Objectives

• To understand the difference between parametric and nonparametric

• Know the difference between medically and statistically significant

• Understand t-Tests, ANOVA and analysis of covariance

Inferential Statistics

• Purpose --- In experimental research uses a sample of the population – inferential statistics permits the researcher to generalize from the sample data to the entire population.

• Aids the researcher in determining if cause and effect relationships exist.

Inferential Statistics

Parametric versus Nonparametric

Assumptions---Parametric

• Parametric Inferential Statistics --- assumes that the sample comes from a population that is NORMALLY DISTRUBUTED & that the variance is similar (homogeneous) between sample and population (or 2 populations)

• The tests are very POWERFUL ---I.e. can recognize if there is a significant change based upon the experimental manipulation

Nonparametric Inferential Statistics --- no Assumptions

• Makes no assumptions about the distribution of the data (distribution free)

• So it does not assume that there is a normal distribution of the data…..etc.

• Is less powerful…meaning that a greater difference (or change) needs to be present in the data before a significant difference can be detected

Usage

• “Generally, it is agreed that unless there is sufficient evidence to suggest that the population is extremely non-normal and that the variances are heterogeneous, parametric tests should be used because of their additional power”

Statistical & Clinical Significance

• It is important to keep in mind that statisticians use the word “significance” to represent the results of testing a hypothesis

• In everyday language and in the clinical setting, a “significant” finding or treatment relates to how “important” it is from a clinical and not a mathematical perspective

Expressions of significance

p values

• p values are statistical expressions of significance• Tells the reader what the chances are that the

outcome was just due to luck• p<.05 is considered statistically significant by

most researchers• p<.01 or <.10 are sometimes used

Confidence Intervals

• Slowly replacing p as an expression of confidence• Written as “95% CI (1.7-2.7)

4 Possibilities

• Clinically & statistically significant• Clinically but not statistically significant• Statistically but not clinically significant• Neither statistically or clinically significant

• Very large groups of subjects can reflect statistically significant differences between two groups …but they may not be medically significant from the perspective of cost, risks, policies etc.

Steps to determine significance

• Determine critical value• Determine what is a clinically significant

improvement• Determine power requirements

Critical Value

• The researcher must establish the value at which they will consider the results “significant”…this is referred to as the CRITICAL VALUE

• There is some subjective and somewhat arbritrary decision to be made in this regard by the researcher

• The customary critical values are either P<.05 or P<.01 but on occasion you will see P<.10

Clinically significant improvement

• The researcher attempts to determine clinical significance by review of literature

• If that cannot be accomplished, often 1/2 of a SD is used

Power requirements

• Researcher must determine the the odds of finding the pre-established clinical improvement.

• Minimum level of detection is 80%

ebook.stat.ucla.edu/calculator/powercalc/

Parametric Statistical Tests

t-Test aka Student t-Test

ANOVA

Analysis of covariance

t- Test

• Developed by Gosset under the pseudonym Student

• 3 different versions of the t-tests that apply to 3 different research designs

• All three forms of the t-Test are based upon the MEANS of two groups

• The larger the difference in the calculated t scores, the greater the chance that the null hypothesis can be rejected

t-Test

• 3 different general ways to use the student t-test

• 2 variations of each…dependent upon the type of hypothesis the researcher uses

• The hypothesis can either be directional or non-directional

Directional / Non-directional Hypothesis

• “Directional” means that the researcher anticipates or expects a specific positive or negative impact from the treatment (or other independent variable)

• “Non-directional” means that the researcher does not know what to expect. Perhaps the treatment will make the patient better or worse

t-Test #1 Single Sample

• Compares the sample to the mean value of the population

• Is not used often because the mean for the population if usually not known

• E.g. Stanford Binet I.Q. test….has a mean of 100 and 1 S.D. of 16 (although not everyone in the U.S. has had the test, enough have been tested to accept the data as representative

t-Test #2 Correlated Groups

• Used when subjects serve as their own controls (or when they are matched to very similar subjects)

• For each subject we could have a pre and a post treatment score (e.g. pain, blood pressure, algometer, cholesterol levels, range of motion…)

• The null hypothesis would be that the difference between pre and post scores would be 0 (treatment is not effective)

• If the difference is sufficient, the null hypothesis can be rejected

T-Test #3 Independent t-Test

• Aka independent groups t-Test

• Most commonly used

• Used when you have 2 groups (2samples) out of an entire population

• Ho = X control = X treatment

Analysis of Variance (ANOVA)

• The t-Test only allows us to compare 2 groups

• What if we have a study comparing 2 or more types of treatment with a controls of both no treatment and placebo?

• ANOVA is designed to handle multiple groups similar to what the t-Test does with 2 groups

Analysis of Covariance (ANCOVA)

• Sometimes studies nuisance variables impact the dependent variable (outcome measures) but not the independent variable (e.g. treatment).

• These unwanted variables can interfere with our analysis of the data

• Example…

Example

• We want to see if one of two treatment protocols will have a positive effect upon patients with low back pain

• The patients are randomly assigned to the treatment and control groups

• We realize from the histories that there are factors that impact recovery from low back pain that we have not accounted for (e.g. obesity, smoking, occupation, age etc. etc.) These factors could impact rate of recovery (dependent variables)

• The Analysis of Covariance pulls those possible confounding… nuisance factors out

Nonparametric Tests

• Wilcoxon Signed Rank Test—

• Wilcoxon Ranked Sum Test—equivalent to the Student t-test

• Kruskal-Wallis Test– equivalent to the one-way analysis of variance

Making Too Much from Research (even if it is well controlled

research)

Review

• Know the difference in parametric and non-parametric tests.

• Know the difference in clinical and statistical significance

• Understand “p” values and confidence intervals• Know the different “t” tests and when each is used

Review

• Know steps to determine significance and effect of critical values, clinical significance and power on calculations

• Know when the ANOVA and ANCOVA is used• Know examples of parametric tests • Know when the hypothesis is directional or non-

directional…• Critical value, clinical significance and power are

established by the researcher.