Ch. 4 Summarizing Data Collected in a Sample

Question 1

Sample

Answer 1

subset of individuals selected from the population at random

should be representative of the population

number of individuals in the sample is less than the number of individuals in the population

Question 2

First step in analysis

Answer 2

characteristic of interest must be summarized using appropriate techniques

Question 3

Types of variables (outcomes, endpoints, characteristics, etc.)

Answer 3

Dichotomous, ordinal, categorical, continuous

Question 4

Dichotomous response

Answer 4

has only two possible responses

Question 5

Ordinal response

Answer 5

more than two possible responses and the responses are ordered, i.e. symptom severity - minimal, moderate, severe

Question 6

Categorical response

Answer 6

more than two possible responses and the responses are not ordered, i.e. race/ethinicity, blood type, marital status

Question 7

Continuous Variables (measurement or quantitative variables)

Answer 7

can theoretically take on an infinite number of values between a fixed min and max

Question 8

Clustered or repeated measures

Answer 8

multiple measurements taken on the same person

Question 9

Statistics

Answer 9

numerical summary measures computed on samples

Question 10

Parameters

Answer 10

numerical summary measures computed on populations

Question 11

Descriptive Statistics for Dichotomous Variables

Answer 11

responses described as “success” or “failure”

Frequency distribution tables (proportions of each response in the sample)

relative frequencies -

Question 12

Descriptive Statistics for Ordinal and Categorical Variables

Answer 12

Cumulative frequency - number of subjects at a certain level or below

cumulative relative frequency - useful for summarizing ordinal variables and indicate the percent of patients at particular level or below

Question 13

Population

Answer 13

collection of all individuals about whom we wish to make generalizations

Question 14

Measurement/Quantitative variables

Answer 14

can take on an unlimited number of responses between a theoretical minimum and theoretical maximum value

Question 15

Descriptive Stats for Continuous Variables - Measures of Center

Answer 15

Sample Size - larger usually better but at a certain point, there is not more benefit from more subjects

Sample Mean - Sum all values and divide by sample size, gives sense of the middle of the data (Xbar), report one more decimal place than the statistics measured

Sample Median - middle value in the ordered data set, separates top and bottom 50%s, if even number of data points, median is mean of two middle points, unaffected by extreme values

When there are no extreme values, the mean and median are close in value

Mode - most frequent value - given in addition to the mean and median and not instead of

Question 16

Descriptive Stats for Continuous Variables - Measures of Variability

Answer 16

Sample Range - depends on scale of measurement

Sample Variation - comes from the squared differences of data set values and the mean of the data set, dividing by (n-1) gives better estimate of population variance (underestimate with n)
(Sum(X-Xbar)sq)/(n-1)

Sample Standard deviation - square root of the variation

Interquartile Range - dataset with outliers, range of the middle 50% of the data, Q3 - Q1
First Quartile - value that holds the first 25% of values below it
Median - divides upper and lower 50% of scores
Upper Quartile - value that holds the upper 25% of values above it

Question 17

Outliers vs. No outliers

Answer 17

Outliers - Median and IQR

No Outliers - Mean and Standard Deviation

Question 18

Tukey Fences for Outliers

Answer 18

Values below Q1 - 1.5(Q3-Q1), or above Q3 + 1.5(Q3-Q1)

Question 19

Box and Whisker Plots

Answer 19

Five number summary - Minimum, Q1, Median, Q3, Maximum