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67 Cards in this Set
- Front
- Back
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formula of a Z-score
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z= raw score - mean value/SD
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formula for paired-t test
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paired-t = mean of difference scores/SD of difference scores
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4 levels of measurement
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Nominal- ie: labels (types of rocks)
Ordinal- rank order, good, better, best (no set distance btw two ranks) ie: manual muscle test (4 out of 5) Interval- can be ranked ie: temperature Ratio- has absolute zero, can be ranked ie: ROM |
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formula for confidence interval
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CI = mean +/- SEM * z
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formula for Standard Error of Mean
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SEM = SD/square root of N
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formula for variance
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s squared= sum of (x - mean) squared /N-1
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formula for SD
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SD= square root of (s squared)
...square root of the varience |
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what is a frequency distribution and what are the 4 ways it can be represented?
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the number of times each score is represented in the data set
**represented by: 1) histogram 2) stem & leaf plot 3) frequency distribution w/percentages 4) grouped frequency distribution w/% (data is lost) |
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when to use median vs. mean
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use median when:
1) you have one or 2 strong outliers 2) when you have ordinal data median= middle value out of list from highest to lowest |
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what does a confidence interval tell us?
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It gives us a sense of how confident we are that our mean value correctly estimates the average of the population
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what does a z-score do?
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it standardizes data to fit in a normal curve
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What is an Alpha Level?
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(when trying to find whether two groups differ from each other)
Confidence level: -set prior to doing the experiment -determines how much uncertainly research is willing to tolerate -usually alpha= .05 or .01 |
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Testing a Hypothesis
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*done when you want to find out whether 2 groups are significantly different)
-do this by finding the Means & SEMs for both groups |
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Null Hypothesis
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-assumes no differences btw two groups (they are the same)
so.. accept null hyp= groups are not significantly different reject null hyp= groups are different |
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Degrees of Freedom
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*DF= the # of values within a data set that are free to vary
*usually DF= N-1 |
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Probability level
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(p)- tells you the likelihood that the null hypothesis (Ho) is true
-if p value is small= it's unlikely that the groups are the same (reject null hyp) *p depends on: -difference btw groups -variability within groups -sample size |
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Probability vs. Alpha
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for a significant difference to exist btw groups, probability level must be LESS than the alpha level!!!
p < alpha |
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t-test for 2 independent groups
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t= (mean 1 - mean 2)/average of 2 variances
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Statistical Errors
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Type I Error= when we reject Ho even though Ho is true
*when p is small (less than alpha) Type I error is unlikely *type I error rate= alpha level Type II Error= accept Ho when Ho ISN'T true *beta level= likelihood of a Type II Error |
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What is Statistical Power?
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power= 1 - beta level
-tells the likelihood that you will find a TRUE difference btw groups (not due to a type II error) *strong power is greater than .80 *>.80 means it's easier to find a difference btw groups |
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Trade-offs btw Type I and Type II Errors
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-reducing Type I Error (alpha) rate, increases the Type II Error (beta) rate
-and vice versa |
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Statistical Power of a t-test increases when...
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-variability within the samples decreases
-differences btw the means of the 2 groups increases -sample size increases |
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How to choose which test to use for Analysis of Differences...
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looking for differences btw groups
1) parametric or non-parametric 2) number of groups 3) scale of measurements (ordinal, raito, interval, nominal) 4) independent or dependent samples |
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When to use parametric tests...
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-when there is random selection from a large population
-sample size is large (greater than 30) -all groups should have similar variance -data is on a ratio or interval scale BUT it's ok to use parametric tests if... -data is unimodal (one peak) -not skewed (peak in center, symmetrical) -variability in all groups is similar -ordinal data is unimodal, has large range and has no floor or ceiling effects |
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Are groups independent?
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there should be:
1) no special relationship btw the data points in group 1 and group 2 2) no relationship btw members of groups ie: separate subjects for the 2 groups |
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Are groups dependent?
