3. Medical Statistics intro Flashcards by Ibby Khan

what is a STATISTIC

a numerical summary of a SAMPLE

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what is a PARAMETER

a numerical summary of the POPULATION

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what is CATEGORICAL data

QUALITATIVE

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what is NUMERICAL data

QUANTITATIVE

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CATAGORICAL data can be split into:

NOMINAL and ORDINAL

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what is NOMINAL vs ORDINAL data with examples
(categorical)

Nominal: categories are mutually exclusive and UNORDERED

eg. sex, blood group, ethnicity, survival after 10 years

Ordinal: categories are mutually exclusive and ORDERED

eg. disease stage, education level, heart murmur grade

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NUMERICAL data can be split into…

DISCRETE and CONTINUOUS

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what is DISCRETE vs CONTINUOUS data (numerical)

Discrete: take only INTEGER VALUES (COUNT 0,1,2..)

eg. NUMBER OF pregnancies, number of asthma exacerbations

Continuous: take ANY VALUE in a given interval

eg. weight, blood pressure, cholesterol levels, age

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PROS and CONS of CONVERTING NUMERICAL to CATEGORICAL

(eg systolic bp (mmHg) —> hypertensive (>140), normotensive (<140)

PROS:
- EASIER to DESCRIBE POPULATION by the % of people AFFECTED
- EASIER to make TREATMENT DECISIONS if population is GROUPED

CONS:
- LOSE INFORMATION
- how to DECIDE CUT OFF? what is abnormal?

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how to DESCRIBE the DISTRIBUTION of CATEGORICAL variables (what to look at)

the category with the LARGEST FREQUENCY (MODAL CATEGORY)
how FREQUENTLY each category was OBSERVED (%)

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how to DESCRIBE the DISTRIBUTION of NUMERICAL variables (what to look at)

SHAPE (do observations cluster in certain intervals?)
CENTRE (where does a typical observation fall?)
VARIABILITY (how tightly are the observations clustering around a centre)

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DESCRIBING CATEGORICAL DATA:

PROPORTION vs PERCENTAGE (how to calculate)

PROPORTION : the NUMBER OF OBSERVATIONS in that category DIVIDED by the TOTAL NUMBER of OBSERVATIONS

PERCENTAGE = PROPORTION X 100

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DESCRIBING CATEGORICAL DATA:

PROPORTIONS and PERCENTAGES are also called … and serve as a way to..

RELATIVE FREQUENCIES

serve as a way to SUMMARIZE the DISTRIBUTION of a CATEGORICAL variable NUMERICALLY

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DESCRIBING CATEGORICAL DATA:

what is the ABSOLUTE CHANGE (and how to calculate)

describes the ACTUAL INCREASE or DECREASE from a REFERENCE VALUE to a NEW VALUE

ABSOLUTE CHANGE = NEW VALUE - REFERENCE VALUE

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DESCRIBING CATEGORICAL DATA:

what is the RELATIVE CHANGE (and how to calculate)

describes the size of the ABSOLUTE CHANGE in COMPARISON to the REFERENCE VALUE
expressed as %

RELATIVE CHANGE = NEW VALUE - REFERENCE VALUE /
REFERENCE VALUE
X100

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DESCRIBING CATEGORICAL DATA:

Percentages are also commonly used to compare 2 numbers. there is REFERENCE VALUE and COMPARED VALUE (compared to reference)

how do you calculate ABSOLUTE DIFFERENCE

ABSOLUTE DIFFERENCE
= COMPARED VALUE - REFERENCE VALUE

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DESCRIBING CATEGORICAL DATA:

Percentages are also commonly used to compare 2 numbers. there is REFERENCE VALUE and COMPARED VALUE (compared to reference)

how do you calculate RELATIVE DIFFERENCE (%)

RELATIVE DIFFERENCE
= COMPARED VALUE - REFERENCE VALUE /
REFERENCE VALUE

X 100

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DESCRIBING CATEGORICAL DATA:

ABSOLUTE vs RELATIVE

ABSOLUTE = difference/change

RELATIVE = Percentage change

eg weight loss 200 kg —> 180 kg
absolute weight loss = 20 kg
relative weight loss = 10% (20/200 x 100)

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DESCRIBING CATEGORICAL DATA:

if a value is 20% MORE than the reference value, it is ….% OF the reference value

120% OF the reference (100 + P)

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DESCRIBING CATEGORICAL DATA:

is a value is 20% LESS than the reference value, it is …% OF the reference value

80% OF the reference (100 - P)

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DESCRIBING NUMERICAL DATA:

what type of graph visualises the DISTRIBUTION of a QUANTITATIVE variable

HISTOGRAM

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DESCRIBING NUMERICAL DATA:

three questions to ask:

does the distribution have a SINGLE MOUND / PEAK (MODE)
what is the SHAPE of the distribution
do the data CLUSTER together, or is there a GAP such that one or more observations noticeably differ from the rest

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DESCRIBING NUMERICAL DATA:

what is UNIMODAL vs BIMODAL distribution

Study These Flashcards

UNIMODAL: SINGLE MOUND/PEAK (mode)

BIMODAL: 2 DISTINCE MOUNDS (modes)

DESCRIBING NUMERICAL DATA:

SHAPE of the distribution can be:

