative) (or interval/ratio data)
- Categorical (qualitative)

Question 8

Categorical Variables

2,1

Answer 8

• ordered/ordinal = rank in categories in an order
• unordered/nominal = place observations in named, unordered groups
  
  • dichotomous/binary

Question 9

Numerical Variables

2

Answer 9

• continuous = on a continuos scale, can take any value in range
• discrete = finite options, usually countable

Question 10

Derived variable

=,

Answer 10

= new variable created from existing variable
variable measured as numerical –> categorical

Question 11

Spreadsheets of datasets

3

Answer 11

• Columns: each represents 1 variable (first usually identifier)
• Rows: each represents data for 1 person (record)
• Cells: value of 1 variable for 1 person = observation

Question 12

Outcome variable

=, (3)

Answer 12

= focus of attention, we try to explain its variation
(dependant variable/response variable/y-variable)

Question 13

Exposure Variable

=, (3)

Answer 13

= influences variation of outcome variable
(independant variable/predictor variable/x-variable)

Question 14

Operationalising Variables

=,

Answer 14

= deciding which category designates individual as having an outcome/exposed
dictates interpretation of results

Question 15

Nominal (unordered categorical) variable measurement

2

Answer 15

• frequencies (no. observations in each category)
• proportions (relative frequencies)

Question 16

Ordinal (ordered categorical) measurement

2

Answer 16

• frequencies
• proportions
• sometimes means and medians

Question 17

Numerical (interval/ratio) measurement

3

Answer 17

• mean
• median
• standard deviation

Question 18

Nominal (unordered categorical) graphical representation

3

Answer 18

• pie chart
• column/bar graph
• stacked column/bar graph

Question 19

Ordinal (ordered categorical) graphical representation

1

Answer 19

• column/bar graph

Question 20

Numerical (interval/ratio) graphical reprentation

4

Answer 20

• bar graph (data grouped)
• histogram (data grouped)
• box and whisker plot (summary statistics)
• line graph (over time)

Question 21

Relative frequencies

=, 3

Answer 21

= proportion/percentage of total number
presented in:
- table
- bar graph
- pie chart

Question 22

Epidemiological prevalence or cumulative incidence

2

Answer 22

Presentation: proportion/percentage
Type: dichotomous categorical variables

Question 23

Frequency distribution

=, 2, 2

Answer 23

= distribution of values of a numerical variable
- first step in analysing numerical data
- displayed in a histogram
- for discrete: individual frequencies displayed
- for continuous: frequencies of formed groups/ranges

Question 24

Histogram vs Bar graph

Answer 24

histogram has no gaps between bars because continous data

Question 25

Histograms show us: | 5

Answer 25

- spread - skew - mode - gaps - unusual values

Question 26

Histogram Shapes

Answer 26

- positively skewed - symmetrical - negatively skewed

Question 27

Positively Skewed | =,

Answer 27

= asymmetrical distribution in which "upper tail is longer than lower tail" (higher frequency at left/lower values) ^\__ mean > median

Question 28

Symmetrical | =,

Answer 28

= symmetrical distribution around centre, bell curve, normal distribution, Gaussian distribution _/^\_ mean, median, mode almost equal

Question 29

Negatively Skewed | =,

Answer 29

= asymmetrical distribution in which "lower tail is longer than upper tail" (higher frequency at higher/right values) /^ mean < median

Question 30

Measures of Central Tendency | 3

Answer 30

- mean - median - mode

Question 31

Measures of Variability | 3

Answer 31

- range - interquartile range/IQR (difference between 1st and 3rd quartiles) - standard deviation

Question 32

Standard deviation (SD)

Answer 32

= measure of spread about mean calculation: 1. differences of each observation from mean taken (deviations) 2. Deviations are squared 3. Add deviations together 4. divide by no. observations - 1 (= variance = SD squared) 5. Square root

Question 33

Theoretical Frequency Distribution/Standard Normal Distribution properties (or PDF = probability density function) | 8

Answer 33

- symmetrical about mean (bell curve) - mean = 0, SD = 1 - tall and narrow for small SD, short and wide for large SD - 68% lie within 1 SD of mean - 95% lie within 2 (actually 1.95) SDs of mean - 99% lie within 3 SDs of mean - use mean and SD to find proportion lying between any two values - probability of any specific value is 0

Question 34

95% reference range/central reference range | =

Answer 34

= range of expected normal values in a population, values that enclose 95% population (1.95 or 2 SD either side of mean)

Question 35

Assumption of Normality | =, 2

Answer 35

= assuming values of a continuous variable are normally distributed before calculations Distribution may be skewed if: 1. Mean and median are very different 2. Very large SD, 95% reference range falls outside of possible values or is negative

Question 36

Aggregated Data | =

Answer 36

= units of observation are combined not individual level

Question 37

Univariate analysis | =

Answer 37

= describes single variable

Question 38

Bivariate analysis | =,

Answer 38

= relationship between 2 variables - exposure --> outcome, test hypothesis

Question 39

When both variables categorical: | 4

Answer 39

display relationship by cross-tabulating in a contingency table - rows: exposure - columns: outcomes (no outcome column eliminated if percentages) used to calculate odds rations

Question 40

Categorical Measures of association | 3

Answer 40

- odds ratio = strength of association between variables (yes/no --> odds for variable 1/odds for variable 2) - risk ratio (only in longitudinal) - prevalence ratio (good for cross-sectional)

Question 41

When both variables numerical

Answer 41

Scatterplot - x-axis: exposure - y-axis: outcome

Question 42

Numerical Measures of Association | ===,4

Answer 42

r = correlation coefficient = strength of linear association between two continuous variables = number of SD that outcome changes for 1 SD when exposed - always between -1 and 1 - r < 0: inverse correlation - r = 0: no association - r > 0: correlation - r = 1: perfect correlation, straight line