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1、A Brief (very brief) Overview of Biostatistics,Jody Kreiman, PhD Bureau of Glottal Affairs,What Well Cover,Fundamentals of measurement Parametric versus nonparametric tests Descriptive versus inferential statistics Common tests for comparing two or more groups Correlation and regression,What We Wont
2、 Cover,Most nonparametric tests Measures of agreement Multivariate analysis Statistics and clinical trials Anything in depth,Why You Should Care,Without knowledge of statistics, you are lost. Its on the test.,I: Variables,Independent versus dependent variables Levels of measurement Kinds of statisti
3、cs,Levels of Measurement,The kind of statistic that is appropriate depends on the way the dependent variable has been measured. Four levels of measurement: Categorical/nominal (special case: dichotomous) Ordinal Interval Ratio,II. What Are Statistics?,Methods for organizing, analyzing, and interpret
4、ing numerical data Descriptive statistics: Organize and summarize data Inferential statistics: Used to make an inference, on the basis of data, about the (non)existence of a relationship between the independent and dependent variables,Kinds of Statistics,When data are measured at the categorical or
5、ordinal level, nonparametric statistical tests are appropriate. Unfortunately, time prohibits much discussion of this important class of statistics. When data are interval or ratio, parametric tests are usually the correct choice (depending on the assumptions required by the test).,Kinds of Statisti
6、cs,It is always possible to “downsample” interval or ratio data to apply nonparametric tests. It is sometimes possible to “upsample” ordinal or categorical data (e.g., logistic regression), but that is beyond the scope of this lecture. Decisions about levels of measurement require careful considerat
7、ion when planning a study.,Kinds of Statistics,Descriptive statistics Inferential statistics,Descriptive Statistics,“Data reduction:” Summarize data in compact form Minimum Maximum Mean Standard deviation Range Etc,Frequency Distributions,Description of data, versus theoretical distribution Data can
8、 be plotted in various ways to show distribution,Theoretical Frequency Distributions,There are lots, but well stick to one for now: the Normal Distribution Described by a mean and a variance, about which more later The assumption of normality,III. Measures of Central Tendency,Mean The average, equal
9、 to the sum of the observations divided by the number of observations (x)/N) Median The value that divides the frequency distribution in half Mode The value that occurs most often There can be more than one”multimodal” data.,Median = 204.08 Mode = about 200.00,Which to Use?,The mode is appropriate a
10、t any level of measurement. The median is appropriate with ordinal, interval, or ratio data. The mean is appropriate when data are measured at the interval or ratio level. The relationship between measures depends on the frequency distribution. When data are normally distributed, all values will be
11、equal.,Mean, Median, and Mode,IV. Measures of Variability,Range (largest score smallest score) Variance (S2=(x-M)2/N) Standard deviation Square root of the variance, so its in the same units as the mean In a normal distribution, 68.26% of scores fall within +/- 1 sd of the mean; 95.44% fall within +
12、/- 2 sd of the mean. Coefficient of variation = the standard deviation divided by the sample mean,Confidence Intervals,Confidence intervals express the range in which the true value of a population parameter (as estimated by the population statistic) falls, with a high degree of confidence (usually
13、95% or 99%). Example: For the F0 data in the previous slides, the mean = 205.15; the 95% CI = 204.70-205.60; the 99% CI = 204.56-205.75. The range is narrow because N is large, so the estimate of the population mean is good.,V. Inferential Statistics: Logic,Methods used to make inferences about the
14、relationship between the dependent and independent variables in a population, based on a sample of observations from that population,Populations Versus Samples,Experimenters normally use sample statistics as estimates of population parameters. Population parameters are written with Greek letters; sa
15、mple statistics with Latin letters.,Sampling Distributions,Different samples drawn from a population will usually have different means. In other words, sampling error causes sample statistics to deviate from population values. Error is generally greater for smaller samples. The distribution of sampl
16、e means is called the sampling distribution. The sampling distribution is approximately normal.,Standard Deviation Versus Standard Error,The mean of the sampling distribution equals the population mean. The standard deviation of the sampling distribution (also called the standard error of the mean) equals the population standard deviation / the square root of the sample size. The standard error is an index of sampling erroran estimate of how much any sample can be expected to vary f
