Descriptive Statistics in cardiovascular research MOST SIMPLE WAY OF DATA HANDLING

Statistics in general

SUBCLAUSE USED FOR

CollectionAnalysis InterpretationPresentation

Reasoning Discussion Calculation Scientific

Inference

STATISTICS IN GENERAL

DESCRIPTIVE INFERENTIAL

Descriptive Statistics

Data analysis begins with calculation of descriptive statistics for the research variables

These statistics summarize various aspects about the data, giving details about the sample and providing information about the population from which he sample was drawn

Each variable’s type determines the nature of descriptive statistics that one calculates and the manner in which one reports or displays those statistics

Simply to describe what's going on in our data

inferential statistics

Trying to reach conclusions that extend beyond the

immediate data alone=INFER We use inferential statistics to try to infer from the

sample data what the population might think/experience Make judgments of the probability that an observed

difference between groups is a dependable one or one that might have happened by chance in this study

Make inferences from our data to more general conditions

http://www.socialresearchmethods.net/kb/statinf.php

KEYWORDS

Population[Orientation] SAMPLE[Representive] VARIABLES[Characteristics] PARAMETERS[quantities that define a statistical model]

DISPLAY OF DESCRIPTIVE STATISTICS

TABLES GRAGHS CHARTS CIRCLE DOT PLOTS BOX-AND-WHISKER PLOTS SCATTERPLOT SURVIVAL PLOTS BLAND-ALTMAN PLOTS

TABLE-1

Variables:

DISCRETE CONTINUOUS Only certain values (fixed and

readily Countable Examples of discrete variablescommonly encountered in cardiovascular research includespecies, strain, racial/ethnic group, sex, education level,treatment group, hypertension status, and New York HeartAssociation class.

Infinite number of values Fixed intervals between adjacent

values They can be manipulated

mathematically, taking sums and differences Age, height, weight, blood

pressure, measures of cardiac structure and function, blood chemistries, and survival time

Discrete variables (categorical)

NOMINAL (UNORDERED) ORDINAL (ORDERED)Take values such as yes/no,Human/dog/mouse, female/male, treatment A/B/C; a nominalVariable that takes only 2 possible values is called binary. OneMay apply numbers as labels for nominal categories, but thereIs no natural ordering

Take naturally ordered values such as New York Heart Association class (I, II,III, or IV), hypertension status (optimal, normal, high-normal,or hypertensive), or education level (less than high school,high school, college, graduate school

Descriptive statistics for Discrete variables

Absolute frequencies (raw counts) for each category Relative frequencies (proportions or percentages of the total Number of observations) Cumulative frequencies for successive categories of ordinal

variables

Collection

Formal Sampling Recording Responses To Experimental Conditions Observing A Process Repeatedly Over Time

Descriptive statistics for continuous variables

Location statistics MEAN MEDIAN MODE, QUANTILES Dispersion statistics[CENTRAL TENDENCY] VARIANCE= STANDARD DEVIATION=S=√S² RANGE INTERQUARTILE RANGE Shape statistics SKEWNESS KURTOSIS

ROBUST

MEDIAN is robust :Not strongly affected by outliers or by extreme changes to a small portion

MEAN is sensitive (not robust) to those conditions MODE is robust to outliers, but it may be affected by data

collection operations, such as rounding or digit preference, that alter data precision.

QUANTILES

Quintiles combine aspects of ordered data and cumulative frequencies

The p-th quantile (0≤p≤1) 100p is an integer, the quantiles are called percentiles Median, or 0.50 quantile, is the 50th percentile, the 0.99 quantile is

the 99th percentile Three specific percentiles are widely used in descriptive statistics,

[100p is an integer multiple of 25] Q1first quartile (25th percentile, 0.25 quantile) Q2second quartile (50th percentile, 0.50 quantile), median Q3third quartile (75th perce ntile,0.75 quantile)

INTERQUARTILE RANGE[IQR]

It is a single number defined as IQ of RQ-3Q1 Variance and standard deviationare affected (increased) by the presence of extreme observations,the IQR is not; it is robust

SKEWNESS[skewness coefficient]

For a given data Distribution is symmetric (skewness=0) A more pronounced tail in 1 direction than the other (left tail, skewness<0; right tail, skewness>0) If skewness=0, the mean= median Right- (left-) skewed distribution has its mean value greater (less than) the median

Kurtosis

a measure of the “peakedness” of a distribution A gaussian distribution (also called “normal”) with a bell-shaped

frequency curve has kurtosis 0 Positive kurtosis indicates a sharper peak with longer/fatter tails

and relatively more variability due to extreme deviations Negative kurtosis coefficient indicates broader shoulders with

shorter/thinner tails

GRAPHS[complementary to tabular]

DOT PLOT of Continuous variable(BMI)

The dot plot is a simple graph that is usedmainly with small data sets to show individual values of sample data in 1 dimension

Box-and-whisker plot= box plot graph

Graph displays values of quartiles (Q1, Q2, Q3) by a rectangular box. The ends of the box correspond to Q1 and Q3, such thatthe length of the box is the interquartile range(IQRQ3Q1). There is a line drawn inside the box at the median, Q2, and there is a “” symbol plotted at the mean.Traditionally, “whiskers” (thin lines) extend out to, at most,1.5 times the box length from both ends of the box: they connect all values outside the box that are not 1.5 IQR awayfrom the box, and they must end at an observed value.Beyond the whiskers are outliers, identified individually by symbols such as circles or asterisks

Univariate Analysis: Look one variable at a time for 3 features

Distribution Central Tendency Dispersion

Of Frequency in %/bar diagram/histogram

Mean Median Mode

RangeStandard Deviation Variance

Correlation[r] is a single 1 number that shows the degree of relationship between 2 variables

-1 to +1

r is also called Karl Pearson’s coefficient of correlation

It is just beginning

With best wishes