Topics: Statistics, Sampling, Experimental Design, Frequency Histograms, Measures of Central Tendency, Measures of Variation, Normal Distribution, and Linear Correlation.
Section 1.1: Introduction to Statistics
Learning Objectives
Definitions of statistics
Examples of population parameters and sample statistics
Classifying variables: quantitative vs. qualitative (nominal, ordinal, interval, ratio)
Key Concepts
Statistics: The study of collecting, organizing, analyzing, and interpreting numerical data.
Individuals: People or objects in a study.
Variables: Characteristics measured or observed in individuals.
Population Parameter: A value that describes a characteristic of a population.
Sample Statistic: A value describing a characteristic of a sample.
Section 1.2: Sampling
Learning Objectives
Define sampling frame and sampling error
Examples of simple random sampling and systematic sampling
Differences between cluster sampling and convenience sampling
Key Concepts
Sampling Frame: List of individuals from which a sample is drawn.
Under Coverage: Omitting population members from the sampling frame.
Sampling Error: The difference between the population mean and the sample mean.
Non-sampling Error: Mistakes in data collection or measurement.
Section 1.3: Experimental Design
Learning Objectives
Steps for conducting a statistical study
Identifying bias in survey design
What is randomization?
Key Concepts
Hypothesis: Statement regarding a population parameter to be tested.
Randomization: Assigning participants randomly to treatment groups.
Blinding: Participants unaware of their group assignment to reduce bias.
Section 2.1: Frequency Tables and Histograms
Learning Objectives
Steps for making a frequency table
Class limits, relative frequency, and significance
Key Concepts
Frequency Table: A table that displays the frequency of occurrences of different classes of data.
Class Limits: The minimum and maximum values in a class.
Relative Frequency: Frequency of a class divided by the total number of observations.
Section 3.1: Measures of Central Tendency
Learning Objectives
Calculate mean, mode, and median
Define trimmed mean and weighted average
Key Concepts
Mean: Average of a data set.
Median: Middle value when data is sorted.
Mode: Most frequently occurring value in a data set.
Trimmed Mean: Average calculated after removing outliers.
Weighted Average: Average where some values contribute more to the final average than others.
Section 3.2: Measures of Variation
Learning Objectives
Calculate range, variance, and standard deviation
Understand the coefficient of variation (CV)
Key Concepts
Range: Difference between the maximum and minimum values.
Variance: Measure of how much values differ from the mean.
Standard Deviation: Square root of variance, indicating spread of data.
Coefficient of Variation: Ratio of standard deviation to mean, expressed as a percentage.
Section 4.1: Normal Distribution and the Empirical Rule
Learning Objectives
Properties of the normal curve
Differences between Chebyshev intervals and the empirical rule
Key Concepts
Normal Distribution: Bell-shaped curve where mean, median, and mode are equal.
Chebyshev’s Theorem: At least 75% of data falls within 2 standard deviations of the mean.
Empirical Rule: In a normal distribution, 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3.
Section 4.2: Linear Regression and Coefficient of Determination
Learning Objectives
Explain least squares line and its equation
Calculate and interpret the coefficient of determination (R²)
Key Concepts
Least Squares Line: Line that minimizes the sum of the squares of the residuals.
Coefficient of Determination (R²): Proportion of variance in the dependent variable predictable from the independent variable.
Summary
Statistics is essential for data analysis and interpretation in various fields, especially in healthcare.
Understanding sampling methods and measures of central tendency is crucial for conducting studies.
The normal distribution and variation are key to analyzing data and making predictions.