Week 12: Statistics, Data Scales, & Descriptive Measures in Research

Statistics

A collection of tools that researchers use when working with data; a branch of applied mathematics used to collect, analyze and interpret numbers.

Statistic

Number that characterizes something about a set of data; typically the average of something.

Statistics and clinical tools features in common

1. Purpose for which design

2. Indications for use

3. Defined method for use

4. Specific information provided when used

5. Limitations beyond which cannot perform properly and/or important caveats

Manual Goniometer

Designed to measure angles; used when a PT needs to quantify joint position & ROM during physical exam; applied with pivot point over axis & arms aligned with relevant bony landmarks; provides information in degrees; has a standard error of measurement plus or minus 4°.

Variable

Characteristics being measured that must vary among individuals/objects; describes something with varying levels of precision; described using 'data'.

variables are described using

data

Dependent Variable

'It depends'; what is being measured, also the outcomes.

Independent Variable

What is being 'manipulated' in the study.

Confounding Variables

Factors that independently affect the relationship between independent & dependent variables; sometimes called 'extraneous'.

Nominal Level Data Scale

Characterized by names, categories, labels; includes dichotomous choices; no rank or known equal distance between categories; exhaustive and mutually exclusive.

Dichotomous

Only two choices for a question, such as yes/no; male/female; agree/disagree; case/control.

Exhaustive

Whole range of possible observations is included.

Mutually Exclusive

Categories don't overlap; every observation only fits into one category.

Ordinal Level Data Scale

Categories ranked or ordered on the basis of operationally defined characteristic or property; classifications incorporate greater and less than.

Likert Scales

Scales containing ranked categories where someone ranks level of agreement to a statement, such as somewhat agree, agree, strongly agree, etc.

Places of Finish in a Race

1st, 2nd, 3rd, etc.; represents ordinal data.

NUMERICAL data scales

Types of data measurement that include interval and ratio levels.

Interval

Has rank order characteristics but also demonstrates known & equal distances or intervals between the units of measurement; not related to a true zero point.

Common examples of interval scale

Cº, calendar year.

Ratio level

Values have rank order, known distance between them, and an absolute zero point.

Examples of ratio level

Age, weight, distance.

Descriptive statistics

Describes data collected by researchers and is used to summarize numerical details about a phenomenon of interest.

Purpose of descriptive statistics

To determine if data are ready for statistical testing in studies of relationships and differences.

Used to provide information about subject and/or environmental characteristics

Measure of central tendency

Refers to measures used to determine the center of data points.

Used to find a single score that is most representative of a single data set

Aka measures of the average value

Measure of central tendency types

mean, median, mode

Mean

Average of all the datapoints; sum of data points divided by number of data points;

mean influenced by

extreme values in data.

Median

Score that is in the middle of the data points (50% above; 50% below); not influenced by extreme values.

Mode

Score that occurs most frequently in a data set.

Frequency

To count things such as numbers of subjects, their characteristics, etc.

Frequency indications for use

In epidemiological papers, to describe phenomena and their characteristics

In all other papers, to describe subjects, test results and or outcomes

Frequency provides

numbers and percentages

mean purpose

• Describe the average of a data set

• Summarise the typical participant response or data when the data is evenly (normally) distributed

Mean in epidemiological papers

To describe phenomena and their characteristics.

Mean in other papers

To describe subjects, test results, and their outcomes.

Mean can be used with what levels of data

Ratio, interval and ordinal

mean info provides

average of all numbers in a data set

Limitations of mean

Influenced by extreme data values because all of the data points are used in the calculation.

Median in epidemiological papers

To describe phenomena and their characteristics.

