A Brief (very brief) Overview of Biostatistics Jody Kreiman, PhD Bureau of Glott

A Brief (very brief) Overview of Biostatistics Jody Kreiman, PhD Bureau of Glott www.phwiki.com

A Brief (very brief) Overview of Biostatistics Jody Kreiman, PhD Bureau of Glott

Young, Cathy, Contributing Editor has reference to this Academic Journal, PHwiki organized this Journal A Brief (very brief) Overview of Biostatistics Jody Kreiman, PhD Bureau of Glottal Affairs What We’ll Cover Fundamentals of measurement Parametric versus nonparametric tests Descriptive versus inferential statistics Common tests as long as comparing two or more groups Correlation in addition to regression What We Won’t Cover Most nonparametric tests Measures of agreement Multivariate analysis Statistics in addition to clinical trials Anything in depth

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Why You Should Care Without knowledge of statistics, you are lost. It’s on the test. I: Variables Independent versus dependent variables Levels of measurement Kinds of statistics 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 as long as organizing, analyzing, in addition to interpreting numerical data Descriptive statistics: Organize in addition to summarize data Inferential statistics: Used to make an inference, on the basis of data, about the (non)existence of a relationship between the independent in addition to dependent variables Kinds of Statistics When data are measured at the categorical or ordinal level, nonparametric statistical tests are appropriate. Un as long as tunately, 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 Statistics 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 consideration when planning a study.

Kinds of Statistics Descriptive statistics Inferential statistics Descriptive Statistics “Data reduction:” Summarize data in compact as long as m Minimum Maximum Mean St in addition to ard deviation Range Etc Frequency Distributions Description of data, versus theoretical distribution Data can be plotted in various ways to show distribution

Theoretical Frequency Distributions There are lots, but we’ll stick to one as long as now: the Normal Distribution Described by a mean in addition to a variance, about which more later The assumption of normality III. Measures of Central Tendency Mean The average, equal 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 at 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 equal. Mean, Median, in addition to Mode

IV. Measures of Variability Range (largest score – smallest score) Variance (S2=(x-M)2/N) St in addition to ard deviation Square root of the variance, so it’s 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 +/- 2 sd of the mean. Coefficient of variation = the st in addition to ard 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 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 relationship between the dependent in addition to 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; sample 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 as long as smaller samples. The distribution of sample means is called the sampling distribution. The sampling distribution is approximately normal. St in addition to ard Deviation Versus St in addition to ard Error The mean of the sampling distribution equals the population mean. The st in addition to ard deviation of the sampling distribution (also called the st in addition to ard error of the mean) equals the population st in addition to ard deviation / the square root of the sample size. The st in addition to ard error is an index of sampling error—an estimate of how much any sample can be expected to vary from the actual population value.

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The Logic of Statistical Tests Hypothesis testing involves determining if differences in dependent variable measures are due to sampling error, or to a real relationship between independent in addition to dependent measures. Three basic steps: Define the hypothesis Select appropriate statistical test Decide whether to accept or reject the hypothesis Hypothesis Testing “If you have a hypothesis in addition to I have another hypothesis, evidently one of them must be eliminated. The scientist seems to have no choice but to be either soft-headed or disputatious” (Platt, 1964, p. 350). Accepting or Rejecting the Null Hypothesis The region of unlikely values is the level of significance, or . Alpha (type I error) represents the likelihood of incorrectly rejecting the null hypothesis. Type II error () is the probability of accepting the null hypothesis when it is actually false. Beta is greatest when alpha is low, sample size is small, effects of independent variable are small, in addition to /or sampling error is high.

Consequences of Statistical Decisions Actual state of affairs Decision VI. Choosing a Statistical Test Choice of a statistical test depends on: Level of measurement as long as the dependent in addition to independent variables Number of groups or dependent measures The population parameter of interest (mean, variance, differences between means in addition to /or variances) Comparing Counts (Categorical Data): the (Chi)-square test Single sample chi-square test: assesses the probability that the distribution of sample observations has been drawn from a hypothesized population distribution. Example: Does self-control training improve classroom behavior Teacher rates student behavior; outcome (the observed frequencies) compared to distribution of behavior ratings as long as entire school (the expected frequencies).

Correlation in addition to Regression: Limitations Outliers R2 versus significance The ‘n’ issue Causation versus association

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