Measurement

Measurements Physical therapists use measurements to help them decide: – What is wrong with a patient – How to treat a patient – When to discontinue treatment. Researchers use measurements to quantify the characteristics they study. This type of information is needed for decision making – how far it can be trusted. framework for understanding and evaluating the measurements used by physical therapists.

Measurement  Measurement  is the systematic process by which things are differentiated.  measurement is not a random process, but one that proceeds according to rules and guidelines.  Differentiation can be accomplished with names, numerals, or numbers

SCALES OF MEASUREMENT A real-number system is characterized by order, distance, and origin. Order means that higher numbers represent greater amounts of the characteristic being measured. Distance means that the magnitude of the differences between successive numbers is equal. Origin means that the number zero represents an absence of the measured quality.

Nominal scales Nominal scales have none of the properties of a real number system. A nominal scale provides classification without placing any value on the categories within the classification. The classification can be identified by name or numeral. – Male, female – Group 1,2,3

Ordinal Scales Ordinal scales have only one of the three properties of a real-number system: order. indicate whether a person or object has more or less of a certain quality. Ordinal scales do not ensure that there are equal intervals between categories or ranks. mathematical manipulations such as addition, subtraction, multiplication, or division of ordinal numbers are not meaningful. Amount of assistance (minimal, moderate or max, stand by or independent)

Assistance Scale

Interval Scales Interval scales have the real-number system properties of order and distance, but they lack a meaningful origin. For example: – Temperature where the zero does not mean the absence of values (arbitrary Zero). – 0 o F or C – Both scales, however, have regular (but different) intervals. – Because of the equal intervals, addition and subtraction are meaningful with interval scales. – However, multiplication and division of Fahrenheit or Celsius temperature readings are not useful.

Ratio Scales Ratio scales exhibit all three components of a real-number system: order, distance, and origin. All the arithmetic functions of addition, subtraction, multiplication, and division can be applied to ratio scales. Length, time, and weight are generally considered ratio scales because their absence is scored as zero, and the intervals between numbers are known to be equal. The Kelvin temperature scale is an example of a ratio scale because the intervals between degrees are equal and the zero point represents the absence of heat.

 Because the scale of measurement determines which mathematical manipulations are meaningful, and which statistical tests are appropriate for which types of measures.

MEASUREMENT RELIABILITY Reliability is the “degree to which test scores are free from errors of measurement. Other terms that are similar to reliability are accuracy, stability, and consistency. Components of Reliability 1.Instrument reliability 2.Intrarater reliability 3.Interrater reliability 4.intrasubject reliability

Instrument reliability Categories of physical therapy measurements: 1.Biophysiological Dynamometer, goniometer,…. a)Test—retest reliability. 2.Self-report Surveys, standardized tests, pain scales, interviews… a)Test—retest reliability, in which subjects take the same test on two or more occasions. b)Parallel-form reliability, in which similar forms of a test are each administered once c)Split-half reliability, in which portions of a test are compared with each other 3.Observational. a)Check list such as movement assessment of infants (MAI) b)Knowledge such as manual muscle testing.  The tester is the instrument – inter- and intrarater reliability.

Intrarater Reliability  Is the consistency with which one rater assigns scores to a single set of responses on two occasions.  Do the same measurement in two different dates.  It is hard to separate the patient performance and the intratater errors.

Interrater Reliability  Is the consistency of performance among different raters or judges in assigning scores to the same objects or responses.  Is determined when two or more raters judge the performance of one group of subjects at the same point in time.  Why in the same time.

Intrasubject Reliability The final component of reliability is associated with actual changes in subject performance from time to time. it is impossible to derive a pure measure of subject variability. Thus, most test-retest reliability calculations reflect some combination of instrument errors, tester errors, and true subject variability.

MEASUREMENT VALIDITY Measurement validity is the appropriateness, meaningfulness, and usefulness of the specific inferences made from test scores. Reliability is a necessary, but not sufficient, condition for validity. An unreliable measure is also an invalid measurement. Distinguish between: – Research validity  as the extent to which the conclusions of research are believable and useful. – Instrument validity  is a quality associated with the way in which test results are applied.

Construct Validity Construct validity is the validity of the abstract constructs that underlie measures. For example: strength is a construct could mean ability to move a body part against gravity, or generate speed-specific torque, Manual muscle tests, work performance tests, may all be valid measures of a particular conceptualization of strength. Be clear about the constructs they wish to measure and use the appropriate test. Then, define how you will opertionlize it. – operational definition is a specific description of the way in which a construct is presented or measured within a study.

