MD Paediatrics (Part 1) - Overview of Basic Statistics

Basic Statistics
Overview for
MD Paediatrics (Part 01)
2014

Contents
• Statistics – Introduction
• Variables & their representations (Tables,Graphs)
• Measures of Central tendency & Dispersion
• Normal Distribution
• Tests of Significance
• Sampling
• Hypothesis testing
– Null hypothesis
– Alternative Hypothesis
– Type 1 & 2 errors
• Study Designs
• Epidemiology

© bdwjayamanne@gmail.com/djayamanne@yahoo.com
01.Statistics
• What is Statistics (සසසස‍සසසස) ?
The science of collection, analysis, and making
inference / conclusion of data.
• Collection
• Analysis
• Making Inference
(* the word statistic(සසසස‍සසසසස) has a different
meaning)

Variable:
A quantity that vary from one unit to another ,the quantity
referred as a variable.
Eg: Height ,Weight,Blood Pressure, Crop yield -one value is no
sufficient
Discrete - Fixed number of possibilities (Blood Group)
Continuous - Infinite number of possibilities (BP) -even within a
finite interval
02.Variables and Constants

Constant
Constant:
Opposite of a variable .If the quantity is not vary from one
unit to another that quantity is referred as a constant.
Eg. Density of an element - one value is sufficient

Levels of measurement in statistics
1. Nominal scale
a. Only indicates category
b. Eg.Religion -Buddhism ,Christianity,Hindu
2. Ordinal scale
a. in addition to the category,allows cases to be ordered by degree
according to the measurement
b. Eg: very poor,Poor,OK,Good,Excellent
3. Interval scale
a. Has units measuring intervals of equal distance between values -
measured in linear scale
b. No true zero
c. Eg: temperature in Celsius ,Date ,Latitude
4. Ratio scale
a. Has true zero
b. Not measured in linear scale

• Four (4) major types of Graphs
– Bar (Pareto Diagram)
– Pictorial
– Pie (circle)
– Line
• Other types
– Histogram(Special Bar graph)
– Stem and Leaf Plot
– Dot Plot (Stem and Leaf + Histogram)
– Box and Whisker Plot
– Scatter plot
Graphs

http://www.sophia.org/tutorials/types-of-graphs
Graphs

Pictogram
Graphs

Box and Whisker plot
Median
Q1
Q3
Box
Whiskers
1. the minimum and
maximum of all of the
data
2. the lowest datum still
within 1.5 IQR the lowest
datum still within
1.5 IQR of the lower
quartile, and the highest
datum still within
1.5 IQR of the upper
quartile(Tukey Box plot)
3. one standard deviation
above and below the
mean of the data
4. the 9th percentile and the
91st percentile
5. the 2nd percentile and
the 98th percentile.

Scatter plot
• 2 variables
Dependent Variable
(y)
Independent Variable
(x)

04.Measures of Central Tendency & Dispersion
Measures of Centre (Central tendency):
1.Mean
2.Median
3.Mode
Measures of Dispersion
1.Range
2.Variance
3.Standard deviation
4.Absolute deviance
5.Quantiles

1.Mean
i) Arithmetic mean
Simply the average
Eg :Average speed
Distance x 60km/h
Distance x 30km/h
Total Distance 2x
Speed = Distance/Time
ii) Harmonic Mean(H)
Suitable for Moving objects Speeds
iii) Geometric Mean(G)
Eg : Calculate average for the rates

2.Median
Value of the middle observation after arranging the data set
to an order (ascending & descending)
Eg:
1)3,8,5 ,Median = 5
2) If 25 observations , Median = Value of the 13 th
observation
Location of the median = (n+12)
Eg: n=24
Median =24+12=12.5 (Average of the 12th and 13th
observation)
Advantages
• Not sensitive for outliers
(Outliers - observations highly deviated from the rest)

3.Mode
Most frequent value of a data set
eg:
2,5,11,5,8,8 - Mode 8
2,5,11,5,8,8,5 - 2 Modes 8 & 5

Measures of Dispersion
1.Range
2.Variance
4.Absolute deviance
5.Quantiles

1.Range
Difference between maximum and minimum .
• Positive value (+)
• No idea about minimum and maximum
2.Absolute deviance
3.Variance
Average of squared deviation of an observation from the mean.
Population (As an estimator of variability)
No variability =0 ,Small variability = small , Large variability
=Large
units Squared of the original unit, Limitation - Unit (Scale)
dependent
SD = Variance ^1/2

