Lecture 1: Introduction

Key Concepts

1. Biostatistics is the application of statistical methods to biological research including laboratory experiments, medical/clincial research, and health service research.
2. Statistical thinking needs to be done early, when you are planing your study and before you start collecting data. In particular, do not just think about the analysis when you are ready to write up your results.
3. There are many resources at Vanderbilt for obtaining study design and analysis advice

Review Questions

1. When and where are the Biostatistics clinic held? Who can attend? What topics are emphasized on each day of the week?
2. From the main course web page, find these useful documents
   • Glossary of statistical terms
   • The article "Detecting skewness from summary information" from the BMJ statistical notes series
   • The manuscript checklist detailing some common statistical problems to avoid.

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Lecture 2: Descriptive statistics

Key Concepts

1. The distribution of a continuous random variable can be summarized by many statistics including the mean, standard deviation, variance, median, and interquartile range, but not all are appropriate in all situations. For example, the mean, sd, and var all assume that the data come from a symmetric distribution; the median and IQR do not require this assumption to be valid measures.
2. Dynamite plots are a poor method for summarizing data as they violate many of the principles of good graphic design. Always consider plots that show all of the underlying data, particularly when doing initial exploratory data analysis.
3. A well-designed figure or table effectively communicate a wealth of information. Poorly designed figures or tables can hide the real story in the data.

Review Questions

1. What are the differences between the (sample) standard deviation and the (sample) standard error of the mean?
2. An investigator is interested in describing the underlying distribution of the CD4 count in a group of subjects. Which of the following summary statistics would be appropriate if the CD4 count comes from a distribution that is (a) symmetric, (b) skewed to the right, (c) negatively skewed, and (d) bimodal?
   • Mean
   • Standard deviation or variance
   • Standard error of the mean
   • Median
   • Interquartile Range
   • Histogram
   • Empirical cumulative distribution function
3. A study has collected ages in a random sample from a population. Consider the empirical cumulative distribution of ages (Figure 1) and the frequency distribution (Figure 2) to answer the following questions. Note that there are 20 subjects in the sample, so each of your answers should be divisible by 0.05 (e.g. 0.05, 0.10, 0.15, etc)
   • What is the estimated probability that age is less than or equal to 35 years?
   • What is the estimated probability that age is greater than 75 years?
   • What is the estimated probability that age is between 35 and 60 years?
   • Describe the shape of the distribution of age using the provided empirical CDF or the probability density (frequency distribution)
   • Examine Figure 1 and Figure 2. How could the figures be improved to better compare the empirical CDF to the frequency distribution?
     

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• Figure 1. Empirical Cumulative Distribution Function (Problem 1):
  

• Figure 2. Probability Density Function (Problem 1):
  

Lecture 3: Ideas behind hypothesis testing

Key Concepts

1. Be able to restate a scientific question into an appropriate, testable null and alternative hypothesis.
2. Understand the (convoluted) logic behind hypothesis testing. In particular, we start with a null hypothesis that is assumed to be true, collect data, and then either reject or fail to reject the null based on how well the data and the null hypothesis agree.
3. Be able to differentiate between type I (alpha) and type II (beta) errors

Review Questions

1. Which of the following statements about p-values are correct? If they are incorrect, why are they wrong?
   • Simply stated, a p-value is the probability that the null hypothesis is false
   • If I conduct the right test and get p = 0.001, my results are significant
   • If I conduct the right test and get p = 0.03, my results are significant
   • If I conduct the right test and get p = 0.08, there is a trend towards significant results
   • If I conduct the right test and get p = 0.85, the null hypothesis is probably true. If we are comparing two treatments and the null is that they are the same, they are probably equally effective.
2. Is it more conservative to use an alpha level of .01 or an alpha level of .05? Would beta be higher for an alpha of .05 or for an alpha of .01?

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Lecture 4: 1-sample tests

Key Concepts

1. Be able to recognize situations where it is appropriate and not appropriate to use a 1-sample t-test
2. Understand the relationships between test statistics and p-values
3. Be able to test a particular null hypothesis using either a confidence interval or p-value

Lecture 5: 2-sample tests

Key Concepts

1. Be able to recognize situations where it is appropriate and not appropriate to use a 2-sample t-test
2. Understand the key inputs (alpha, standard deviation, effect size, etc.) used to make sample size or power calculations. Also, know where to find these inputs in the literature or obtain them using pilot studies.
3. Be able to carry out simple sample size/power calculations using the PS software, web resources, or other software packages.