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data points in one groups will be matched with those in another
ie: pretest/postest data or matched pairs data (by age) |
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Steps for Statistical Testing
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1) state the null and alternative hypothesis
2) decide on alpha level 3) determine if groups are independent or dependent 4) decide if parametric assumptions are met 5) decide on statistical test 6) determine degrees of freedom 7) calculate statistic (t, f, chi-squared) 8) find p 9) see if p > alpha and decide whether to accept or reject null hypo 10) evaluate statistical conclusion in clinical context |
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what is an independent variable?
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typically the variable that is being manipulated ie: type of exercise program
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what is a dependent variable?
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the result of the independent variable
ie: greater strength due to a certain exercise program |
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what is analysis of differences?
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primary purpose of the study is to compare groups and determine if there is significant differences btw the groups
ie: looking at cause-effect |
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what is analysis of relationships?
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primary purpose of the study is to explain how strongly one variable relates to another within one overall set of subjects
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what is descriptive analysis?
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primary purpose is to document the # of ppl who have a condition
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Explain this design: 1 ind var w/2 ind levels, dep var analyzed one at a time
what statistical tests could be used? |
ie:
ind var= postop protocol 2 ind levels= clinics 1 & 2 dep var= ROM scores tests to use: for parametric--> independent t test for nonparametric --> Mann-Whitney, Wilcoxon rank sum (ordinal), or Chi-square (categorical) |
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Explain this design: 1 ind var w/2 OR MORE ind levels, dep var analyzed one at a time
what statistical tests could be used? |
ie:
ind var= postop protocol 2 or more ind levels= clinics 1,2&3 dep var= ROM scores tests to use: for parametric--> one-way ANOVA for nonparametric --> Kruskal-Wallis or Chi-square |
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Explain this design: 1 ind var w/2 dep levels, dep var analyzed one at a time
what statistical tests could be used? |
ie:
ind var= postop protocol 2 dep levels= at 2 timepoints (3 wks, 6 wks postop) dep var= ROM scores tests to use: for parametric--> paired-t test for nonparametric --> Wilcoxon signed rank, McNemar |
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Explain this design: 1 ind var w/2 OR MORE dep levels, dep var analyzed one at a time
what statistical tests could be used? |
ie:
ind var= postop protocol 2 or more dep levels= at 3 timepoints (3 wks, 6 wks, 6 mo postop) dep var= ROM scores tests to use: for parametric--> repeated measures ANOVA for nonparametric --> Friedman's ANOVA |
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F statistic
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F= MS between/MS within
(like t test or chi-squared) |
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formula for paired-t test
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paired-t= mean of difference scores/SD of difference scores
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when do you use a paired-t test?
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when you want to compare 2 time points within one data set (ie: ROM from 3 wks and 6 wks)
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When to use Mann-Whitney test
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-2 independent groups (2 clinics)
-ordinal data |
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When to use Chi-Square test
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-2 or more ind groups (2 or 3 clinics)
-nominal (categorical) data |
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When to use a One-Way ANOVA
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-interval/ratio data
-3 or more independent levels of ind var (3 or more clinics) |
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When to use an independent t test
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-interval/ratio data
-2 independent groups (levels) |
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When to use Kruskal-Wallis test
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-ranking data
-3 or more independent groups |
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What is between-subjects?
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Factorial
-each group is exposed to a different treatment |
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What is within-subjects?
