pfd LIU.txt

• CATEGORY
• NO ORDER
• categorical measures that do not have an order
• ---e.g. color (red/blue/green/etc);
• types of teeth (molars/incisors/premolars/canine)

• CATEGORY
• ORDER of intensity
• catagoical measures that have an order of intensity/degree
• ---e.g. stage of oral cancer (stages i---iv); curvature of dental
• root (straight/slight curvature/pronounced curvature)

• CONTINUOUS
• NO TRUE ZERO
• ex: dates

• CONTINUOUS
• TRUE ZERO
• ex. perio pocket depth

• Interval: measures that do not have a true zero; the relative difference is the key
• ---e.g. temperature; dates;
• Ratio: measures that have a true zero
• ---e.g. depth of periodontal pocket; size of oral lesion.

• Distance between the largest and the smallest observation
• Simplest measure of variability

• Point below which a specified percent of observations lie
• Percentile of an observation x is given by:

(# of obs less than x) + 0.5 /total number of obs in data X 100

• The value on which a distribution tends to
• center
• Mean: the arithmetic average
• Median: the middle item of the data set
• Mode: the most frequent value

• Measures the likelihood that the true value of a population parameter (e.g., mean) is within the margin of error of the sample estimate.
• 95% CI is the range of values that would cover the true population parameter 95% over time.
• 95% CI for a normal distribution: will “capture” µ 95% of the time.

•  Dispersion
•  Variance --- measures the variation
•  Standard Deviation (SD)---the square root of the
• variance, denoted by σ , has the same unit as x
•  Standard Error (SE)---an estimate of the precision of parameter estimates. It measures the variability of an estimate due to sampling:
•  Kurtosis---characterizes the relative peakedness or
• flatness of a distribution (-2 to infinity)
•  Skewness---measures the asymmetry of a distribution: (-3 to 3

• Most commonly used method to describe categorical measures
•  Consists of categories, the number of observations
• and percentage corresponding to each category:

Most frequent value

•  Goal: judge the evidence for a hypothesis
•  Steps for hypothesis testing
• ♦ Stating the null & alternative hypothesis
• ♦ Choosing an appropriate statistical test
• ♦ Conducting the statistical test to obtain the pvalue
• ♦ Comparing the p-value against a fixed cutoff for statistical significance – α (usually 0.05) and make conclusion 12

• REJECT TRUE NULL
•  Reject a null hypothesis when it is true---we have
• committed a Type I error (α error—0.05).

• ACCEPT FALSE NULL
•  Accept a null hypothesis when it is false---we have
• committed a Type II error (β error—0.2).

Probability that the test statistics assumes a value as extreme as, or more extreme than, that observed, given that the null hypothesis is true.

• (1-β) Probability that you reject the
• null hypothesis, given that the alternative hypothesis
• is true.

• Statistical procedures based on distribution assumptions
•  t-test
•  Analysis of Variance (ANOVA)
•  Chi-Square test

• Statistical procedures not based on distribution assumptions
•  Sign-test
•  Kruskal-Wallis test (non-parametric ANOVA)

Compare whether two independent groups have the same mean of a normally distributed variable with unknown variance.

• Test means among multiple groups
• Uses F-test. It is a generalization of t-test and equivalent to t-test if comparing two groups.
• Data will need to satisfy several assumptions (e.g., the outcome has a normal distribution; equal variance for each group; the data are independent between and within groups.)
• Example
• Null=means of all groups are equal
• F-stat exceeds the critical value for 5% level with a p-value of 0.000<0.05
• not all means of three groups are the same.
• Pairwise comparison of means

• Compare observed data with the data we would expect to
• obtain according to a specific hypothesis.
•  Steps of χ2
• goodness of fit test
• ---Divided the data into c categories;
• ---Estimate k parameters of the probability model with your
• hypothesis;
• ---Compute observed and corresponding expected cell
• frequencies;
• ---Test Statistic:
• 1. Create 6 intervals (categories): X ≤16.25, 16.25 < X ≤ 17.20, 17.20 <
• X ≤ 18.15, 18.15 < X ≤ 19.10, 19.10 < X ≤ 20.05, and 20.05 < X.
• 2. Null hypothesis H0
• : the underlying distribution from which the
• measurements came is N(18.37, 1.92), i.e. the normal distribution
• with mean 18.37, variance 1.92.
• 3. Calculate the observed frequency and expected frequency.
•  The p-value is 0.1072, we will accept the null hypothesis .

•  Used to test if there is a difference between paired
• samples.
•  Independent pairs of sample data are collected:
• (x1,y1) (x2, y2)…, the difference of the pairs are
• calculated, and zeros are ignored.
•  The null hypothesis is: equal numbers of positive
• and negative differences.
• ---A one-sided sign test has p-value 0.1719 indicating that it is not significant at 5% level---no statistically significant difference in # of patients seen between the two offices.

•  Based on the rank of observations to compare the distribution of a continuous variable among more than two groups—non-parametric ANOVA.
•  The only assumption required for the population distributions is that they are independent, and continuous.
•  Many software provide such test (e.g., kwallis in STATA.)

• Continuous outcome
• Merger of ANOVA and Regression

• binary outcome
• Simple --- single predictor
• Multiple --- two or more predictors
• Dependent variable is binary
• Logistic function is non-linear in terms of the probability of event

• continuous outcome
•  Simple --- single predictor
•  Multiple --- two or more predictors
• dependent->independent
• predicted->predictors
• response -> explanatory
• outcome->covariates

•  The dependent variable is binary (e.g. whether inflammation of the gingiva presents.)
•  Logistic function is non-linear in terms of the probability of event.
• The parameter estimates can be expressed as odds ratio, which describe the relationship between exposure and
• outcome, controlling for other factors.

•  A method for comparing mean values of the outcome between groups when adjusting for covariates (e.g., compare mean LOA across groups, adjusting for age)
•  The response is continuous and the covariates can be both continuous and categorical
•  An extension of ANOVA or a combination of ANOVA and linear regression

• Desired outcome of a study, planning to have enough sample size is of prime importance.
• – Due to limitations of resources and availability of subjects, we can only get limited sample size.

• Five key factors
• 1. Sample size--the minimum number of unique subjects in your data required to detect a certain difference
• 2. Effect size--the difference between parameters to be tested, (e.g., difference in LOA between groups)
• 3. Significance level (Type I error)--the probability that we reject a null hypothesis when it is true(commonly at 0.05)
• 4. Power --the probability of rejecting a null hypothesis when it is false (equals to 1-Type II error; commonly at 0.8)
• 5. Variability -- variation of the outcome measure