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Descriptive Statistics Calculations and Practical Application

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Descriptive Statistics Calculations and Practical Application. Part 1. Content. Measurement and Scale of Measurement Descriptive Statistics Central Tendency Variability Box Plot Descriptive Graphics Friendly Introductory Statistics Help (FISH) Hand Calculations.

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### Descriptive Statistics Calculations and Practical Application

Part 1

Content
• Measurement and Scale of Measurement
• Descriptive Statistics
• Central Tendency
• Variability
• Box Plot Descriptive Graphics
• Friendly Introductory Statistics Help (FISH)
• Hand Calculations
Measurement - the assignment of numbers to objects or events according to rules.
• Rules: - provide meaning to numbers

- provide guidelines for assigning numbers

• Measurement Scales
• Nominal
• Ordinal
• Interval
• Ratio
• Operational Definition - specifies the instrument or operations to be used for measuring the variable (gives the rules for assigning numbers).
Measurement Scale
• Process of Assigning numbers that represent attributes or properties
• Scale
• Nominal: Category
• Ordinal: Category Rank (must have at least 5 ranked categories to be considered ordinal)
• Interval: Category Rank Distance
• Ratio: Category Rank Distance Zero Point
Standardized Instruments
• Person made with psychometrics
• have reliability/validity statistics
• meaningful difference
• ability to detect difference (responsiveness)
• interval “like” properties of known standard deviation for a given clinical condition
• Eliminates need to develop own instrument
• May require training for proper administration
• The instrument must be appropriate for:
• the specific research purpose/design
• the specific population
Self Efficacy

Self Esteem

Sickness Impact Profile

Beck Depression Scale

Beck Anxiety Scale

Functional Scales

Fatigue Inventory

Quality of Life

Stroke Impact Scale

DASH

Development

Achievement

Personality

Learning Style

Aptitude

Attitude

Berg Balance Scale

Many Others

Examples (Interval Like) Clinical Tests
Measures

Variable things measured to represent concept studied

• Independent variable (IV), treatment, cause
• Dependent variable (DV), outcome, result
Central Tendency
• Sample Mean:
• Sample Median: Middle Score
• Sample Mode: Most Frequent Score
Visual of Variability with Same Mean Value

Low Variability

High Variability

Measures of Variability

Sample Range: Difference between high and low score

Interquartile Range: Difference between 75th percentile to 25th percentile

Sample Variance:

Sample Standard Deviation:

Standard Error Of The Mean (SEM):

Box Plot Graphic (ideally median is in center of box and whiskers are equal above and below the box)

75 Percentile Upper Hinge (88)

Interquartile Range = 2

25 Percentile Lower Hinge (86)

To open the link, you may have to right mouse, click if you are not in the Powerpoint Show mode.

What is variance and what is standard deviation?
• Variance is the average squared deviation from the mean
• σ2 population variance equals sum (Σ) of squared deviations from the mean divided by N ; it is the average squared deviation from the mean (mean square)
• S2 sample variance equals sum (Σ) of squared deviations from the mean divided by n-1; it is an adjusted average squared deviation from the mean based on a sample measure (still a type of mean square)
• Standard Deviation is the square root of variance
• Population standard deviation, σ is the square root of population variance
• Sample Standard deviation, S is the square root of sample variance

What is Standard Error of the Mean: (error)standard error of the mean is an estimate of the amount that an obtained mean may be expected to differ by chance from the true population mean. http://medical-dictionary.thefreedictionary.com/standard+error+of+the+mean

The larger the n the smaller the SEM. The smaller the Std Dev, the smaller the SEM

Example using Friendly Introductory Statistics Help (FISH), enter data STEP 1 and perform STEPS 2-10 to check your calculations.
If you don’t have access to a PC for FISH here is a good site for descriptive statistics

http://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php

See if you can proceed to the next Excel Workbook to calculate measures of central tendency and variation