STAT E102 Midterm Review March 15, 2006 Review Topics Populations, parameters, sampling Types of data i.e., nominal, ordinal, discrete, continuous Graphical/tabular representations of data Summary statistics Central tendency: mean, median, mode Variability: variance, standard deviation, range, interquartile range Populations, parameters, sampling Types of data i.e., nominal, ordinal, discrete, continuous Graphical/tabular representations of data Summary statistics Central tendency: mean, median, mode Variability: variance, standard deviation, range, interquartile range Review Topics Normal distribution Standardization Z-statistic Probability, conditional probability, Bayes Theorem Diagnostic/screening tests Sensitivity, specificity, predictive value CLT, sampling distributions Normal distribution Standardization Z-statistic Probability, conditional probability, Bayes Theorem Diagnostic/screening tests Sensitivity, specificity, predictive value CLT, sampling distributions Review Topics Hypothesis testing, p-values, alpha 1- vs. 2-sided T distribution, t-tests 1- vs. 2-sample Independent vs. paired (for 2-sample) Type I / Type II error Power, sample size estimation Hypothesis testing, p-values, alpha 1- vs. 2-sided T distribution, t-tests 1- vs. 2-sample Independent vs. paired (for 2-sample) Type I / Type II error Power, sample size estimation Question #1 A clinical trial is in development to compare a new drug for Progressive Multifocal Leukoencephalopathy (PML) to placebo. It is decided that a 2-sample independent t-test will compare the groups at the end of the trial with respect to a continuous variable endpoint. Early drafts of the study protocol estimate that the sample size would be 200 (100 per group). However, a recently completed study suggests that the variability of the endpoint in the two groups is larger than originally planned (i.e., larger than assumed in the original sample size calculations). The sample size is re-estimated using the new variability estimates from the recently completed trial. The result is: A) A larger total sample size B) A smaller total sample size C) The sample size does not change D) We cannot perform a t-test on these data any longer A clinical trial is in development to compare a new drug for Progressive Multifocal Leukoencephalopathy (PML) to placebo. It is decided that a 2-sample independent t-test will compare the groups at the end of the trial with respect to a continuous variable endpoint. Early drafts of the study protocol estimate that the sample size would be 200 (100 per group). However, a recently completed study suggests that the variability of the endpoint in the two groups is larger than originally planned (i.e., larger than assumed in the original sample size calculations). The sample size is re-estimated using the new variability estimates from the recently completed trial. The result is: A) A larger total sample size B) A smaller total sample size C) The sample size does not change D) We cannot perform a t-test on these data any longer Question #1 Sample size equation: n = [(z /2 + z )() / ( 1 - 0 )] 2 Variability is represented by in the numerator. As variability (standard deviation ) increases, n increases. The result is: A) A larger total sample size B) A smaller total sample size C) The sample size does not change D) We cannot perform a t-test on these data any longer Sample size equation: n = [(z /2 + z )() / ( 1 - 0 )] 2 Variability is represented by in the numerator. As variability (standard deviation ) increases, n increases. The result is: A) A larger total sample size B) A smaller total sample size C) The sample size does not change D) We cannot perform a t-test on these data any longer Question #2 T-tests are most useful for what type of data (variables)? A) Continuous B) Ordinal C) Nominal D) Binary T-tests are most useful for what type of data (variables)? A) Continuous B) Ordinal C) Nominal D) Binary Question #2 T-tests are used for continuous data. Recall: Ordinal data have natural order without defined magnitude (ex. low, moderate, high) Nominal data have categories with no order or rank (ex. gender, race) Binary data are discrete data with only two possible outcomes (ex. cancer vs. no cancer) A) Continuous B) Ordinal C) Nominal D) Binary T-tests are used for continuous data. Recall: Ordinal data have natural order without defined magnitude (ex. low, moderate, high) Nominal data have categories with no order or rank (ex. gender, race) Binary data are discrete data with only two possible outcomes (ex. cancer vs. no cancer) A) Continuous B) Ordinal C) Nominal D) Binary Question #3 The probabilities that a 25- to 34-year old U.S. males cholesterol level belongs to one of the following intervals are listed. What is the probability that a male from this population has cholesterol