Median in other papers

To describe subjects, test results, and their outcomes.

median can be used with

ratio, interval and ordinal data

Mode indications

In epidemiological papers, to describe phenomena and their characteristics

In all other papers, to describe subjects, test results and their outcomes

Mode can be used with

any level of data

can have more than 1

mode

range purpose

to describe variability

range can be used with

ratio, interval, ordinal data

limitations to range

Affected by extreme values, does not use all data

Range

The highest and lowest data values or the difference between them.

range indications for sue

Often used to supplement info about the mean or median

Standard Deviation purpose

Describes variability in the data set around the mean.

SD indications for use

In papers that are purely descriptive in nature

In all other papers, to describe subjects, test results and outcomes

SD levels

calculated as deviation of data from the mean

When data are normally distributed

68% of data will lie within 1SD SEM SEE

96% of data will lie within 2 SD SEM

99% of data will lie within 3 SD SEE

Interpercentile range purpose

To describe the variability in a data set

Interpercentile range

indications for use

to supplement the median

Interpercentile range levels of data

May be used with any level of data

Division points may be tentiles, quartiles

Interpercentile range key point

Not greatly influenced by extreme values

Interpercentile Range

Ranges that contain a certain % of the scores (e.g., 25th percentile).

Coefficient of Variation purpose

To measure the variation relative to the mean

Coefficient of Variation indications for use

To compare variation among scored collected from tools with different units of measurement

To compare variation among repeated scores from the same tool

CoV calculated as

Calculated as a ratio of the SD over the mean

Skewness purpose

To describe the shape of the curve created by the data points.

Skewness indication for use

To determine whether the values in the data set are normally distributed

Skewness calculated as

part of the summary description of data

skewness occurs when

there are outliers in the set

Standard Error of Measurement purpose

To determine the variability in repeated measures of an individual.

Standard error of measurement indication for use

To differentiate between true change and error when measures are repeated in a study

SEM (both) method of use

Estimated mathematically because it is logistically impractical to perform enough repeated measures to obtain this value

standard error of measurement info provided

SD of measurement errors

Standard Error of the Mean purpose

To determine the variability in repeated samples from the same population.

Standard Error of the Mean indications for use

May be reported in addition to or instead of the standard deviation

Standard Error of the Mean info provided

Standard deviation of the population for sampling distribution

Standard Error of the Estimate purpose

To determine the variability around a line through a collection of data points.

Standard Error of the Estimate indications for use

Studies about prognostic factors

Standard Error of the Estimate method of use

Calculated as distance of the data from the line

Standard Error of the Estimate info provided

Summary of the deviation of data points from the line

Effect Size Purpose

To determine the extent of a relationship between or difference between variables.

effect size indications for use

Studies about prognostic factors, interventions and outcomes

effect size methods for use

Used with ratio or interval level measures

effect size info provided

Magnitude of a relationship or a difference

absolute effect size

uses the raw scores obtained

relative effect size

interpretations of effects are often sized relative to our expectations (seen as big if they affirm new hypothesis or small if they reinforce old theories)

measures of variability types

range, variance, standard deviation CV

Measures of Variability

Describes how much individual values vary from the mean or average.

SD describes

how much individual values vary from the mean or average;

How far away from the mean does each individual score lie

Variance

Average of the square deviations of the mean.

Percentiles

Ranges with certain % of scores.

Standard Deviation (SD)

Square root of the variance.

Larger SDs

Indicate values very scattered around the mean.

Calculated as Deviation

Calculated as deviation of data from the mean.

68% of Data

Will lie within 1 SD when data are normally distributed.

96% of Data

Will lie within 2 SD when data are normally distributed.

99% of Data

Will lie within 3 SD when data are normally distributed.

Standard Deviation in Units

Value of SD is in the original units of measurements.

Relative Variability

Divides SD by its mean for a measure of relative variability (ratio).

Smaller SD

Means values are closer to the average.

Larger SD

Means the values are farther away from the average.

Outlier

Data value that is very different from the rest of the values.

Box and whiskers chart

Boxes represent the 25th-75th percentile; line in middle of a box represents the 50th percentile.

Whiskers

Represent range of values not including outliers.