Sensitivity(ability of a test to detect true positives = true postitives / (true positive + false negatives)

Specificity (ability of a test to detect true negatives = true negatives / (true negatives + false postives)

Accuracy = (true positives + true negatives) / (false positives + false negatives)

Positive Predictive value(probability that an individual actually has the condition if the test is positive) = True positives / (true positives + false positives)

Negative Predictive value(probability that an individual does not have the condition if the test is negative) = true negatives / (true negatives + false negatives)

Prevalence = number of cases in a population at a given time.

Incidence = Number of newly diagnosed cases over a specific time period.

Alpha (Type I) error

- error in hypothesis testing where a statistically significant association is found when none exists (false positive).
- rejecting a true null hypothesis
- controlled by increasing the significance level.
- Statistical significance provides the probability of committing a Type I error and is demonstrated by the P value.
- P<0.05 = 5% probability of committing a Type 1 error

Beta (Type II) error

- error in hyposthesis testing in where no statistically significant association is found when there is a true association (false negative).
- may occur if study lacks power, ie you need more data to prevent Type II errors.
- accepting a false null hypothesis
- Power analysis is used to determine if the sample size is large enough to demonstate statistical significance.
- In general the power of a study shoud be at least 0.8 (80%)

**Discrete Data**

- Discrete data falls into specific categories such as gender or the presence or absence of a risk factor such as smoking.
- Chi-square test
- Yates correction for continuity
- Fishers exact test

**Continuous Data**

- Continuous data can be displayed on a curve such as height, weight, or 40-yard dash time.
- Student's t-test (one sample{normal distribution}, independent two-sample{normal distribution} and paired{not-independent})
- ANOVA

ANOVA

- test of choice for multiple groups of continuous data.
- used to compare means of three or more groups.
- useful only for normally distributed, independent data.
- One-way ANOVA: used to test differences bewtween 3 or more independent groups.
- One-way ANOVA for repeated measures: used when the subjects are dependent groups (same subjects used for each treatment).
- 2by2 ANOVA: used to evaluate effects of two or more treatment variables.
- Posterior comparisions = Bonferroni method, student-Newman-Kauls procedure, Tukey method, Scheffe method.

T-Test

- used for comparison of two groups of continuous data.
- Paired t-test = dependent = used for two groups of paired (same individual) and normally distributed continous data.
- Student t-test = independent = used for two independenet groups of normally distributed data.

Chi-Square Test

- used for measuring binary or ordinal data.
- compares discrete (categorical) variables as opposed to continuous variables.

Fischers Exact Test

- used for measuring binary or ordinal data

Kruskal Wallis Test

- used for nonparametric testing with more then two groups.
- used to compare medians of three or more independent groups where the data is not normally distributed.

Mann-Whitney Test

- used to compare two groups of nonparametric data.
- nonparametric statistical significance test for assessing whether the difference in medians between 2 observed distributions is statistically significant. Requires two independent samples.

Wilcoxon Test

- used to compare two groups of nonparametric data.

Simple Regression

- used to determine if these is a relationship between a dependent variable and an independent variable.

Logistic Regression

- assesses the effect of one or more variables on one dichotomous variable. Dichotomous variables have on two variables (male/female).

Bonferroni Correction

- performed to adjust for the number of comparisons and decrease the risk of committing a type I error. Performed by dividing the p value by the number of comparisions.

Relative Risk

- Magnitude of association between exposure to a risk factor and an injury.
- Determined by dividing the incidence of those exposed most to an injury by the incidence of the control group.

Absolute Risk

- the arithmetic difference in the rate of adverse outcomes between control and experimental subjects.

Incidence

- the proportion of new cases within a specific time interval

Odds Ratio

- compares a study group with a control group with the probability of exposure with a specific outcome compared to the probability of an exposure without the same outcome.

Prevalence

- the proportion of individuals with a disease or condition at a single point in time.

Confidence Interval

- range between two estimated values.
- 95% confidence interval = +/- 1.96 * (SEM). SEM=standard error of the mean=standard deviation/square root of n.

Scheffe comparision

- post hoc test that assess group differences following ANOVA

Newman-Keuls

- post hoc test that assess group differences following ANOVA

Correlation Analysis (r value)

- provides unitless number that summarizes strength of association between 2 variables.
- The closer the value is to 1 or -1 the stronger the association.
- Positive number means as the values change in the same direction.
- Negative number means the values are inversely related.

R^{2}

- the coeffecient of determination
- represents the percentage of the independent variable that explains the variance in the study

Variance

- =standard deviation squared

Poisson Regression

- analysis in which the dependent varialbe in an experiment or observational study is a count the follows the Poisson destribution.

Analysis of Covariance

- tests for equality among group means, when the value of the dependent variable is affected by additional information related to the independent variable.

Validity

- degree to which the measuremen represents a true value

Reliability

- ability of researchers to reproduce or repeat the same measurements.

Tests for Interobserver reliability

- kappa coefficient, weight kappa, Cronback's alpha
- Person product-moment correlation for continuous variables

**Descriptive Study**

- demonstrate associations between disease and variables, but do no demonstrate cause-effect relationships.
*Case report / case series**Correlational Study*: large sample study identifying associations between disease and variables.*Cross sectional study*: takes a snapshot of a population and derives assocations with disease. Does not determine case and effect.

**Analytical Study**

- allow for hypothesis testing and statical analysis
- Cohort study: condition is not manipulated but observed and recorded. Can be retrospective or prospective
- Case-Control study: cohort study with participants selected based on disease. Beneficial for rare diseases. Can not be used for rare exposures, cannot directly measure incidence, subject to selection and recall bias.
- Prospective Cohort study: minimizes potential bias and inscreased strength of conclusions.

**Intervention Study**

- clinical trials
- prospective, randomized, single vs double blinded
- Reduces bias and confounding

Selection Bias: study error resulting when comparisions are made between groups that differ in important ways other than the factor under consideration

Measurement Bias: study error resulting when quantitative or qualitative data collected from the treatment groups differ. Generally found in retrospective studies.

Sampling Bias: study error which occurs when patients in the study differ systematically from the population in which the results are generalized.

Publication Bias: research error which occurs when published studies differ systematically from unpublished studies which may be of higher quality, but not show as great a statistical significance.

References:

- Wojtys EM, AJSM 1996;24:564
- Kuhn JE, AJSM 1996;24:702
- Greenfield ML, Wojtys EM, Kuhn JE. A statistics primer. Tests for continuous data. Am J Sports Med. 1997 Nov-Dec;25(6):882-4.
- Kuhn JE, Greenfield ML, Wojtys EM. A statistics primer. Statistical tests for discrete data. Am J Sports Med. 1997 Jul-Aug;25(4):585-6.
- Kocher MS, JBJS 2004;86A:607

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