1 - Intro to Stats

Question 1

What are the 3 common scales of measurement for variables in medicine?

Answer 1

• Nominal
• Ordinal
• Numeric (interval or ratio)

Question 2

Describe nominal measurement

Answer 2

• Simplest b/c data fits in categories in no particular order
• No actual measurement
• Often dichotomous or binary (yes/no, male/female)
• Can be multiple categories
• Generally described in percentages or proportions

Question 3

Describe ordinal measurement

Answer 3

• Inherent order to the categories
• Summary statistic (median)
• Often used in assessment of pt risk
• Difference between 2 adjacent categories isn’t the same throughout the scale

Question 4

Describe numerical measurement

Answer 4

• Differences have meaning on numerical scale

- 2 types of numerical scales - interval and ratio

Question 5

Describe the difference between interval and ratio

Answer 5

• Interval - difference between any pair of levels is the same (ex: temperature 10-15 = 20-25), but no meaningful zero value
• Ratio - interval scale w/ meaningful zero value (ex: time)

Question 6

What are the 3 types of variables? Give examples of each

Answer 6

• Continuous (age, time)
• Discrete (number of houses on a street)
• Summary statistics (mean and SD)

Question 7

What are the 3 measures of middle?

Answer 7

Mean, median, and mode

Question 8

Describe mean

Answer 8

• Arithmetic average
• Mean = sum of x/n (x = individual observation; n = number of observations)
• Used w/ numerical variables; shouldn’t be used w/ ordinal variables (but often is)

Question 9

Describe median

Answer 9

• Middle observation
• Arrange the observations from smallest to largest; count and find the middle
• For odd number of observations - median is the middle observation
• For even number - median is average of the values on either side of the middle

Question 10

Describe mode

Answer 10

• Value that occurs most frequently

- Data can have more than 1 mode (bimodal distribution)

Question 11

Which measure of middle should be used in skewed distributions?

Answer 11

• Use mean in symmetric (normal) distributions

- Use median for ordinal data or numerical data that is skewed (mean very sensitive to extreme values in small datasets)

Question 12

What are the 4 measures of spread (dispersion)?

Answer 12

• Range
• Standard deviation/ variance
• Percentiles
• Interquartile range

Question 13

Describe range

Answer 13

• Difference between the smallest and largest observation

- Minimum and maximum may also be given

Question 14

Describe the standard deviation formula

Answer 14

• s = square root of [(sum of x - /x) ^ 2 / (n - 1)]
• x = value
• /x = mean
• n = sample size

Question 15

What is variance?

Answer 15

Sum of x - /x before square root is taken

Question 16

Describe percentiles

Answer 16

• Percentage of a distribution that is equal to or below a particular number
• Median = 50th percentile
• Common example = physical growth charts for children

Question 17

What is interquartile range?

Answer 17

• Difference between the 25th and 75th percentiles (1st and 3rd quartiles)
• Describes the middle 50% of the distribution regardless of the shape

Question 18

When should standard deviation be used?

Answer 18

W/ mean w/ symmetric data

Question 19

When should percentiles and interquartile range be used?

Answer 19

W/ median for ordinal data or skewed numerical data

Question 20

Describe tabular presentations

Answer 20

• Nominal and ordinal data presented as proportions or percentages
• Summarized in frequency tables

Question 21

What is the purpose of contingency tables?

Answer 21

To facilitate simultaneous examination of multiple distributions (variables)

Question 22

What are 4 types of numerical data?

Answer 22

• Stem-and-leaf plots
• Five number summary
• Boxplots
• Grouped frequency tables

Question 23

Describe a boxplot

Answer 23

• Upper and lower hinges of the box are made w/ 1st and 3rd quartile
• Median is the line in the box

Question 24

How is symmetry of a boxplot evaluated?

Answer 24

• Evaluated by symmetry of the hinges w/ respect to median
• If hinges equidistant from median = data is symmetrical
• If upper hinge further away from median = data positively skewed
• If lower hinge further away from median = data negatively skewed

Question 25

Describe a box and whisker plot

Answer 25

Same as boxplot but whiskers drawn from upper and lower hinges to largest/smallest non-outlying values

Question 26

Describe a modified boxplot

Answer 26

- Outliers are identified by an asterisk | - Boundary for outliers = 1.5x interquartile range from the box

Question 27

Describe how to construct a grouped frequency table

Answer 27

- Group observations on variable into contiguous, non-overlapping (preferably equal) class intervals (bins) - Place each observation into only one bin - Tabulate frequency of observations in each bin - Can calculate relative frequency proportion or percentage - Can also tabulate cumulative frequency and cumulative relative frequencies - How many bins (k) and how wide (w)

Question 28

What are some "rules" for grouped frequency tables?

Answer 28

- Poor grouping = loss of information (may emphasize or hide elements of the variable) - Too few bins = loss of info - Too many = cumbersome, data gaps - General rule = 5-20 class intervals

Question 29

Describe guidance for grouped frequency tables

Answer 29

- w = R/k | - w = width of the bin, k = # of bins, R = range

Question 30

What is the difference between histograms and bar charts?

Answer 30

Histogram bars are generally joined b/c they represent a continuous distribution

Question 31

What is a frequency polygon?

Answer 31

- Created by linking the mid-points of successive bins | - Polygon finished by joining to x-axis at point corresponding to the mid-point of the extreme zero-frequency bins

Question 32

How can you use a histogram to find the mean?

Answer 32

Mean = [sum of (f * xmid)] / sum of f - f = frequency - x mid = midpoint of x value range