Statistics & Their Use

OBJECTIVES  Understand the reason for and use of statistics  Review descriptive statistics  Measures of central tendency  Measures of variability  Measures of relationship  Inferential Statistics  Parametric  Non-parametric

What are statistics for?  Painting a mathematical picture….or simplifying large sets of data  Identifying if relationships exist  Establishing the probability of a cause and effect relationship  ETC…..

How many tests are there?  There are well over 100 statistical calculations and tests  However, many are rarely if ever used  Therefore, we will focus on those that are used most often…

Which tests should you know?  The New England Journal of Medicine from Vol 298 through 301 – (760 articles) were reviewed to determine what statistical tests are most important to learn to understand the scientific literature.

FINDINGS  “A reader who is conversant with some simple descriptive statistics (percentages, means, and standard deviations) has full statistical access to 58% of the articles.

Findings  “Understanding t-test increases this access to 67 percent.  “Familiarity with each additional test gradually increases the percentage of accessible articles.”

Descriptive Statistics  Purpose --- To simply describe things the way they are  NOT to establish a possible cause & effect relationship

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.

Descriptive Statistics

Measures of Central Tendency Mode --- most frequently occurring score Median (Mdn) --- score physically in the middle of all scores Mean (M or X) --- arithmetic mean--- i.e. sum of scores divided by the number of scores

Mean  Is generally the preferred measure of central tendency  Is used frequently for other calculations

Means of 2 data sets

Measures of Variability (dispersion)

Measures of Variability  If scores are similar….ergo they have low variability (homogeneous)  If scores are dissimilar…ergo they have high variability (heterogeneous)  Two sets of scores may have the exact same mean but one set may have low variability and the other very high….therefore… measures of variability help DESCRIBE these differences

Range  Simplest measure of variability  The difference between the lowest and highest score  Usually reported in the literature as “range” but on occasion as “R”  The range is an unstable calculation because it is only based upon 2 scores

Standard Deviation & Variance  These measures are calculated based upon ALL data scores and are therefore better represent the data set  They are used with other statistical calculations

Variance  Related to the amount that an individual score VARIES from the mean.

Standard Deviation  Is the square root of the variance

Standard Deviation (aka S.D.)

Correlations  Measures of central tendency and variability describe only ONE variable  CORRELATIONS describe the relationship between TWO variables  Correlations can be positive, negative or zero  Correlations range from +1 through -1

Correlations  +.95, +.87, High positive correlations  +.19, +.22, Low positive correlations  +.03, -.02, No relationship  -.23, -.19, Low negative correlations  -.94, -.88, High negative correlations

Spearman’s Rho & Pearson  Pearson’s product-moment correlation is a parametric test (for continuous data….blood pressure, weight, etc.)  Spearman’s Rho is non-parametric ( for rank data…male/female, etc.)  Kappa value ---used often for determining degree of inter and intra- examiner agreement

Kappa  Commonly used in chiropractic & medical literature to convey the degree of int er examiner and/or int ra examiner reliability  Interexaminer– two or more examiners checking/evaluating or testing for the same finding  Intraexaminer– one examiner checking/evaluating or testing for the same finding on two different occasions  Kappa calculates the degree of agreement between the first and second check/evaluation or test

Summary  Descriptive statistics do just that  They describe the distribution of data toward the center (mean, median, mode) and they describe the variability away from the center (range, variance, standard deviation)  They also determine if there is a relationship between 2 (or more) variables

Summary  Of the 100+ statistical tests only a few are frequently used  You can intelligently read and understand nearly 70% of the biomedical literature with an understanding of descriptive statistics and the t-test  Correlations are an important and often used type of descriptive statistics  Descriptive Statistics must be well understood in order to understand inferential statistics

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

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”

Parametric Statistics 3 most commonly used tests & some related concepts commonly expressed in the literature

Statistical & Medical 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

4 Possibilities  Medically & statistically significant  Medically but not statistically significant  Statistically but not medically significant  Neither statistically or medically 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.

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

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

Directional Hypothesis/Non… & Critical Value  These two decisions need to be made before the study is started and will determine to some degree if your results will be significant  …

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 dependent 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

Summary  “Significance” is used in different ways…statistical & medical  The most commonly used inferential statistical test is the Student t-Test (which has 3 versions depending what you are comparing) it only compares 2 group(s)/sample  Hypothesis can be directional or non- directional…  Critical value is established by the researcher BEFORE the study is started (.01,.05,.10)

Summary….contd.  Parametric tests assume several things related to a relatively normal distribution of data  Analysis of variance is used for comparing more than two variables  Analysis of Covariance is used to account for and remove the effects of nuisance variables

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