Organizing, Displaying, and Describing Data

Question 1

What is a variable

Answer 1

• Any characteristic that can & does assume different values for different people, objects, or events being studied

Question 2

What are the four measurement scales for variables

Answer 2

• Nominal
• Ordinal
• Interval
• Ratio

Question 3

Describe nominal

Answer 3

• Numbers are simply used as a code to represent characteristics.
• There is no order to the categories.
• The assignment of numbers to categories is arbitrary
• Ex: gender or ethnicity

Question 4

Describe ordinal

Answer 4

• Numbers represent categories that can be placed in a meaningful numerical order (e.g., from lowest to highest).
• There is no information regarding the size of the interval between the different values.
• The size of the interval may be different between the different categories.
• There is no “true” zero.
• EX: pain scale 1 = no pain, 2 = a little pain, 3 = some pain, 4 = a lot of pain

Question 5

Describe interval

Answer 5

• Numbers can be placed in meaningful order.
• The intervals between the numbers are equal.
• It is possible to add and subtract across an interval scale.
• There is no true zero, so ratios cannot be calculated.
• Ex: Fahrenheit temp., SAT, or GRE

Question 6

Describe ratio

Answer 6

• Numbers can be placed in meaningful order.
• The intervals between the numbers are equal.
• There is a “true” zero, determined by nature, which represents the absence of the phenomena.
• Almost all biomedical measures (weight, pulse rate, and cholesterol level) are of ratio scale.
• Ex: weight, age, # of min. spent exercising, cholesterol level, or # of wks pregnant

Question 7

What is the goal of displaying data

Answer 7

• To get a feeling for the distribution of the data

Question 8

Define the parts of displaying data

Answer 8

• Central tendency: most frequently occurring values
• Dispersion: how the values are spread out
• Shape and skewness: symmetry or asymmetry of the distribution of the values
• Outliers: unusual values that do not fit the pattern of the data

Question 9

Describe frequency distributions

Answer 9

• A table that shows classes or intervals of data with a count of the number in each class. The frequency (f) of a class is the number of data points in the class.

Question 10

Define class width

Answer 10

• The distance b/w lower (or upper) limits of consecutive classes

Question 11

Define range

Answer 11

• The difference b/w the max and min data entries

Question 12

Describe histograms

Answer 12

• A way of organizing the data in visual form
• Data have to be at least ordinal in scale

Question 13

What are the rules for histogram construction

Answer 13

• The values of the variable being graphed are on the x-axis
• Class intervals are used (mutually exclusive, exhaustive, & even widths)
• The bars of the histogram touch

Question 14

Describe a stem and leaf plot

Answer 14

• Each number is separated into a stem (usually the entry’s leftmost digits) and a leaf (usually the rightmost digit)
• Allows us to see the shape of the data as well as the actual values

Question 15

What is the advantage and disadvantage of using a graphical method for describing data

Answer 15

• Advantage: Its visual representation
• Disadvantage: Its unsuitability for making inferences (our main goal)

Question 16

What are some numerical methods for describing data

Answer 16

• Frequency distribution table
• Histograms
• Stem and leaf plot
• Pie chart
• Scatter plot
• Times series chart

Question 17

Describe the differences between mode, median, and mean

Answer 17

• Mode: most frequently recurring value (appropriate for nominal, ordinal, interval, & ratio data); if no entry is repeated then there is no mode
• Median: the value that is in the middle of the distribution (appropriate for ordinal, interval, & ratio data); middle entry when all entries are put in order & if it’s a even # of entries take the mean of the 2 middle values
• Mean: the arithmetic average of the distribution ( appropriate for interval & ratio data); sum of all values divided by total entries

Question 18

Define an outlier

Answer 18

• A data entry that is far removed from the other entries in the data set

Question 19

Comparing mean, median, and mode which ones are affected by an outlier

Answer 19

• Mean is affected while median and mode are not influenced by extreme values

Question 20

Define midrange

Answer 20

• The average of the highest and lowest value in the data set
• Very easy to find but highly effected by the extreme values

Question 21

Describe a weighted mean

Answer 21

• It’s the mean of a data set whose entries have varying weights
• Ex: homework is 30%, exams are 50%, and projects are 20% of your final grade

