Statistics I for QBIC. Contents and Objectives. Chapters 1 7. Revised: August 2013

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1 Statistics I for QBIC Text Book: Biostatistics, 10 th edition, by Daniel & Cross Contents and Objectives Chapters 1 7 Revised: August 2013

2 Chapter 1: Nature of Statistics (sections ) Objectives and activities in Statistics Individuals, variables, and data Types of data: qualitative (categorical) and quantitative Measurement scales: nominal, ordinal, interval, ratio Statistical methods: Descriptive and Inferential Descriptive statistics Inferential statistics Basic concepts in inferential statistics Population Sample Representative sample Simple random sampling Inferential statistics scheme Role of probability in inferential statistics

3 Chapter 2: Descriptive Statistics (sections ) Organizing data: frequency tables and graphs Frequency graphs for categorical data: bargraphs and piecharts Frequency graphs for quantitative data: histograms and stem and leaf diagrams Frequency curves. Special cases Measures of central tendency: mean, median, mode Comparing the measures of center for grouped data Measures of variability or spread: range, variance, standard deviation and coefficient of variation Outliers. Effect of outliers on the measures of center and spread Use of the calculator s statistical functions for the computation of the sample mean and standard deviation Measures of relative standing: percentiles and quartiles Describing the center and spread of a data set with the Five Number Summary and Box Plot

4 Chapter 3: Probability (sections ) Basic concepts in probability Random experiment Sample space Sample points Event Impossible event Certain event Venn diagram Finite probability models Assigning probabilities to events Equally likely sample points Not equally likely sample points Compound events: Intersection, Union, and Complement Mutually exclusive events Conditional probability: computation and interpretation Independent events Probability Rules Addition Complement Conditional Multiplication Bayes Theorem Sensitivity and specificity of clinical tests. Predictive values Computing probabilities using: Venn diagrams Contingency tables Probability trees

5 Chapter 4: Probability Distributions (sections ) A. Basic concepts Random variable Discrete and continuous random variables. Examples Discrete probability distribution B. Discrete Probability Distributions General Discrete Model Properties of a discrete probability distribution Discrete probability tables Discrete probability graphs: point-line graphs & bar graphs Computing and interpreting probabilities of events for a discrete random variable Mean and Standard deviation of a discrete random variable. Computation and interpretation Binomial Distribution Independent Bernoulli trials Binomial random variable Parameters: number of trials (n) and rate of success (p) Probability formulas and tables Mean and standard deviation Word problems

6 Hypergeometric Distribution (Optional) Random experiment Hypergeometric variable Probability formula Mean and standard deviation Word problems Poisson Distribution Random experiment Poisson variable Parameter: mean number of occurrences Poisson probability formula and table Word problems C. Continuous Probability Distributions Introduction Continuous random variables Density curves Computing probabilities as areas under a density curve

7 Normal Probability Distribution Normal random variable Normal density curve. Properties Graphing normal curves Interpreting the areas under the normal curve Empirical rule Computing and interpreting z-scores Standard Normal Curve (SNC). Properties Use of the Standard Normal Table (z-table): (1) Finding areas/probab (2) Finding z-scores Areas under any normal curve Solving word problems Student s t Probability Distribution T random variable T density curve. Properties Degrees of freedom Use of the t-table: (1) Finding t-values (2) Bracketing areas/probab Exponential and Other Continuous Distributions (Optional) Definition of the random variables Density curves Computing probabilities Applications

8 Chapter 5: Sampling Distributions (sections and 5.5) A. Basic Concepts in Inferential Statistics Population Sample Representative sample Sampling techniques Simple random sampling Parameter Statistic Sampling distribution B. Sampling distribution of the sample mean Properties Central Limit Theorem Maximum sampling error C. Sampling distribution of the sample proportion

9 Chapter 6: Estimation (sections , 6.5) A. Basic concepts in estimation Estimation Estimator Point estimates Interval estimates Margin of error Confidence coefficient/level Confidence interval Precision B. Computing and interpreting confidence intervals for: One population mean One population proportion using a large sample C. Determining the appropriate sample size (Optional)

10 Chapter 7: Hypothesis testing based on a single sample (sections 7.1, 7.2 & 7.5) Elements of hypothesis testing Research hypothesis Statistical hypotheses: null and alternative Test statistic (TS) Rejection region (RR). Location and critical values Type I and II errors. Probabilities Alpha and Beta Significance level of the test P-value approach P-values Computing p-values with the z-table Bracketing p-values with the t-table Interpreting p-values Two approaches for testing hypotheses 1) TS vs. RR 2) p-value vs. significance level Conducting tests of hypotheses about (1) One population mean (2) One population proportion

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