Statistics

Question 1

Categorical Data

Answer 1

“observations or variables that are classified or categorized by means of labels or other descriptive terms. In the examples listed above, the AB blood type and the 5-point scale (ranging from ‘poor’ to ‘excellent’) are categorical measures” (6)

Question 2

Quantitative Data

Answer 2

“observations, counts and measures made by determining quantities or by assigning number values to the data” (6)

Question 3

Nominal Data

Answer 3

categorial data that “fall into categories that have no inherent order (ie, the categories serve simply as names). Examples of such categories are occupation, country of birth, language spoken at home, and blood type” (6)

Question 4

Dichotomous (Binary) Data

Answer 4

“a special kind of nominal data that fall into one of only 2 possible categories and are frequently used in health research. Examples of the categories used to describe dichotomous data are female/male, treatment/control, diseased/not diseased, and alive/dead” (6)

Question 5

Ordinal Data

Answer 5

“exhibit an inherent ranking (eg, from lowest to highest)” (6)

Question 6

Discrete Data

Answer 6

“whole numbers; their values are presented only as integers” (7). Examples are number of teeth with cavities, number of pregnancies, number of children in a family (7)

Question 7

Continuous Data

Answer 7

“include a full range of possible fractional values—that is, no matter how close any 2 values are to one another, other values always exist between them” (7). Examples are blood pressure, height, temperature, and age (7-8).

Question 8

True Zero Point

Answer 8

E.g. birth or Kelvin 0. “relative measures involving multiplication and division (eg, x is twice as big as y) can be performed only with continuous data that have a true zero point” (8)

Question 9

Ratio Data

Answer 9

“Continuous data with a true zero point” (8).

Question 10

Interval Data

Answer 10

Continuous data without a true zero point (8).

Question 11

Descriptive Statistics

Answer 11

“provide the most basic form of data summarization and are usually the starting point of any data analysis” (13-14). E.g. bpm of 40 medical writers and editors.

Question 12

Graphical Displays

Answer 12

“frequently used to summarize and present data” (14)

Question 13

Frequency Distribution

Answer 13

A graphical display that indicates how often each value occurs in the data set (14).

Question 14

Central Tendency

Answer 14

the data’s tendency to cluster near the central value (15).

Question 15

Variability/Dispersion/Spread

Answer 15

The spread of the data points (15).

Question 16

2 Needed Elements to Summarize Data

Answer 16

1) Measure of central tendency

2) Measure of variability (16).

Question 17

Mean (arithmetic)

Answer 17

The average value (16)

Question 18

Median

Answer 18

Middle value of a sequential set of data, or its 50th percentile, value at which half of the data points and half are lower (16)

Question 19

Mode

Answer 19

Most frequently occurring value in a set of data (16).

Question 20

3 Measures of Central Tendency

Answer 20

Mean, median, mode

Question 21

Range

Answer 21

Difference between lowest and highest values of a data set (17). Usually written as minimum followed by maximum value.

Question 22

Interquartile range (IQR)

Answer 22

“the range between the data’s first quartile (25th percentile) and third quartile (75th percentile)—the middle 50% of data values” (17). Often reported witht he median, allowing one to work out quartiles (17).

Question 23

Standard Deviation (SD)

Answer 23

“the average distance between each data point and the mean value of the distribution” (18). *“The SD should be used and reported with the mean only when the data are normally distributed (or nearly so)” (18).

Question 24

Standard Deviation Calculation

Answer 24

1. Calculate the mean.
2. Determine the distance of each data value from the mean.
3. Square each of these calculated differences (distances) from the mean to convert the negative values to positive values….(Note: If we don’t perform this step, then when we add these 40 differences, as we will do in the next step, we will obtain a total of zero because all of the positive differences will be exactly balanced by the negative differences.)
4. Add these 40 squared differences (this yields a number called the sum of squares) and divide the total by the number of values minus 1…to obtain the average squared distance from the mean….This number is known as the variance. (The sum of the squares is divided by n-1 rather than by n because this slight increase in the average distance provides a more accurate estimate of the variability of the data.)
5. Finally, find the square root of the variance…to determine the standard deviation” (18-19)

Question 25

3 Measures of Variability

Answer 25

Range, Interquartile Range, Standard Deviation

Question 26

3 Properties of Normal/Bell-Shaped/Gaussian Distributions

Answer 26

1) Mean, median, and mode are exactly equal in value.
2) Frequency distribution is symmetrical about its center (the mean).
3) [T]he area under the curve can be precisely defined by the mean and standard deviation (SD), as follows:
a) ~68% of the data points fall within ± 1 SD of the mean,
b) ~95% of the data point fall within ± 2 SD of the mean,
c) ~99% of the data points fall within ± 3 SD of the mean” (19)

Question 27

Skewed distribution

Answer 27

Asymmetrical (non-normal/-Gaussian) distributions of data (19).

Question 28

Outlier

Answer 28

A data point far away from the center of the data distribution (20).

Question 29

3 Examples of Skewed Distributions

Answer 29

1) Laboratory values for which the clinically normal (ie, expected) range lies near zero (eg, serum bilirubin or urinary protein concentration)…because abnormal values can be quite high on one side of the distribution but can never be less than zero on the other side.
2) Birth weight
3) Number of days in a hospital stay (22).

Question 30

How to describe skewed distributions

Answer 30

Use the median and interquartile range (IQR) (22).

Question 31

Reporting consequence for most biological data not being normally distributed

Answer 31

The median and IQR should appear more frequently in medical literature than the mean and SD (22).

