EBP 1 Module 7 - Dichotomous Variables and Measurable Risk

What are the measures of central tendency?

mean, median, mode

Purpose of Mean

Describes the average value of a dataset

When should mean be used?

Interval or ratio data

When researchers want the central value of numerical measurements

How is mean calculated?

Add all values together and divide by the total number of observations.

What does the mean tell us?

Average value of the data

Indicates where scores tend to cluster

What are limitations of the mean?

Sensitive to extreme values (outliers)

Mean shifts toward the tail in skewed distributions

Generally not recommended for ordinal data (such as Likert scales) unless transformed, although researchers sometimes still use it

Purpose of Median

Identifies the middle score.

When to use the median?

Ordinal data

Interval and ratio data

Skewed data

How to calculate the median?

Arrange scores from lowest to highest and locate the middle value.

What does the median tell us?

Middle of the distribution

Better measure of center when outliers exist

What are the limitations of the median?

Does not use every value in the dataset

Less affected by extreme scores than the mean

Purpose of Mode

Identifies the most frequently occurring value.

When to use the mode?

Nominal data

Also appropriate for ordinal, interval, and ratio data

How to calculate the mode?

Determine which value occurs most often.

What does the mode tell us?

Most common observation/value

What are the limitations of the mode?

May not represent the center of the data

Multiple modes or no mode may exist

What are the measures of variability?

range, standard deviation, interpercentile range, coefficient of variation

Purpose of Range

Measures the spread of data.

When to use the range?

Quick summary of variability.

How to calculate the range?

Highest value − Lowest value

or

Report the lowest and highest values

What does the range tell us?

Overall spread of scores

What are the limitations of the range?

Only considers two values

Does not describe how the remaining scores are distributed

Purpose of Standard Deviation (SD)

Measures variability around the mean.

When to use the SD?

Interval and ratio data when researchers want to describe dispersion.

What does the SD calculate?

Calculates the average distance each score lies from the mean.

What information does the SD give us?

Small SD = scores clustered closely/more consistent

Large SD = scores spread farther apart/more variability

Researchers usually report:

Mean ± SD

to provide a complete description of the data.

What are the limitations of SD?

Most meaningful when data are normally distributed

Purpose of Interpercentile Range (IR)

Shows where a score falls compared to the rest of the population.

When to use IR?

Comparing individuals to a reference population.

Example: Growth charts.

How to determine the IR?

Divide data into equal portions (percentiles, quartiles, deciles, etc.).

What does the IR tell us?

Relative standing within a population.

What are limitations of the IR?

Does not describe every individual value.

Purpose of Coefficient Variation (CV)

Compares variability between different measurements.

When to use CV?

Comparing different measurement methods

Comparing repeated measures

How to calculate CV?

CV = SD ÷ Mean

Reported as a percentage.

What information does CV give us?

Relative variability independent of measurement units.

What are the limitations of the CV?

Requires a meaningful mean for interpretation.

What are measurements of error statistics?

SEM, SEM, SEE

Purpose of Standard Error of Measurement (SEM)

Measures error associated with repeated measurements; determines whether observed change exceeds measurement error

When to use SEMeasurement?

Assessing measurement reliability.

How is SEMeasurement calculated?

Calculated from repeated measurements of the same variable.

What information does SEMeasurement give us?

How much measured values vary because of measurement error.

Example from chapter:

Manual goniometer SEM = ±4°

Improvement >4° → likely true change

Improvement 1-4° → may simply be measurement error

Purpose of Standard Error of the Mean (SEM)

Measures sampling variability.

When to use SEMean?

Determining how well a sample mean estimates the population mean.

How is SEMean calculated?

Based on repeated sampling from the same population.

What information does SEMean give us?

Smaller SEM = sample mean is likely closer to the true population mean.

Purpose of Standard Error of the Estimate (SEE)

Measures prediction accuracy.

When to use SEE?

Regression or prognostic studies.

What does the SEE calculate?

Calculates the SD of the distances between observed data points and the prediction line.

What information does the SEE give us?

Smaller SEE = more accurate predictions.

What are the limitations of the SEE?

Only useful when making predictions from regression models.

What are different ways to distribute/describe the distribution of the data?

histograms and line plots, normal, skewed

Purpose of Histograms and Line Plots

Visualize how data are distributed before statistical testing

Why do we use histograms/line plots?

Determine readiness for statistical testing.

What information do histograms/line plots give us?

Researchers can determine if data are:

Normally distributed

Positively skewed

Negatively skewed

What is normal distribution?

Describes data that form a bell-shaped curve and data that is appropriate for many parametric statistical tests

What information does a normal distribution give us?

Predictable percentages of observations lie within:

1 SD

2 SD

3 SD

from the mean.

What are limitations of normal distribution?

Outliers can distort normality.

What does positive skew look like?

Tail extends to the right because of unusually high values.

What are the effects of a positive skew?

Mean pulled right

Median lies between mean and mode

Mode changes the least

What does negative skew look like?

Tail extends to the left because of unusually low values.

What are the effects of a negative skew?

Mean pulled left

Median between mean and mode

Mode least affected

Purpose of Subject Characteristics

Describe who participated in the study.

When to use subject characteristics?

Summarize characteristics using descriptive statistics used in all clinical research.

Examples of subject characteristics

Age

Sex

Race

Weight

Diagnosis

Medications

Comorbidities

Functional status

What information does subject characteristics give us?

Allows clinicians to determine:

Whether subjects resemble their patient

Whether groups were similar at baseline

Whether results are generalizable

Purpose of Frequencies

Describe categorical data and show how common or uncommon a characteristic is

How are frequencies reported?

Counts (n)

Percentages (%)

Purpose of Effect Size

Measures the magnitude of a relationship or treatment effect to show whether a statistically significant finding is also clinically meaningful; how large? how meaningful?

When to use effect size?

When comparing interventions or examining relationships.

What is absolute effect?

Difference between groups

What is relative effect size?

accounts for variability between groups

Relative effect sizes for group differences

0.20 = Small

0.50 = Moderate

0.80 = Large

1 = Very large

Relative effect size for relationships

±0.10-0.30 = Small

±0.30-0.50 = Moderate

≥±0.50 = Large