Basic statistics for physiotherapists.

Question	Answer
Measures of central tendency	mean, median, mode
Mean	average of all scores
Median	midpoint of all scores
Mode	most frequently occurring score
mean is appropriate for what data types?	interval, ratio
median is appropriate for what data types?	ordinal data
mode is appropriate for what data types?	nominal
Measures of variability	range, standard deviation, normal distribution, percentiles & quartiles
Range	difference between highest and lowest score
Standard Deviation	variability of scores from the mean. most frequently used
How to calculate SD	subtract each score from mean, square each difference, add up all squares, divide by number of scores
Normal distribution	symmetrical bell shaped curve indiecating distribution of scores. Mean/median/mode all similar.
Inferential statistics	allow determination of how likely results can be generalized to a population
Standard error of measurement	an estimate of expected errors in a score, measure of response stability or reliability
Tests of significance	estimation of true differences not due to chance, rejection of null hypothesis
Alpha level	probability level - reselected level of statistical significance. Most commonly .05 or .01 (.05= only 5x out of 100 is the difference due to chance)
Degrees of freedom	based on # of subjects and groups, allows determination of level of significance
Standard error	result of sampling error, expected chance variation among the means
Type 1 error	Null hypothesis rejected when it is true.
Type 2 error	Null hypothesis is not rejected when it is false. means concluded to be due to chance when truly different
How to decrease type 1/2 errors	increase sample size, random selection, valid measures
Parametric statistics	Interval or Ratio data
Assumptions for parametric statistics	normal distribution (usu large representative samples this is met), random sampling performed, variance in groups is equal
T-test	parametric test of significance used to compare 2 independent groups created by random assignment and ID difference at a selected probability level
T-test for independent samples	compares 2 independent groups
T-test for paired samples	compares 2 matched samples (does therapy incr fxn in siblings with autism)
One-tailed T-test	based on directional hypothesis. Evaluates differences in data on only one end of distribution (neg or pos)
Two-tailed T-test	based on a nondirectional hypothesis. Evaluates differences in data on both ends of a distribution. Tests of signif are almost always two-tailed
Inappropriate use of T-test	use to compare more than 2 means within a single sample.
ANOVA	parametric test used to compare 3 or more independent tx groups at a selected probability level.
Simple (one-way) ANOVA	compares multiple groups on a single IND variable. Ex: Balance Master score for 3 different age groups
Factorial ANOVA	compares multiple groups on two or more IND variables. Ex: 3 levels of ankle injury compared for balance and sensory
ANCOVA	Parametric test used to compare 2 or more treatment groups or conditions while also controlling for the effectss of intervening variables.
Nonparametric statistics	ORDINAL or NOMINAL data, testing not based on population parameters
When to use nonparametric	parametric assumptions cannot be met. used with small sample, ordinal or nominal level data. Less powerful than parametric
Chi square test	nonparametric test of significance. Used to compare data in the form of frequency counts in 2 or more mutually exclusive categories (rate treatment preferences)
Correlational statistics	used to determine the relative strength of a relationship between 2 variables
Pearson product-moment coefficient (r)	used to correlate CONTINUOUS data wi
Linear Regression	used to establish relationship between two variables as a basis of prediction
Spearman's Rank	NONPARAMETRIC test to correlate ORDINAL data.