5. Quantiles(සසසස)
Dividing ordered data into q essentially equal-sized data subsets is the motivation for
q-quantiles
Eg:
• Median - 2nd quartile is called the median
• Quartiles - 4 quantiles (Q)
• Percentiles -100 quantiles (P)
• Deciles - 10-quantiles are called deciles (D)
Quartiles(Q) (සසසසසසස)
Q1 - 1st quartile
Q2 - 2nd quartile/Median
Q3 - 3rd quartile
Q1 is the value of the observation ,divide the data set 25% to the left and 75% on to
the right.
Q2 Value of the observation divide the data set 50% to the both sides
Inter Quartile range
IQR = Q3-Q1

05.Normal Distribution
Most important distributions in Statistics
1.Normal Distribution
2.Poisson Distribution
3.Binomial Distribution
Normal Distribution(s)
A. Normal Family of Distributions
B. Standard Normal Distribution
Estimates
Mean Variance (standard deviation)
Skewness Kurtosis

Normal Family of Distributions
Different means
SD Constant
Different SD
Mean Constant

Mean and SD both different

Normal Family of Distributions
• Mean = Median = Mode
• 68% of Data between -1SD and -1SD
• 95% of Data between -2SD and +2SD
• 99.7% of Data between -3SD and +3SD

Skewness
simply
Skewness = (Mean - Mode ) / SD
Positively /Right Skewed
Right tail is longer
Mode < Mean < Median
More than 50% data > Mean value
Negatively /Left Skewed
Left tail is longer
Median <Mean Mode
More than 50% data < Mean value

Multimodal Distributions
Bimodal Distributions - 2 modes

Standard Normal Distribution
Z

• Mean = 0
• Variance = SD = 1
• Skewness = 0
• Kurtosis =0
Standard Normal Distribution

Parametric VS Nonparametric
General rule
• Measurement Scale Nominal or Ordinal usually
Nonparametric Tests used
• Interval & Ratio-Scale variables - Parametric test
• Test of Normality
– Shapiro-Wilk Test
– Kolmogorov-Smirnov Test
– Anderson-Darling Test
– Chi square Test

05.Parametric Tests VS Nonparametric Tests
Mean
SD
Pearson Correlation
One sample t test
Independent Sample t test
Related Sample t test
One Way ANOVA
Two Way ANOVA
Median
IQR / Range
Spearman Correlation /
Kendall's Tau
Sign Test
Mann-Whitney U Test / Rank
Sum test
Wilcoxon sign ranked test
Kruskal Wallis Test
Friedmann Test / Quade test
Parametric Nonparametric

06.Sampling
a.Probability sampling
1. Every element has a known nonzero
probability of being sampled and
2. involves random selection at some point.
i. Simple Random Sampling
a. With replacement
b. Without replacement
ii. Systematic Sampling
iii. Stratified Sampling
iv.Probability Proportional to Size Sampling
v. Cluster or Multistage Sampling

b.Non-probability Sampling
• Convenience, Haphazard or Accidental Sampling
• The sample is composed of whatever persons can be most easily
accessed to fill out the survey
• Quota Sampling /ad hoc quotas
• The sample is designed to include a designated number of people with
certain specified characteristics. For example, 100 coffee drinkers. This
type of sampling is common in nonprobability market research
surveys
• Purposive Sampling or Judgmental sampling.
– A researcher decides which population members to include in the sample
based on his or her judgement. The researcher may provide some
alternative justification for the representativeness of the sample
• Snowball sampling(Respondent Driven Sampling):
Eg :Social Networks
– Often used when a target population is rare, members of the target
population recruit other members of the population for the survey
• Deviant Case (Special case of Purposive Sampling)
• Case study
Sampling

07.Hypothesis Testing
Goal: Make statement(s) regarding unknown
population parameter values based on sample
data
Elements of a hypothesis test:
*Null hypothesis - Statement regarding the value(s) of
unknown parameter(s). Typically will imply no association
between explanatory and response variables in our applications
(will always contain an equality)
Alternative hypothesis - Statement contradictory to the null
hypothesis (will always contain an inequality)

What to test
Effect or Difference we are interested in..
*Difference in Means or Proportions
*Odds Ratio (OR)
*Relative Risk (RR)
*Correlation Coefficient
*Clinically important difference
*Smallest difference considered biologically or
clinically relevant

Null Hypothesis
*Usually that there is no effect
*Mean = 0
*OR = 1
*RR = 1
*Correlation Coefficient = 0

Alternative Hypothesis
*Contradicts the null
*There is an effect
*What you want to prove ?