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Repeated measures
-each group is exposed to all of the levels of treatment |
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Types of ANOVA for 2+ ind var
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1) 2 Way Factorial ANOVA
-2 between-subjects factors 2) 2 Way Repeated Measures ANOVA -2 within-subjects factors (repeated measures) 3) 2 Way Mixed Design -1 between-subjects and 1 within-subjects |
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Two-Factor (3x2) ANOVA
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-has 2 ind var, one with 3 levels, one with 2 levels
ie: ind var #1= clinic, levels= clinics 1, 2 &3 ind var #2= gender, levels= male and female |
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Two-Factor (3x3) Mixed ANOVA
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-2 ind var, each with 3 levels
-one ind var is between-subjects and the one is within-subjects ie: 3 clinics, 3 timepoints **this is what a typical RTC would use |
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When to use a MANOVA
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when there are several dependent variables being measured under the EXACT SAME CONDITIONS
-alternative to running separate ANOVAs |
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What is an ANCOVA
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analysis of covariance
-allows you to remove the effects of an intervening variable (ie: age or gender) before testing whether ind var (clinic) influences the dep var (ROM) |
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Pearson Product Moment Correlation
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(r)= calculates how strongly related variables are of interval/ratio data
*r < .40 = weak relationship *r between .40 and .70 = moderate relationship *r > .70= strong relationship |
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When to use point-biserial correlation
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-when 1 variable is continuous and 1 is dichotomous
(ie: 1 is MMT and the other is can or cannot STS w/o hands) |
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Linear Regression
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calculates the best-fitting line for the data
-allows researcher to predict future characteristics based on previously collected data |
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Multiple Regression
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predicts a quantitative dependent variable based on several predictor variables
ie: predict gait velocity at 6 months (using 3 month range of motion and age) |
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Logistic Regression
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dichotomous dependent variable (yes or no) and interger/ratio predictor variable (age)
ie: what is the likelihood a pt will use a cane 6 mo after knee surgery? -dichotomous: need device? yes or no -predictor: age, balance function, gait speed etc - |
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Nonlinear Regression
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lets you see how well 2 continuous variables are related on a curve
ie: growth curves for children w/CP btw age and growth |
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Intraclass Correlation Coefficient
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ICC--> most commonly used, has advantages:
-measures both relative and absolute reliability -for more than 2 raters (PTs) ie: 2 PTs measuring pts ROM at separate clinics -want to be sure they are consistent with each other -have them both measure the same 10 pts 3 times each -use ICC to assess reliability |
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absolute vs. relative reliability
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relative reliability= relationship btw 2 or more sets of repeated measures
*measured by correlation coefficient absolute reliability= examines variability of scores from measurement to measurement *measured by SEM (standard error of measurement) |
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3 Versions of ICC
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ICC (1,1): Inter-rater reliability
-tests specially trained raters reliably to each other ICC (2,1): Inter-rater reliability -raters are not unique- typical of all other raters -how reliable are PTs in general at observing ROM? ICC (3,1): Test-Retest reliability -one rater makes multiple observations and you want to consider his consistency |
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APA citation
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Devine, P. G., & Sherman, S. J. (1992). Intuitive versus rational judgment and the role of stereotyping in the human condition: Kirk or Spock? Psychological Inquiry, 3(2), 153-159. doi:10.1207/s15327965pli0302_13
*all lines after first are indented *journal article is italicized *only first letter of article name is capitalized *full page numbers *authors' first and middle initials with periods separating |
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when would you use Kappa & Weight Kappa?
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-to measure reliability for categorical (Kappa) and ordinal (weight Kappa) data
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when would you use ICCs?
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-test-retest reliability
-inter-rater reliability -when you want to test absolute and relative reliability |
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statistical approaches to reliability
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-Measures of AGREEMENT
*Correlation + t test *Regression *ICC *Kappa & Weighted Kappa -Measures of typical amount of error *Standard Error of Measurement *Minimum Detectable Change *Minimal Clinically Important Difference |
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Standard Error of Measurement
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tells you the average amount of error
SEM= SD of sample/square root (1-r) ***the smaller the SEM, the more reliable the measurement |
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Minimum Detectable Change
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Confidence Interval for Measurement Errors
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Minimum Clinically Important Difference
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Tries to establish how large a change is needed for it to be clinically significant
*often determined by surveys, expert opinion etc |
