odds ratio

Categorical (nominal)

A categorical variable is one that has two or more categories, which has values that you can put into a countable number of distinct groups based on a characteristic. Examples: race, sex, age group, and educational level I one that has two or more categories but there is no intrinsic ordering to the categories. for example gender. Purely categorical variabe is one that simply allows you to assign catgories but you cannot clearly order the variables. Categories but no ordering or direction Ex: gender, race, eye color, political party

Distribution

A normal distribution of data is one in which the majority of data points are relatively similar, meaning they occur within a small range of values with fewer outliers on the high and low ends of the data range. When data are normally distributed, plotting them on a graph results a bell-shaped curve. In such a distribution of data, mean, median, and mode are all the same value and coincide with the peak of the curve.

One-way ANOVA

A one-way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables • • •One independent variable •Example: Comparing shoulder elevation ROM gains in patients after shoulder surgery •Clinic 1 vs. Clinic 2 vs. Clinic 3 •HO: μC1 = μC2 = μC3 •HA: μC1 ≠ μC2 ≠ μC3

sample vs population

A population data set contains all members of a specified group (the entire list of possible data values) A sample data set contains a part, or a subset, of a population The size of a sample is always less than the size of the population from which it is taken

Analysis of Variance (ANOVA)

Analysis of variance, or ANOVA, is a statistical method that allows a comparison of more than two groups at the same time to determine whether a relationship exists between them • Partitioning the total variation in a set of data into two or more components to understand the contribution of each component to the total •Variation between groups •Variation within groups

Measures of Association

Association: A statistical relationship between two or more variables. A measure of association quantifies the relationship between exposure and disease among the two groups Risk: Probability of an individual developing a disease or change in health status over time The measures of association described in the following section compare disease occurrence among one group with disease occurrence in another group. Examples of measures of association include •Absolute Risk (incidence, prevalence) •Relative Risk, (risk ratio, rate ratio) •Odds Ratio • When should one use relative risk and odds ratio? In retrospective (case-control) studies, where the total number of exposed people is not available, RR cannot be calculated and OR is used as a measure of the strength of association between exposure and outcome. By contrast, in prospective studies (cohort studies), where the number at risk (number exposed) is available, either RR or OR can be calculated.

Ordinal

If the variable has a clear ordering, then that variable would be an ordinal variable. For example, educational experience with values If these categories were equally paces then the variable would be an interval variable Ordered categories in ranking order: Differences cannot be measured. Ex: socioeconomic status

Inferential

Methods used to make 'inferences' about a larger group or population on the basis of information derived from a sample Ex./ t-test, chi-square, Wilcoxon, ANOVA, regression

Descriptive

Methods used to organize and produce summarized information on data Ex./ rate, mean, standard deviation, frequencies

Numerical variable

Numeric (continuous) variables are also known as quantitative variables. Numeric variables can be further categorized as either interval or ratio variables interval: variable is similar to an ordinal varibale, except that the intervals between the values of the interval varibale are equally spaced. Meaningful order, measure the differences (excluding ratios) Difference between measurement but no zero is not starting point. Differences can be measured. Ex: temperature (Farenheit), temperature (Celcius), pH Ratio: When number have units that are of equal magnitude as well as rank order on a scale. Meaningful order, measure the difference (including ratios). Difference between measurement with zero. Ex: heart rate, blood pressure, distance

Odds ratio

Odds Ratio (OR) is a measure of association between exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure Important points about Odds ratio: •OR >1 indicates increased occurrence of event •OR <1 indicates decreased occurrence of event (protective exposure) •Look at CI and P value for statistical significance of value • The magnitude of the odds ratio is called the "strength of the association." The further away an odds ratio is from 1.0, the more likely it is that the relationship between the exposure and the disease is causal. •An OR of 1.0 (or close to 1.0): odds of exposure among case-patients are the same as, or similar to, the odds of exposure among controls. The exposure is not associated with the disease. •Greater than 1.0: odds of exposure among case-patients are greater than the odds of exposure among controls. The exposure might be a risk factor for the disease. •Less than 1.0: odds of exposure among case-patients are lower than the odds of exposure among controls. The exposure might be a protective factor against the disease

Variation

Range: The spread, or the distance, between the lowest and highest values. To get the range for a variable, you subtract its lowest value from its highest value •The interquartile range is the distance or range between the 25th percentile and the 75th percentile • • Variance: Average of the squared differences from the mean and the symbol is σ2 It is also called mean square deviation •The larger the variance, the further the individual cases are from the mean •The smaller the variance, the closer the individual scores are to the mean • • Standard Deviation: Square root of the variance and the symbol is σ •Larger SD = greater amounts of variation around the mean •Like the mean, the SD will be inflated by an outlier

descriptive statistics

Summarize Data •Central Tendency (Mean, Median, Mode) •Variation (Range, Interquartile Range, Variance, Standard Deviation) Types of descriptive statistics Organize Data Tables •Frequency Distributions •Relative Frequency Distributions Graphs •Bar Chart or Histogram •Stem and Leaf Plot •Frequency Polygon

odds ratio

When you are interpreting an Relative Risk or Odds Ratio, it is often helpful to look at how much it deviates from 1 and always check a 95% confidence interval. •95 % CI value should include odds ratio value. •Both lower and upper CI value should be either less than 1 or greater than 1. •The odds ratio can be positive or negative. •You can interpret the odds ratio without p value . Example - Scenario -1 Odds ratio: 1.09 and 95% Confidence interval: 1.01 -1.15 Interpretation; Odds ratio is significant positively - It means that one group the outcome is 9% more likely. p-value: 0.003 Example - Scenario -2 Odds ratio: 1.09, 95% Confidence interval: 0.99 -1.15 Interpretation; Odds ratio is not significant because lower confidence interval (0.99) is less than 1. p-value: 0.6 Example - Scenario -3 Odds ratio: 0.90, 95% Confidence interval: 0.89 - 0.98 Interpretation; Odds ratio is significant negatively - Then one group the outcome is 10% less likely p-value: 0.002 Example - Scenario -4 Odds ratio: 0.90, 95% Confidence interval: 0.89 - 1.01 Interpretation; Odds ratio is not significant because upper confidence interval (1.01) is higher than 1. p-value: 0.7

Chi-square Test

•A chi-square statistic is one way to show a relationship between two categorical variables. Chi-squared statistic tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population. • •Compare discrete outcomes •Nominal •Ordinal •H0: The distribution of the outcome is independent of the groups •HA: There is a difference in the distribution of responses to the outcome variable among the comparison groups

Relative risk

•If RR is > 1 Increase risk of developing disease/outcome •If RR is < 1 Decrease risk of developing disease/outcome •If RR is = 1 No risk of developing disease/outcome •It indicates the likelihood that someone who has been exposed to risk factors will develop the disease, as compared with one who has not been exposed •Calculate: Dividing the risk (incidence proportion, attack rate) in group 1 by the risk (incidence proportion, attack rate) in group 2

Symmetric distributions

•In symmetric distributions, the mean, median, and mode are the same • •In skewed data, the mean and median lie further toward the skew than the mode

Repeated Measures ANOVA

•Multiple measurements taken on groups over time • • •Analogous to a paired t-test •With multiple (> 2) measurements •With > 2 groups