Post on 22-Aug-2014
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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