Null hypothesis
(H0) is true
Null hypothesis
(H0) is false
Reject null
hypothesis
Type I error
False positive
Correct outcome
True positive
Fail to reject null
hypothesis
Correct outcome
True negative
Type II error
False negative

Eg Mean Birth Weight
National =2.5kg | Sample 2.6 kg
Null hypothesis = H0 = There is no difference between
sample mean and National (population) mean
Alternate Hypothesis
• Ha = Sample mean is different from National Mean
Or
• Ha1= Sample mean is higher than national mean
• Ha2= Sample mean is lower than national mean

Descriptive Analytical
•Case Report
•Case Series
•Cross – Sectional D.
•Ecological
•Prevalence
/Surveillance
•Cohort Studies
•Case Control(Trohoc)
•Cross –Sectional Analytical
Randomized
Non-
Randomized
08.

LANCET
2002:359:57 -

Observational - Descriptive
• Frequency, Natural History, Possible
determinants
• No comparisons groups
• Useful for hypothesis generation about
causal associations
• E.g.:
– Case Reports (SLJOP) –www.sljol.info
– Case series
– Descriptive Cross Sectional
– Ecological/Population – Correlations

• Always have a comparison/control group
• Allows determination of causal association
• Hypothesis testing
• E.g.
– Cohort study
– Case Control Study (Trohoc Study)
– Analytical Cross Sectional Study
Observational - Analytical

LANCET
2002:359:57 -
61

Cohort Studies
• Types
– Prospective
– Retrospective
– Ambi-directional

Cohort studies - Advantages
• Temporality can be established
• Incidence can be calculated.
• Several possible outcome related to exposure
can be studied simultaneously.
• Provide direct estimate of risk.
• Since comparison groups are formed before
disease develops certain forms of bias can be
minimized like misclassification bias.
• Allows the conclusion of cause effect
relationship

Cohort studies - disadvantages
• Large population is needed
• Not suitable for rare diseases.
• It is time consuming and expensive
• Certain administrative problems like loss of
staff, loss of funding and extensive record
keeping are common.
• Problem of attrition(drop outs) of initial
cohort is common
• Study‍itself‍may‍alter‍people’s‍behavior‍

Case Control Studies

Case Control Studies - Advantages
• Quick, less expensive
• Well suited for disease with long latent
period
• Optimal for evaluation of rare diseases
• Can study etiological factors for a single
disease
• Requires small sample than a cohort study
• No attrition (drop outs) problem
• Ethical problems are minimal, no risk to
subjects

Case Control Studies - Disadvantages
• More prone to bias -Relies on records or
recall of exposure information
• Validation of exposure data often difficult
• Selection of appropriate control group may be
difficult
• Inefficient for evaluation of rare exposure
• Cannot directly measure incidence, can only
estimate relative risk
• Study of natural history of disease not
possible

• Data Analysis / Presentation - Basic
– Rates
– Proportions with 95% Confidence Interval
– Percentages
– Odds Ratio (95% CI) – Case control & Cross sectional
– Relative Risk (95% CI)
– Attributable Risk/ Risk difference
– Attributable Risk ratio / Aetiologic Fraction Cohort
– Population Attributable risk
– Number Needed to Treat /Harm

Prevalence
The proportion of a population found to have a condition /
disease
1.Point Prevalence
2.Period Prevalence
3.Lifetime Prevalence
09.Epidemiology - Introduction to terms

Incidence
The number of new cases during some time
period
1.Incidence Proportion /Cumulative Incidence
2.Incidence (Density)Rate/ Person-time
Incidence rate

Thank you

MD Paediatrics (Part 1) - Overview of Basic Statistics

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MD Paediatrics (Part 1) - Overview of Basic Statistics