Descriptive statistics part one
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Descriptive Statistics: Part One. Farrokh Alemi Ph.D. Kashif Haqqi M.D. Objectives Definitions Sampling methods Types of variables. Reliability and validity Average Median Mode. Table of Content. Objectives.

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Descriptive Statistics: Part One

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Descriptive statistics part one

Descriptive Statistics: Part One

Farrokh Alemi Ph.D.

Kashif Haqqi M.D.


Table of content

Objectives

Definitions

Sampling methods

Types of variables

Reliability and validity

Average

Median

Mode

Table of Content


Objectives

Objectives

  • Define validity and reliability and explain the role of each in assessing the quality of data.

  • Distinguish among nominal, ordinal, and numeric data, as well as discrete and continuous data.

  • Given a set of numerical data, calculate the mean, median and mode, and state the relative advantages of each as a measure of central tendency.

Back to Table of Content


Definition of variables

Definition of Variables

  • A variable is an attribute of a person or an object that varies.

  • Measurement are rules for assigning numbers to objects to represent quantities of attributes.

Back to Table of Content


What is statistics

What Is Statistics?

  • Statistics is the science of describing or making inferences about the world from a sample of data.

  • Descriptive statistics are numerical estimates that organize and sum up or present the data.

  • Inferential statistics is the process of inferring from a sample to the population.


Definition

Definition

  • Datum is one observation about the variable being measured.

  • Data are a collection of observations.

  • A population consists of all subjects about whom the study is being conducted.

  • A sample is a sub-group of population being examined.


Sampling methods

Sampling Methods

  • Random sample: all subjects have equal chance of inclusion in the study.

  • Systematic sampling: selecting the kth numbered subject.

  • Stratified sample: random sampling within pre-defined groups of subjects.

  • Staged sampling: A small random sample is made and if its results are ambiguous then another larger random sample is collected.

Back to Table of Content


Types of variables

Types of Variables

  • A discrete variable has gaps between its values. For example, sex is a discrete variable. If male is 1 and female is 0, values in between have no meaning.

  • A continuous variable has no gaps between its values. All values or fractions of values have meaning. Age is an example of continuous variable.

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Types of variables continued

Types of Variables (Continued)

  • Nominal scale assign numbers to attribute to name the category. The numbers have no meaning by themselves, e.g. DRG code.

  • Ordinal scale assign numbers so that more of an attribute has higher values, e.g. Severity.

  • In an interval scale the interval between the numbers has meaning, e.g. Fahrenheit scale

  • Ratio scale is an interval scale where zero has true meaning, e.g. Age.


Reliability and validity

Reliability and Validity

Back to Table of Content


To be valid you must have a reliable measure but you can have an invalid measure that is reliable

To Be Valid You Must Have a Reliable Measure. But You Can Have an Invalid Measure That Is Reliable.


Example of reliability calculation

Example of Reliability Calculation

  • Next page shows a table from Hayward, RA, McMahon LF, Bernard AM. Evaluating the care of general medicine inpatients: how good is implicit review? Annals of Internal Medicine, volume 118(7), 1993, pp 550-556.

  • Two reviewers rated the quality of health care delivered in the same case. The Table shows inter-rater reliability.

  • 00000605-199304010-00010.


Inter rater reliability

Inter-rater Reliability


Average

Average

  • The mean, arithmetic average, is found by adding values of the data and dividing by the number of values. The mean of 3, and 4 is 3.5.

  • The geometric average is found by multiplying the values of the data and taking the power of one divided by the number of values. The geometric average of 3 and 4 is square root of 3 times 4.

  • Can you calculate the mean and geometric average for 3, 4, and 5?

Back to Table of Content


Example

Example

  • The mean of 3, 4 and 5 is the sum of these numbers divided by 3.

  • The geometric average of 3, 4 and 5 is the cube root of 3 times 4 times 5. To calculate the cube root in excel you write a formula like: =(3*4*5)^0.33

  • The answer is 3.86. Open Excel and verify that you can do this.


Difference between mean and geometric average

Difference Between Mean and Geometric Average

  • A geometric average is used when averaging probabilities.

  • A mean is used in most other context.


Median

Median

  • The median is the halfway point in a data set.

  • To calculate median arrange data in order. Calculate half of the observations by dividing the number of values by 2 and rounding the value to the lower number. Count half the values and use the next value as median.

Back to Table of Content


Example1

Example

  • The median for age of 7 patients (23, 45, 56, 23, 34, 65, 25) if given by:

    • Order the list of values: 23, 23, 25, 34, 45, 56, 65.

    • There are 7 observations. Divide 7 by two and round to lower number and you get 3.

    • Skip the first 3 and the median is the next number. In this example, 34 is the median.

    • Do this in Excel.


Descriptive statistics part one

Mode

  • The most frequent value observed is the mode.

  • Mode is always an observed value in the data set.

  • To calculate the mode, count the number of times each value is repeated. The value with most repetition is the mode.

  • Do this in Excel.

Back to Table of Content


Example for mode

Example for Mode

  • Age data: 23, 45, 56, 23, 34, 65, 25.

  • 23 is repeated twice.

  • All other values are repeated once.

  • The mode is 23.


Differences in measures of central tendency

Differences in Measures of Central Tendency

  • Mode, median and mean could be three different numbers in asymmetrical distributions of data.

  • For any data set there is only one mean and median but there may be many modes.

  • Median is less influenced by the extreme values than mean.

  • Mean is almost never observed, median is observed in only odd numbered data sets and mode is always observed in the data set.


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