Question 32

2 Ways to Recognize Skewed Distributions from Mean and SD

Answer 32

1) Difference between mean and SD produces an impossible result (eg, negative tumor size)
2) Mean differs markedly from median (23-24)

Question 33

Parametric Statistical Tests

Answer 33

Those that should be applied to normally distributed data (24)

Question 34

Nonparametric Statistical Tests

Answer 34

Those that should be applied to non-normally distributed data (24)

Question 35

How to Summarize Nominal Data

Answer 35

Using simple counts or percentages of categories; depicted with dot, pie, or bar charts (25).

Question 36

How to Summarize Ordinal Data

Answer 36

As for nominal data, using simple counts or percentages of categories; depicted with dot, pie, or bar charts (25).

Question 37

How to Summarize Discrete Data

Answer 37

Because they represent numeric counts, using measures of central tendency and dispersion (26).

Question 38

Census

Answer 38

Data from every individual in a population

Question 39

Standard Error of the Mean (SEM)

Answer 39

An estimate of the variability among sample means. Calculated in order to get closer to the variability of a population than does standard deviation of a single sample (35-36).

Question 40

SEM Calculation

Answer 40

Standard deviation / [divided by] square root of sample size (36).

Question 41

Importance of SEM

Answer 41

–“[P]erhaps the greatest value of the SEM is…that it enables us to determine the proportion of sample mean values that will be expected to fall within certain portions of the normal distribution (eg, 68% of all possible sample mean values will occur within ±1 SEM of the ‘true’ [population] mean value)” (36).

Question 42

How to report precision of mean estimate w/SEM

Answer 42

Eg, “The estimated mean (SEM) heart rate of the population is 80 (0.8) bpm” (36)

Question 43

In medical sciences, the preferred way of reporting precision of estimate

Answer 43

Mean + 95% Confidence Interval (CI) (2 SEMs).

Question 44

[95%] Confidence Interval (CI)

Answer 44

Along with the mean, the preferred way in medical sciences to report the precision of an estimate. 95% CI = 2 SEMs.

Question 45

How to reduce the width of the Confidence Interval

Answer 45

Increase the sample size (38).

Question 46

Null Hypothesis

Answer 46

The hypothesis that the intervention has no effect on the data (45).

Question 47

Test Statistic

Answer 47

A description of how closely observed data matches prediction of null hypothesis. In the example, the number of SEMs between the mean heart rate difference observed and that predicted under the null hypothesis. ([Dif observed - null hypothesis]/SEM)(47).

Question 48

One Key Takeaway of Statistics Book (via example)

Answer 48

Find the observed mean, SD, and SEM; see how much the observed mean differs from the mean (often 0) in the null hypothesis; divide by 1 SEM to determine the test statistic, how much this is in SEMs; consult a statistical (often t) table that tells you probability for this SEM difference; and draw a conclusion based upon that probability (47).

Question 49

P [ital] value

Answer 49

“[T]he probability that, if the null hypothesis is true, chance alone could have produced a result as extreme as the one observed” (47). I.e., the probability that this could have happened by chance.

Question 50

Common P value

Answer 50

.05. : “As a matter of convention, researchers commonly set the P value (the level at which results will be classified as statistically significant) at .05. This means that they are willing to accept a 5% chance that they could wrongly conclude that an observed result was real when, in fact, it was due to chance” (47).

Question 51

Clinically Important

Answer 51

Demonstrating (in clinical trials, between the control and study group) a large enough difference to have a practical impact on the patient (47).

Question 52

Paired t [ital] Test

Answer 52

Performed on a “study [that] uses paired data[: for instance,] two measurements from the same person at different times” (48).

Question 53

Alpha (α) Level

Answer 53

The conventional p [ital] threshold of .05 (49).

Question 54

Common Features of Statistical Tests in Medical Science

Answer 54

All of these tests determine the difference between the observed results and the results that would be expected according to the null hypothesis; they then standardize this difference between observed and expected results by dividing it by the applicable measure of variability (eg, the SEM)” (49).

Question 55

X^2 (chi-square) Test

Answer 55

“used to assess the statistical significance of results obtained with categorical data” (49). [Mnemonic: “Chi” for “Categorical.”] Eg, a study of relapse/no relapse and percentages of individuals who fall into each camp (49).

Question 56

t [ital] Test

Answer 56

“used to determine the statistical significance of the difference between the means obtained from 2 (and only 2) independent samples” (49). [Mnemonic: “t” for “two”]

Question 57

Analysis of Variance (ANOVA) Test

Answer 57

“an extension of the t test…used to compare the means obtained from 3 or more groups” (50). N.b.: “The results of an ANOVA indicate only whether a statistically significant difference exists; they don’t indicate which group or groups are different from the others” (50).

Question 58

Parametric Statistical Tests

Answer 58

Tests involving “parameters (measurable characteristics) such as group means, SD, and variance.” The t [ital] [, paired t,] and ANOVA are parametric tests. N.b.: “researchers should use these parametric statistical tests only for data that are roughly normally distributed” (50).

Question 59

Nonparametric Statistical Tests

Answer 59

To be performed on study data that are not normally distributed (50).

Question 60

Wilcoxon Signed Rank Test

Answer 60

“[T]he nonparametric alternative to the paired t test” (50).

Question 61

Kruskal-Wallis Test

Answer 61

“[T]he nonparametric alternative to ANOVA” (50).

Question 62

Type I Error

Answer 62

“[M]istakenly concluding that there is an effect when in fact there isn’t one” (50)

Question 63

Type II Error

Answer 63

“[I]ncorrectly conclud[in]g that there is no effect, when in fact there really is one” (50).

Question 64

How to Present Statistical Significance and Clinical Importance

Answer 64

“many scientific publications expect authors to present both P values [for statistical significance] and [95%] confidence intervals [for clinical importance]” (51).