Question 22

What are the measures of dispersion and their goal

Answer 22

• Goal is to get a feeling for the spread of the data
• Range: difference b/w the highest & lowest value in a data set (appropriate for ordinal, interval, & ratio data)
• Interquartile range: the value that is in the middle of the distribution (appropriate for ordinal, interval, & ratio data)
• Standard deviation: average distance of each point from the mean (appropriate for interval & ratio data)

Question 23

Describe symmetrical distributions

Answer 23

• Data are evenly distributed about the center
• There is the same amount of data on the right & left side of the distribution
• Not all symmetrical distributions are “normal”

Question 24

Describe skewed distributions

Answer 24

• Data are not evenly distributed about the center
• Can be “right skewed” or “left skewed”

Question 25

Define deviation

Answer 25

• Difference b/w the entry & the mean of the data set

Question 26

Guidelines for finding the sample standard deviation

Answer 26

1) Find the mean of the sample data set
2) Find the deviation of each entry
3) Square each deviation
4) Add to get the sum of squares
5) Divide by n-1 to get the sample variance
6) Find the square root of the variance to get the sample standard deviation

Question 27

Describe the empirical rule for standard deviation

Answer 27

• For data with a (symmetric) bell-shaped distribution the standard deviation has the following characteristics
  1) ~68% of the data lie within 1 standard deviation of the mean
  2) ~95% of the data lie within 2 standard deviations of the mean
  3) ~99.7% of the date lie within 3 standard deviations of the mean

Question 28

Describe standard error

Answer 28

• The values of a specific variable from a sample are an estimate of the entire population of individuals who might have been eligible for the study
• A measure of the precision of a sample in estimating the population parameter
• Dependent on sample size: larger the sample, the smaller the standard error

Question 29

Standard error of the mean equation

Answer 29

• Standard deviation ÷ square root of (sample size)
• if sample greater than 60

Question 30

Describe confidence intervals

Answer 30

• Range of values which we can be confident includes the true value
• Defines the “inner zone” about the central index (mean, proportion or ration)
• Describes variability in the sample from the mean or center
• Will find CI used in describing the difference b/w means or proportions when doing comparisons b/w groups
• Ex: 95% CI indicates that we are 95% confident that the population mean will fall within the range described

Question 31

Describe quartiles & percentiles

Answer 31

• Useful for comparing scores within one data set
• Ex: if a score is in the 80th percentile (P80) it means that 80% of all the scores fall at or below this score in the distribution & 20% of all the scores fall above this value

Question 32

Describe quartiles

Answer 32

• The 3 quartiles, Q1, Q2, and Q3 approximately divide an ordered data set into four equal parts
• Q1 is the median of the data below Q2
• Q2 is the median
• Q3 is the median of the data above Q2

Question 33

Describe the interquartile range (IQR)

Answer 33

• The difference b/w the third and first quartiles

Question 34

Define fractiles, percentiles, and deciles

Answer 34

• Fractiles: numbers that partition, or divide, an ordered data set
• Percentiles: they divide an ordered data set into 100 parts (there are 99 percentiles)
• Deciles: they divide an ordered data set into 10 parts (there are 9 deciles)

Question 35

Define hypothesis

Answer 35

• Statement about a population, where a certain parameter takes a particular numerical value or falls in a certain range of values.

Question 36

Define null hypothesis (H0)

Answer 36

• “Innocent until proven guilty”
• Usually states that no difference b/w test groups really exists
• Fundamental concept in research is the concept of with “rejecting” or “conceding” the H0

Question 37

Limitations of significance tests

Answer 37

• Statistical significance does not mean practical significance
• Significance tests don’t tell us about the size of the effect (like a CI does)
• Some tests may be “statistically significant” just by chance
• Be skeptical when you hear reports of new medical advances
• There may be no actual effect
• If an effect does exist, we may be seeing a sample outcome in right-hand tail of sampling distribution of possible sample effects, and the actual effect may be much weaker than reported.

Question 38

Difference between confidence interval and P-value

Answer 38

• CI will give information about the size of the difference & the strength of the evidence
• P-value will tell you whether or not there is a statistically significant difference

Question 39

Describe clinical importance

Answer 39

• A medical judgement not statistical
• Clinicians should change practice only if they believe the study has definitively demonstrated a treatment difference and that the treatment difference is large enough to be clinically important.

Question 40

Clinical importance depends on your knowledge of

Answer 40

• A range of possible treatments
• Their costs
• Their side effects