Computers(and softwares) are - Lunds universitet · Measuresof dispersion • Symmetric...

Biostatistics for biomedical professionBIMM34

Karin Källen & Linda Hartman

November-December 2015

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Who needs a course in biostatistics?• - Anyone who uses quntitative methods to interpret biological

processes.

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But really….is it necessary withtodays advanced computersand statistical packages?

Now more than ever!

Computers (and softwares) aredumb like stones!

They just do what we tell themto.

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• An imaginary 2 x 2 table:

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• Correct hypothesis correct basic design

• Poorly specified hypothesis poor design

• Adequate methods

• Sub-optimal methods


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• Porly specified hypotesis poor design



• The draw-back of studieswith these characteristics

will be detected.


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• In a good design the useof non-optimal statistical methods could bias the results but the effects

are seldom strong.


will be detected.


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• Over-belief in sophisticated statistical methods is depressingly

common. Could be difficult to detect.



are seldom strong.


will be detected.

The objectives of the currentcourse in biostatistics• An imaginary 2 x 2 table:

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• Utilization of braincapacity when designing

knowlege of basicstatistical methods

correct interpretation ofthe results.

• Over-belief in sophisticated statistical methods is depressingly

common. Could be difficult to detect.



are seldom strong.


will be detected.

Statistics

Population

Sample

Probability

Inferential statistics

Descriptivestatistics

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Statistics

• Descriptive statistics

Methods to summarize (the variables in) a sample

• Summary measures

• Graphical methods

• Inferential statistics

Methods to learn about the population that the sample is drawn from

• Effect measures (w confidence intervals)

• Tests (ttest chi2-test Mann-Whitney …)

• Regression modeling

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Today:Basic• numerical

summaries of data• graphical

summaries of data

Types of data

Categorical Quantitative

Binary/dichotomous

Nominal Discrete ContinuousOrdinal

2 categories

>=2 categories

Order mattersOnly wholenumbers as values

Data thatcan take anyvalue

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Types of data - exercise

• Categorize the following measurements in binary/nominal/ordinal/discrete/continuous

1. Blood serum bilirubin (μg/ml)

2. Hair colour (Blonde Brunette Redhead and Grays)

3. Vital status (Dead/alive)

4. BMI (kg/m2)

5. # Bacteria in a sample

6. Smoking status (Non-smoker/0-10 cigarettes per day/>10 cigarettes per day)

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Types of data

Binary

Categorical Quantitative

Nominal Discrete ContinuousOrdinal

Discrete variables with only a few possiblevalues are often analysed with the same methods as for ordinal variables.

Discrete variables with many possible valuesare often analysed with the same methods as for continuous variables.

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Summary measures & Graphical presentationChapter 2 & 3 in Norman & Streiner

Chapter 3 & 4 in Kirkwood and Sterne

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Graphical presentation 1: HISTOGRAM

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Split the data in intervals count the number (proportion) in eachinterval:

• The width of the bar tells you the interval

• The height of the bar tells youthe number (proportion) of observations in each interval

Summary measures:• Central Tendency measures

Describe a “center” around which the measurements

in the data are distributed

• Dispersion (or Variability) measures

Describe “data spread” or how far away

the measurements are from the center.

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Central tendency measures• Median

‐ The middle observation if data are sorted

• Mean‐

‐ The sum of the observations devided by the number of observations

• Mode‐ The most frequently occuring value

𝑿 =𝑿𝟏 + 𝑿𝟐 + ⋯+ 𝑿𝑵

𝑵=𝟏

𝑵

𝒊=𝟏

𝑵

𝑿𝒊

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Central tendency - exercise

Exercise 3.2 a-c

• Calculate the mean median and mode of a dataset with the following values: 4 8 6 3 4

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Central tendency cont.

Maternal Vitamin D:• Mean = 2.3• Median= 2.2

Child Vitamin D:• Mean = 1.4• Median = 1.2

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Central tendency

Mean or medianThe choice depends on the distribution of the data:

• Symmetric data • Asymmetric data • Ordinal data

Symmetric distribution Asymmetric distribution(positive skew)

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Central tendency

Symmetric continuous data

Maternal height:Mean=166 cm Median= 166.5 cm

Symmetric data:• Mean = median• Use the mean

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Central tendency

Assymetric continuous data

Vitamin D in child:Mean= 1.4Median= 1.2

Asymmetric data:• Mean ≠ median• Use the median

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Central tendency

Assymetric continuous dataCD16 in % of granulocytes

CD16 in % of granulocytes:Mean= 7.3Median= 4.8

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Central tendency

Ordinal data

(Kasner 2006)

(Hacke et al. 2008)

Use the median!

Exercise:• What is the median in the Alteplase group?• What is the median in the Placebo group?

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Central tendency

Nominal data

Measures of central tendency are not meaningful.

