Introductory Statistics for Environmental Sciences: Lecture Supplement and Workbook

Chapter 1 INTRODUCTION TO STATISTICS AND SAMPLING
Section 1 WOLF CASE STUDY
IMPORTANT TERMINOLOGY
Section 2 DATA
SAMPLING
Section 3 SOURCES OF ERROR
EXPERIMENTAL DESIGN
SUMMARY

Chapter 2 ORGANIZING AND GRAPHING DATA
Section 1 ORGANIZING QUALITATIVE DATA
Section 2 ORGANIZING QUANTITATIVE DATA
STEM AND LEAF PLOT
SUMMARY

Chapter 3 DESCRIPTIVE MEASURES
Section 1 DESCRIPTIVE MEASURES
MEASURES OF CENTER
Mean
Median
Mode
Section 2 MEASURES OF DISPERSION
Range
Variance
Standard Deviation
Coefficient of Variation
Empirical Rule
Section 3 GROUPED DATA
WEIGHTED AVERAGE
Section 4 MEASURES OF POSITION
Z-scores
Percentiles
Quartiles
Outliers
Section 5 THE FIVE NUMBER SUMMARY AND BOXPLOTS
SUMMARY

Chapter 4 CORRELATION AND SIMPLE LINEAR REGRESSION
Section 1 IDENTIFYING AND QUANTIFYING BIVARIATE RELATIONSHIPS
Scatterplots
Linear Correlation Coefficient
Section 2 ORDINARY LEAST SQUARES REGRESSION
Slope
Y-Intercept
Shortcut Formulas
Prediction
Section 3 THE COEFFICIENT OF DETERMINATION
Residuals
SUMMARY

Chapter 5 PROBABILITY
Section 1 PROBABILITY RULES
COMPUTING PROBABILITIES
Relative Frequency Approximation
Classical Approach
Subjective Probabilities
Section 2 THE ADDITION RULE
Contingency Tables
Complements
Section 3 THE MULTIPLICATION RULE
‘AT LEAST’ PROBABILITIES
Section 4 CONDITIONAL PROBABILITY
Section 5    COUNTING METHODS
Permutations
Combinations
SUMMARY

Chapter 6 DISCRETE PROBABILITY DISTRIBUTIONS
Section 1 RANDOM VARIABLES
PROBABILITY DISTRIBUTION
THE MEAN OF A DISCRETE RANDOM VARIABLE (EXPECTED VALUE)
THE VARIANCE AND STANDARD DEVIATION OF A DISCRETE RANDOM VARIABLE
Section 2 BINOMIAL DISTRIBUTION
Computing Binomial Probabilities
The Mean and Standard Deviation of a Binomial Random Variable
Binomial Probability Histograms
SUMMARY

Chapter 7 CONTINUOUS PROBABILITY DISTRIBUTIONS
Section 1 CONTINUOUS PROBABILITY DISTRIBUTIONS
Uniform Probability Distribution
Normal Probability Distribution
Standard Normal Distribution
Section 2 THE STANDARD NORMAL DISTRIBUTION
Area to the Left of the Z-score
Area to the Right of the Z-score
Area between Two Z-scores
Using EXCEL to Find Area
Finding Z-scores for a Given Area
Area to the Left
Area to the Right
Area in between Two Z-scores
Section 3 APPLICATIONS OF THE NORMAL DISTRIBUTION
Finding the Area for a Normal Random Variable
Finding the Value of a Normal Random Variable
Section 4 ASSESSING NORMALITY
SUMMARY

Chapter 8 SAMPLING DISTRIBUTIONS
Section 1 SAMPLING DISTRIBUTIONS
Normal and Non-Normal Distributions
Section 2 THE DISTRIBUTION OF THE SAMPLE PROPORTION
SUMMARY

Chapter 9 STATISTICAL INFERENCE: CONFIDENCE INTERVALS
Section 1 CONFIDENCE INTERVALS
Confidence Intervals about the Mean ()When the Population Standard Deviation ()Is Known
Determining Sample Size When Estimating the Mean
Section 2 CONFIDENCE INTERVALS ABOUT THE MEAN () WHEN THE POPULATION STANDARD DEVIATION IS () UNKNOWN
Section 3 CONFIDENCE INTERVALS ABOUT THE POPULATION PROPORTION (p
The Sample Proportion
The Assumption of Normality When Estimating Proportions
Determining Sample Size When Estimating a Population Proportion
SUMMARY
Confidence Interval Summary
Sample Size

Chapter 10 STATISTICAL INFERENCE: HYPOTHESIS TESTING
Section 1 HYPOTHESIS TESTING
The Fundamentals of Hypothesis Testing
Components of a Formal Hypothesis Test
The Null and Alternative Hypotheses
TYPES OF ERRORS
GUILTY OR NOT GUILTY?
Writing a Good Conclusion
Section 2 HYPOTHESIS TEST ABOUT THE POPULATION MEAN () WHEN THE POPULATION STANDARD DEVIATION () IS KNOWN
The Classical Method for Testing a Claim about When Is Known
Testing a Hypothesis Using P-values
Computing P-values
Testing a Hypothesis about a Population Mean Using Confidence Intervals
Section 3 HYPOTHESIS TEST ABOUT THE POPULATION MEAN () WHEN THE POPULATION STANDARD DEVIATION () IS UNKNOWN
The Classical Method
P-value Approach
CONCLUSION
Section 4 HYPOTHESIS TEST FOR A POPULATION PROPORTION (p)
SUMMARY: PUTTING IT ALL TOGETHER USING THE CLASSICAL METHOD

Chapter 11 STATISTICAL INFERENCES FOR TWO POPULATIONS
Section 1 INFERENCES ABOUT THE DIFFERENCES OF TWO POPULATIONS
INFERENCES ABOUT TWO MEANS WITH DEPENDENT SAMPLES—MATCHED PAIRS
Hypothesis Tests with Matched Pairs
Construct and Interpret a Confidence Interval about the Differences of the Data for Matched Pairs
Section 2 INFERENCES ABOUT TWO MEANS WITH INDEPENDENT SAMPLES
TWO-SAMPLE HYPOTHESIS TEST
Construct and Interpret a Confidence Interval about the Difference of Two Independent Means
Section 3 INFERENCES ABOUT TWO POPULATION PROPORTIONS
HYPOTHESIS TEST FOR TWO POPULATION PROPORTIONS
Using the P-Value Approach
Construct and Interpret a Confidence Interval about the Difference of Two Proportions
SUMMARY

Chapter 12 CHI-SQUARE TESTS
Section 1 THE CHI-SQUARE DISTRIBUTION
Goodness-of-Fit Test
Section 2 TEST FOR INDEPENDENCE
HYPOTHESIS TEST FOR INDEPENDENCE
Section 3 TEST FOR HOMOGENEITY OF PROPORTIONS
CASE STUDY: GREY WOLF
SUMMARY

MINITAB COMPUTER LABS
1 INTRODUCTION TO MINITAB
2 DESCRIPTIVE STATISTICS
3 CORRELATION AND REGRESSION
4 NORMAL PROBABILITY PLOTS AND CONFIDENCE INTERVALS
5 HYPOTHESIS TESTING WITH ONE SAMPLE
6 TWO POPULATION TESTING
7 CHI-SQUARE TESTS FOR GOODNESS-OF-FIT AND INDEPENDENCE