EIP Unit 4: Descriptive Statistics and Variability

Descriptive Statistics

Summarizes and describes data characteristics collected by the researchers

Measure of Central Tendency

Identifies the central point around which some of the data tends to cluster

Mean

- represents the average of all the data points

- most commonly used in descriptive statistics

- typically calculated with ratio or interval level data

Median

represents the value that is in the middle of the data points

Mode

represents the value that occurs most frequently in the data set

ratio or interval level data

represents actual quantities of something with discrete increments between each value

Variability

the degree to which scores are distributed around the central value

Standard Deviation

a value that summarizes the average absolute distance of all the individual scores from the mean scores

How is a relative variability expressed as percentage?

coefficient of variation (CV)

Standard Error of Measurement (SEM)

degree of error associated with how much a measurement will vary from the original value each time it is repeated

Standard Error of the Mean (SEM)

provides an assessment of the variation of errors that occurs when repeated samples of a population are drawn

Positively Skewed Distribution

Tail on the right side of the distribution.

What side of the bell curve is the "skew" associated with?

the small tail side

What % falls between 1 SD of the mean?

68%

What % falls between 2 SD of the mean?

95%

Effect Size

descriptive statistics used to provide information about the magnitude of study findings

Which is used to describe nominal level data: mean, median, or mode?

Mode

What measures characterize variablitiy?

range, standard deviation and/or interpercentile range

What does a bigger standard deviation (SD) indicate?

greater variability in the data set

what is the limitation of using range for variability?

it does not provide information about each score

How is the coefficient of variation (CV) calculated?

- dividing the standard deviation (SD) by its mean

- units of measurement cancel out allowing for comparison between or among different types of measures

- typically used to evaluate data that have been collected one time

SEM for a manual goniometer was noted previously to be +/- 4°. Consider the patient who is working to recover knee flexion after an operative procedure. Physical therapists commonly measure the affected joint before and after providing interventions. If the increase in range of motion is between 1° and 4°, then it is likely that _________________ is at work.

standard error of measurement

what does "normally distributed" mean?

- data that create a bell curve

- a predictable % of the scores can be located between 1,2, or 3 SD away from the mean score

bell curve

foundation for a group of tests referred to as parametric statistics

What % fall between 3 SD of mean?

99.7%

- Height

- Weight

- Diagnosis(es)

- Number and/or type of comorbidities

- Health or functional status

- Mental or cognitive status

- Type of assistive device required for mobility

- Number and/or type of medications

- Number and/or type of diagnostic tests

Subject characteristics: clinical information

- Age

- Sex

- race/ethnicity

- Education level

- Socioeconomic status

- Employment status

- Marital status

- Presence and/or type of insurance

Subject characteristics: demographics

differences between or among groups

effect size between 0 and 1

- 0.20

- 0.50

- 0.80

effect size: 0.20

small effect

effect size: 0.50

moderate effect

effect size: 0.80

large effect

differences in relationship between or among variables

effect size between -1 and 1

(0.1 to 0.3 OR -0.1 to -0.3)

(0.3 to 0.5 OR -0.3 to -0.5)

(0.5 or greater OR -0.5 or greater)

effect size 0.1 to 0.3 OR -0.1 to -0.3

small effect

Based on the range of ages in the subject pool, you would expect a plot of these data to create a curve that is:

normally distributed (bell shaped)

3 multiple choice options

The variable "sex" is quantified using which descriptive statistic?

percentile

3 multiple choice options

A sampling distribution data indicates a mean of 63. The SD of the error terms in this sampling distribution is referred to as the:

standard error of the mean

3 multiple choice options

what is the absolute effect size in this study?

1.5

3 multiple choice options

What does the SD of "+/-5" represent?

variability of data points around the mean

3 multiple choice options

The subjects rated their depression using the following scale: 0 = none, 1 = mild, 2 = moderate, 3 = severe. The most frequent response selected was 1 (mild). Which of the following does this result represent?

the mode

3 multiple choice options

z-score

- statistical measure that quantifies the distance between a data point and the mean of a dataset

- expressed in terms of SD

A measure of central tendency is conducted on for a study that investigates pain related to region of the body. Subjects are to choose the region of the body where pain is most prevalent with categories of "head" "Upper trunk" "Lower trunk" "Arms and Hands" and "Legs and feet." What type of central tendency is most appropriate?

Mode

3 multiple choice options

When analyzing scores of a dataset, the frequency of the number 20 was most prevalent. What type of descriptive statistic is indicated?

Mode

3 multiple choice options

What is Type II Error?

Failure to reject a null hypothesis that is actually false (false negative)

3 multiple choice options

Which of the following statistics is a measure of central tendency?

Mean

3 multiple choice options

The results of an ordinal data set are: 5, 5, 10, 15, 10, 5, 20. What is the median?

10

3 multiple choice options

The results of an ordinal data set are: 5, 5, 10, 15, 10, 5, 20. What is the mode?

5

3 multiple choice options

Why are samples important to use within research design?

With enough subjects, results are more generalizable to a population

3 multiple choice options

Where does 95% of the population fall in a normal distribution?

2 SDs above and below the mean

3 multiple choice options

Results of a research study indicate a 0.8 effect size. How would this value be interpreted?

large effect size

3 multiple choice options

A researcher scores students on their ability to pass an exam. Approximately 60% of the scores were >95, 20% of scores were between 70-95, and the remaining 20% were below 70. What kind of distribution would you expect based on these results?

negative Skew

3 multiple choice options