Content Validity  Content validity is the extent to which a measure is a complete representation of the concept of interest.  Content validity is more often a concern with self-report or observational tools.  Content validity evaluated by knowledgeable peers before it is used.

Criterion Validity  Criterion validity is the extent to which one measure is systematically related to other measures or outcomes.  Criterion validity compares administration of different measures.  Therefore the correlation coefficients used to determine relative reliability are often used to measure criterion validity as well.

STATISTICAL FOUNDATIONS OF MEASUREMENT Seven basic concepts underlie most of the measurement 1. Frequency distribution 2. Mean 3. Variance 4. Standard deviation 5. Normal curve 6. Correlation coefficient 7. Standard error of measurement.

Statistical Reasoning

Types of statistics 1. Frequency distribution. 2. Descriptive statistics a)Central Tendency I.Arithmetic Mean II.Median III.mode b)Variability I.Range II.Variance III.Standard deviation (SD) IV.Normal distribution 3. Inferential statistics

Frequency distribution 1. Frequency Distribution  than the number of times each score is represented in the data set.

Mean  The arithmetic mean of a data set is the sum of the observations divided by the number of observations.  It is the most important concept in statistics.  But, misleading if there is an outlier.

Mean  Example:  If we have two program to improve the ROM of knee after TKA:  Program 1  70, 78, 75, 74, 72, 75, 71, 70. (Mean =73.125)  Program 2  120, 110, 75, 74, 72, 75, 71, 70. (Mean= )

Median Is the mid-score in a set of measurement. Arrange values You can use the stem plot. ◦ e.g. 2,5,8,10,11. (median=8). ◦ e.g 2,5,8,10,11,14. (median= (8+10)/2=9). But it gives you incomplete information about the data. ◦ e.g. 2,5,8,10,11. ◦ e.g. 5,7,8,40,70.

Mode  Is the most commonly occuring score in a set of data.  e.g. 78,79,80,80,90,98. (mode=80)  Also, you may have more then one mode.  e.g. 78,79,80,80,90,90,98. (mode=80 & 90)

Which one to use?

Range  Is the difference between the lowest and the highest scores in a set of data.  e.g. 78,79,80,80,90,90,98  The range = 98-78=20.  But it lacks the full information about the score distribution.  e.g. 1,8,9,10,11,16,18,21.  The range 21-1=20.

Variance The variance is a measure of the variability around the mean within a data set. To calculate the variance, a researcher converts each of the raw scores in a data set to a deviation score by subtracting the mean of the data set from each raw score. Square each score and add up all scores and divide the result by the numbers of scores. The variance indicates how high or low a raw score is compared with the mean.

Variance

Standard Deviation  The standard deviation is the square root of the variance and is expressed in the units of the original measure.

Normal Curve The distribution of groups of measurements frequently approximates a bell-shaped distribution known as the normal curve. The normal curve is a symmetrical frequency distribution that can be defined in terms of the mean and standard deviation of a set of data. Any raw score within the distribution can be converted into a z score, which indicates how many standard deviations the raw score is above or below the mean.

Inferential statistics Inferential statistics are used to draw inferences (logical conclusions) about a population from a sample. Consider an experiment in which 10 subjects who performed a task after 24 hours of sleep deprivation scored 12 points lower than 10 subjects who performed after a normal night's sleep. Is the difference real or could it be due to chance?

Determining Statistical test What you need to know: 1. Is it experimental design or correlational design. ◦ Depending on your hypothesis.  Looking for difference or no difference.  Predicting similar pattern. 2. Who are the subjects you used. ◦ Sam subject ◦ Different subjects

Determining Statistical test 3. How many condition (variable or factor or measurements) you have. ◦ Is it two or more. 4. Level of measurement: ◦ Nominal ◦ Ordinal ◦ Interval ◦ Ratio

 Then decide which statistical test you will use.  Chose one of the following:  Parametric tests  Non-parametric tests.

Experimental (non-corrlational design)

Correlation Coefficient Is a statistical summary of the degree of relationship that exists between two or more measures. The relationship can be between either different variables e.g. weight and height. Correlation coefficients can also have values from 0.0 to — 1.0. A negative correlation indicates an inverse relationship between variables. R is used as a general symbol for a correlation coefficient.

Correlational Design

Standard Error of Measurement knowing the relationship between repeated measurements If the researcher wish to know how much a score is likely to vary with repeated measurements of the same subject. To determine the amount of measurement error, a researcher can take many repeated measures of the same subject and calculate the standard deviation of the scores; this standard deviation is known as the standard error of measurement (SEM).