Study These Flashcards

SYMMETRIC: left half is mirror image of right half

SKEWED TO THE LEFT (NEGATIVELY SKEWED) : LONGER LEFT TAIL

SKEWED TO THE RIGHT (POSITIVELY SKEWED): LONGER RIGHT TAIL

DESCRIBING NUMERICAL DATA: is LEFT SKEWED data positive or negative and give an example of a left skew

NEGATIVELY SKEWED longer, skewed left tail eg LIFE SPAN relatively low deaths at young age, most deaths at older age

DESCRIBING NUMERICAL DATA: is RIGHT SKEWED data positive or negative and give an example of a right skew

POSITIVELY SKEWED longer, skewed right tail. starts high and slopes down eg. INCOME most observations at low income, relatively few are rich

DESCRIBING NUMERICAL DATA: in a NORMAL DISTRIBUTION what is the 68-95-99.7 % RULE

- within 1 STANDARD DEVIATION of the MEAN (above/below): 68% of observations - within 2 STANDARD DEVIATIONS of the MEAN: 95% of observations - within 3 STANDARD DEVIATIONS: ALL or NEARLY ALL observations

DESCRIBING NUMERICAL DATA: NORMAL DISTRIBUTION what % of observations are within 1 STANDARD DEVIATION

68%

DESCRIBING NUMERICAL DATA: NORMAL DISTRIBUTION what % of observations are within 2 STANDARD DEVIATIONS

95%

How to calculate MEAN

sum of all values / total number of values

MODE is most often used with which data type

CATEGORICAL DATA

the SHAPE of a distribution INFLUENCES whether the MEAN is LARGER or SMALLER than the MEDIAN how is the MEAN in relation to the MEDIAN in a SYMMETRIC DISTRIBUTION

MEAN = MEDIAN at the middle peak

the SHAPE of a distribution INFLUENCES whether the MEAN is LARGER or SMALLER than the MEDIAN how is the MEAN in relation to the MEDIAN in a LEFT SKEWED DISTRIBUTION

MEAN is SMALLER than the MEDIAN (usually) (median is closer to peak, mean is closer to long tail in unimodal)

the SHAPE of a distribution INFLUENCES whether the MEAN is LARGER or SMALLER than the MEDIAN how is the MEAN in relation to the MEDIAN in a RIGHT SKEWED DISTRIBUTION

MEAN is LARGER than the MEDIAN (usually) (median closer to peak, mean closer to long tail in unimodal)

for SKEWED DISTRIBUTIONS is mean or median PREFERRED

MEDIAN because it better represents what is TYPICAL

is MEDIAN affected by OUTLIERS

RESISTANT to outliers

is MEAN affected by OUTLIERS

YES NOT RESISTANT to outliers

is MODE affected by OUTLIERS

NO outliers do NOT affect mode

what is affected severely by OUTLIERS

RANGE so not very informative MEAN and STANDARD DEVIATION are also sensitive to outliers

STANDARD DEVIATION measures the..

SPREAD of data

STANDARD DEVIATION gives a measure of ... by ...

VARIATION by summarising the deviations of each observation from the mean and calculating an adjusted average of these deviations see calculation

what is the VARIANCE of a set of values

SQUARE of STANDARD DEVIATION variance = s ^2

the LARGER the STANDARD DEVIATION the ...

GREATER the VARIABILITY

when does S = 0 (standard deviation)

when all observations have the same value otherwise s > 0

STANDARD DEVIATION and variance UNITS

same units as the original observations variance has squared units

can OUTLIERS and SKEWS AFFECT STANDARD DEVIATION

NOT RESISTANT strong skewness and outliers can greatly INCREASE S

the INTERQUARTILE RANGE IQR is ..

the DISTANCE between the THIRD QUARTILE and FIRST QUARTILE IQR = Q3 - Q1 gives the spread of MIDDLE 50% of data

how do you calculate when an observation is a POTENTIAL OUTLIER

1.5 X IQR potential outlier if 1.5 x IQR below Q1 or above Q3

PERCENTILES: a pth percentile is a value such that..

p % of the observation falls below or at that value eg. 90th percentile 90% of data falls below that percentile, 10% above

QUARTILES: Q1,Q2,Q3 divide a set of date into ... groups with ...% of the values in each group

4 groups 25%

the 5 NUMBER SUMMARY is the basis of a BOX PLOT and consists of:

- MINIMUM VALUE - Q1 - Q2 (MEDIAN) - Q3 - MAXIMUM VALUE potential outliers marked separately and may be above maximum/ below minimum

what is a Z SCORE and how do you CALCULATE it

the NUMBER OF STANDARD DEVIATIONS that a given value is ABOVE/BELOW the MEAN Z = OBSERVATION - MEAN / STANDARD DEVIATION

a POSTIVE and NEGATIVE Z SCORE indicates...

Positive: Observation is ABOVE the Mean Negative: Observation is BELOW the mean

what does a Z SCORE of 2 say

that the data value is 2 STANDARD DEVIATIONS ABOVE the MEAN (-2 means 2 s BELOW mean)

Z SCORES allows us to tell..

how UNUSUAL an observation is LARGER Z SCORE (positive or negative) = MORE UNUSUAL (-1.3 is more unusual than 1.2)

an observation from a BELL-SHAPED distribution is a POTENTIAL OUTLIER if its Z SCORE is

BELOW - 3 or ABOVE 3 (3 standard deviations out)

3. Medical Statistics intro Flashcards

(56 cards)