OT 667

1
OT 667

• Levels of Measurement, Descriptive Statistics,
  and Measures of Relationship

2
Why do we measure things?
3
In order to

• Describe
• Compare
• Categorize levels of function
• Document improvement
• Demonstrate efficacy

4
One way to manipulate numbers

• Statistics (measures of a sample) or
• Parameters (measures of a population) can
• be used to organize, summarize and
• analyze measurements to give information

5
Levels of Measurement

• Nominal categorical variables (gender, hair
  color, ethnicity)
• Ordinal rank order of observation (muscle
  testing, pain levels, military rank)
• Interval equal intervals between scores but no
  true zero (calendar years, degrees centigrade or
  Fahrenheit
• Ratio true equal intervals between units,
  measured from true zero (distance, age, time,
  weight, strength, blood pressure)

6
Kinds of Statistics

• Descriptive statistics the use of measures to
  describe aspects of a sample or population
• Inferential statistics the process of drawing
  inferences/making judgments about samples that
  are generalized to the larger population

7
Descriptive Statistics

• Measures of central tendency
• Measures of variability
• Relationship to the normal curve

8
Measures of Central Tendency

• Mode - the most frequently occurring score in a
  distribution
• Median the exact middle score in a distribution
• Mean the average score of a distribution

9
Levels of Measurement and Measures of Central
Tendency

• Mode Median Mean
• Nominal Ordinal Interval
• Ordinal Interval Ratio
• Interval Ratio
• Ratio

10
Measures of Variability

• Range the difference between the highest and
  lowest scores in a distribution
• Variance the mean of the squared deviation
  scores
• Standard Deviation the square root of the
  variance most consistently used variation score

11
Correlation Coefficients
12
The Role of Correlational Studies

• Exploration to set up future studies
• Preliminary research to experimental studies
• Commonly used in cross-sectional research
• Establishment of reliability

13
Meaning of correlation

• Two variables have a relationship
• The nature of the relationship is unclear
• A relationship DOES NOT imply causality
• Further investigation of the relationship may
  reveal it is spurious
• High correlations depend on high levels of
  variability

14
Variable Independence

• Correlation coefficients should only be
  calculated between variables that are independent
  of each other
• This means that you could not correlate variables
  such as number of bites eaten in a meal and
  ability to swallow, since the ability to swallow
  is a component of the number of bites you eat in
  a meal

15
Which means.

• If you have two variables and measure them in a
  population that is not heterogenous and both
  levels are high, the correlation will be low
• This is called restriction of the range
• The formula for calculating correlation
  coefficients is based on the variability of the
  scores on the different variables, so without a
  range of scores in a sample, the coefficient will
  be low

16
Magnitude and Direction

• Correlations are within a range of 1 to 1
• Variables that are positively correlated are
  highly related variables that have high scores
  correlate with each other variables that have
  low scores correlate with each other
• Variables that are negatively correlated indicate
  that those variables that score high correlate
  with those variable that score low.

17
Venn Diagrams..
18
The nature of relationships

• Correlation coefficients describe linear
  relationships (ROM/muscle testing)
• Curvilinear relationships (gross motor skills
  over the lifespan) are not well described by
  correlations

19
(No Transcript)
20
Prediction from correlations

• Correlations are used with other statistical
  procedures for the purpose of prediction
• A study including a number of variables first
  identifies those with strong correlations
• Follow-up analyses are done using a procedure
  called regression, which can predict certain
  behaviors based on the strength of the
  relationship between variables

21
Correlation Coefficients

• Pearsons used with continuous variables on an
  interval or ratio level
• Spearmans used with ordinal level data
• Phi coefficient used with 2 dichotomous
  variables
• Point and rank biserial coefficents used with
  one dichotomous variable and one continuous
  variable