Use number of observations and proportions

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Barchart

Central tendency measures Summary

Type of data Central tendencymeasure

Symmetric data Mean

Asymmetric data Median

Ordinal Median

Nominal -

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Measures of dispersion

• Symmetric distribution – measure based on mean

• Assymetric distribution or ordinal data – measure NOT basedon the mean

A measure of dispersion refers to how closelythe data cluster around the measure of central tendency

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Spread/distributionSmall spread

Big spread

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Descibing the spread of the data

• If we look at the average diviation from the mean:

n

xxi

n

xxi

• The average diviation from the mean equals 0.

xi(xi- 𝐱)

150

152

161

177

155

160

162

158

-9.375

-7.375

1.625

17.625

-4.375

0.625

2.625

-1.375

0

X= 159,375

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Describing the spread of the

dataIf we square every term we solve the problem with 0,

then divide by n to get mean deviation:

n

xxi 2

1

2

n

xxi

To get a better estimate we use n-1 in the denominator

This is called the VARIANCE!

The variance is expressed in cm which is unpractical

since the mean length is expressed in cm2

150

152

161

177

155

160

162

158

-9.375

-7.375

1.625

17.625

-4.375

0.625

2.625

-1.375

(x- 𝐱)2

87.89

54.39

2.64

310.64

19.14

0.39

6.89

1.89

0 483.87

= 60.48

(x- 𝐱)2

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Descibing the spread of the data

1

2

n

xxs

i

By taking the square root of the variance, you

get the standard deviation (standard deviation

= SD) which has the same units as what you

measured

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Ex: Variance = s2 = 60.5 cm2

s = sqrt(60.48) = 7.8 cm

PercentileDescribes how many percent of the observations that lies below ex:

• 10% found below 10th percentile

• 20% found below 20th percentilen etc

Quartile

• Divide data into four equal groups;

• Lower quartile – 25th percentile

• Median – 50th percentile

• Upper quartile – 75th percentile

Q1 = (n+1)/4, Q2 = 2(n+1)/4 (Median), Q3 = 3(n+1)/4 of ordered observations

• Interquartile range (IQR) = The difference between the upper and the lower

quartiles

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Measures of dispersion

• Standard deviation – The mean deviation from the mean value

• Percentiles & quartiles

– Splits the data in fixed proportions

• Range – The difference between min and max

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Measures of dispersion -exercise

Exercise 3.2 d-e

• Calculate the standard deviation and rangefor a dataset with the following values: 4 8 6 3 4

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RobustnessHighly skewed data

Fig 3-10

Measure WITHOUT largestobservation

WITH largestobservation

Mean 3.9 6.1

Median 4 4

Range 5 42

SD 1.4 9.3

QL; QU 3; 5 3; 5

Robust to extreme observations

Sensitive to extreme observations

Use Median & Quartiles for skeweddata

Graphicalpresentation!

+

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Summary: Summary measures

Type of data Central tendencymeasure

Dispersion measure

Symmetric data Mean Standard deviation

Asymmetric data Median Percentiles (e.g. QL andQU )

Ordinal Median Percentiles

Nominal - -

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Graphical presentation 2: BOX-PLOT

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383339N =

Fiskkonsumtionsgrupp

HögMediumLåg

CB

_153 (

ng/g

lip

idvik

t)

3000

2000

1000

0

Low medium high

Fish consumption

Outlier O

Observationes more than 1.5 IQR outside the box

Extreme values *Observations more than 3 IQR outside the box

Lowest ”normal” value

Lower quartile QL

Median

Upper quartile QU

Highest ”normal” value

(Inner fence)

IQR=QU –QL = Box-length

Box-plot - exercise

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• How can you use the boxplot to judge if a distribution is symmetricor asymmetric?

Use the examples in yourdiscussion

Box-plot: Exercise 2

Blood pressure was mesured in 39 women:

BP=138 140 141 142 142 142 142 142 143 143 144 144 144 144 145 147 147 147 147 149 149 150 150 151 152 154 154 157 157 157 158 159 161 162 162 166 167 167 170 mmHG

(Results are sorted)

• Create a boxplot of Blood-pressure

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2013

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Box-plot vs histogram, ex contBlood pressure was measured in 39 women:

BP=138 140 141 142 142 142 142 142 143 143 144 144 144 144 145 147 147 147 147 149 149 150 150 151 152 154 154 157 157 157 158 159 161 162 162 166 167 167 170 mmHG

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10

15

Fre

qu

en

cy

130 140 150 160 170bp_before

median: 149Q1: 143Q3: 157

min: 138max: 170

IQR=Q3-Q1=14

Box-plot cont

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Whats wrong with Figure 3-7?

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Summary:‐ Types of variables (binary/nominal/ordinal/discrete/continuous)- Descriptive statistics

- Central tendency measures (mean median)- Dispersion measures (standard deviation percentiles)

- Graphical presentation- Barplot- Histogram- Boxplot

Wednesday lecture:

Subject Norman &Streiner

Kirkwood and Sterne

Normal distribution 4 5

Population, samples generalisability

6 7

Reference interval, Confidence interval

6 4.5, 6, 7

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