Medical Statistics Part-I:Descriptive statistics
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This document provides an overview of descriptive statistics used in cardiovascular research. Descriptive statistics summarize and describe data through calculations of central tendency, dispersion, and shape. They are used to analyze variables that are discrete (categorical nominal and ordinal) or continuous. Common descriptive statistics include mean, median, mode, range, variance, standard deviation, quartiles, interquartile range, skewness, and kurtosis. Graphs such as dot plots, box plots, and histograms can complement tabular descriptive statistics to display patterns in the data. Univariate analysis examines one variable at a time to understand its distribution, central tendency, and dispersion.
![KEYWORDS
Population[Orientation]
SAMPLE[Representive]
VARIABLES[Characteristics]
PARAMETERS[quantities that define a statistical model]](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/descriptivestatistics-140213120407-phpapp02/85/Medical-Statistics-Part-I-Descriptive-statistics-6-320.jpg)
![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](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/descriptivestatistics-140213120407-phpapp02/85/Medical-Statistics-Part-I-Descriptive-statistics-18-320.jpg)
![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)](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/descriptivestatistics-140213120407-phpapp02/85/Medical-Statistics-Part-I-Descriptive-statistics-20-320.jpg)
![INTERQUARTILE RANGE[IQR]
It is a single number
defined as IQ of RQ-3Q1
Variance and standard deviation
are affected (increased) by the presence of extreme observations,
the IQR is not; it is robust](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/descriptivestatistics-140213120407-phpapp02/85/Medical-Statistics-Part-I-Descriptive-statistics-21-320.jpg)
![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](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/descriptivestatistics-140213120407-phpapp02/85/Medical-Statistics-Part-I-Descriptive-statistics-22-320.jpg)
![GRAPHS[complementary to
tabular]](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/descriptivestatistics-140213120407-phpapp02/85/Medical-Statistics-Part-I-Descriptive-statistics-26-320.jpg)
![Correlation[r] is a single 1 number that shows
the degree of relationship between 2
variables
-1 to +1](https://izqule7twkl7vq3ljkxejyz-s-a2157.bj.tsgdht.cn/descriptivestatistics-140213120407-phpapp02/85/Medical-Statistics-Part-I-Descriptive-statistics-32-320.jpg)
Medical Statistics Part-I:Descriptive statistics
- 1. Descriptive Statistics in cardiovascular research MOST SIMPLE WAY OF DATA HANDLING
- 2. Statistics in general SUBCLAUSE USED FOR Collection Analysis Interpretation Presentation Reasoning Discussion Calculation Scientific Inference
- 4. 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
- 5. 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
- 6. KEYWORDS Population[Orientation] SAMPLE[Representive] VARIABLES[Characteristics] PARAMETERS[quantities that define a statistical model]
- 7. DISPLAY OF DESCRIPTIVE STATISTICS TABLES GRAGHS CHARTS CIRCLE DOT PLOTS BOX-AND-WHISKER PLOTS SCATTERPLOT SURVIVAL PLOTS BLAND-ALTMAN PLOTS
- 8. TABLE-1
- 10. Variables: DISCRETE CONTINUOUS Only certain values (fixed and readily Countable Examples of discrete variables commonly encountered in cardiovascular research include species, strain, racial/ethnic group, sex, education level, treatment group, hypertension status, and New York Heart Association 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
- 11. Discrete variables (categorical) NOMINAL (UNORDERED) ORDINAL (ORDERED) Take values such as yes/no, Human/dog/mouse, female/male, treatment A/B/C; a nominal Variable that takes only 2 possible values is called binary. One May apply numbers as labels for nominal categories, but there Is 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
- 12. Categorical A categorical variable (sometimes called a nominal variable) is one that has two or more categories, but there is no intrinsic ordering to the categories. For example, gender is a categorical variable having two categories (male and female) and there is no intrinsic ordering to the categories. Hair color is also a categorical variable having a number of categories (blonde, brown, brunette, red, etc.) and again, there is no agreed way to order these from highest to lowest. A purely categorical variable is one that simply allows you to assign categories but you cannot clearly order the variables. If the variable has a clear ordering, then that variable would be an ordinal variable, as described below.
- 13. Ordinal An ordinal variable is similar to a categorical variable. The difference between the two is that there is a clear ordering of the variables. For example, suppose you have a variable, economic status, with three categories (low, medium and high). In addition to being able to classify people into these three categories, you can order the categories as low, medium and high. Now consider a variable like educational experience (with values such as elementary school graduate, high school graduate, some college and college graduate). These also can be ordered as elementary school, high school, some college, and college graduate. Even though we can order these from lowest to highest, the spacing between the values may not be the same across the levels of the variables. Say we assign scores 1, 2, 3 and 4 to these four levels of educational experience and we compare the difference in education between categories one and two with the difference in educational experience between categories two and three, or the difference between categories three and four. The difference between categories one and two (elementary and high school) is probably much bigger than the difference between categories two and three (high school and some college).
- 14. Ordinal In this example, we can order the people in level of educational experience but the size of the difference between categories is inconsistent (because the spacing between categories one and two is bigger than categories two and three). If these categories were equally spaced, then the variable would be an interval variable
- 15. Continuous variables Continuous variables can have an infinite number of different values between two given points. As shown above, there cannot be a continuous scale of children within a family. If height were being measured though, the variables would be continuous as there are an unlimited number of possibilities even if only looking at between 1 and 1.1 meters.
- 16. 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
- 17. Collection Formal Sampling Recording Responses To Experimental Conditions Observing A Process Repeatedly Over Time
- 18. 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
- 19. 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.
- 20. 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)
- 21. INTERQUARTILE RANGE[IQR] It is a single number defined as IQ of RQ-3Q1 Variance and standard deviation are affected (increased) by the presence of extreme observations, the IQR is not; it is robust
- 22. 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
- 23. 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
- 27. DOT PLOT of Continuous variable(BMI) The dot plot is a simple graph that is used mainly with small data sets to show individual values of sample data in 1 dimension
- 28. 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 that the 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 away from the box, and they must end at an observed value.Beyond the whiskers are outliers, identified individually by symbols such as circles or asterisks
- 31. Univariate Analysis: Look one variable at a time for 3 features Distribution Central Tendency Dispersion Of Frequency in % /bar diagram/histogram Mean Median Mode Range Standard Deviation Variance
- 32. Correlation[r] is a single 1 number that shows the degree of relationship between 2 variables -1 to +1
- 34. r is also called Karl Pearson’s coefficient of correlation
- 35. It is just beginning With best wishes