Hypothesis Testing

Scientific Hypotheses and the Scientific Method

• Science- Search for natural explanations of natural phenomena 
• Methodology- Scientific Method 

Scientific Method 

1. Obtain background information (literature search and review, Internet, lab observations) know what's known and what's unknown 
2. Ask biological questions- what questions: descriptive research, how questions: search for casual mechanisms 
3. Develop testable hypotheses
4. Design experiment to test hypothesis 
5. Collect Data
6. Analyze data
7. Interpret results 
8. Answer biological questions- Did data and results support the hypothesis 
9. Present the results- oral or written presentations for publication in a scientific journal 

Statistical Hypotheses and Statistical Testing 

• Null Hypothesis- no differences from experimental hypotheses, no relationship 
• Alternate Hypothesis- opposite the Null Hypothesis 
• Two-tailed and one-tailed variations 

Properties of Data and Variable in Statistics

All scientific data in Science:
Measurements in the Metric System

• Volume (mL or cc)
• Distance (m or km)
• Temperature (°C)
• Weight (g) 

Types of Data:

• Ratio-constant size interval between values. Commonly used. True zero. Ex: most measurements weight, volume, length, etc. 
• Interval- Constant size interval between values, arbitrary zero. Ex: temperature, time of day, date of year
• Ordinal- ordered or ranked data, no numerical difference between data. Ranking. Ex: darker versus lighter, shorter versus taller, faster versus slower
• Nominal- non-numeric qualities or artistes, names, qualitative data. Ex: colors, gender, locations.

Variables:

• Continuous- data where there are an infinite number of values between any two individual values ex: 2.7 and 2.8
• Discrete-integers (counts) ex: 35 seals, 15 subjects

Measurement Concepts:

• Accuracy-About the measuring device. Refers to how close a measurement is to the real measurement, evaluates measuring device. Ex: a scale or balance is only accurate to the nearest 0.1g
• Precision-About the researcher. Refers to how close repeated measurements are to each other. 
• Significant Digits- Implied range
• Rounding Rules- If x>5 then round up. If x<5 then do not round. 

Definitions

Definition of Statistics:

1. Statistics: science or discipline, branch of mathematics. The science of how to make statistics. Concerned with the study and development of concepts ex: data, statistical testing, probability distributions

2. Statistics: numerical summary of data, descriptive or inferential statistics. Used to estimate or make inferences about populations parameters. Ex: population mean, population variance, population standard deviation

3. Statistics: test status that is a result of a statistical test, result of computation. The results of a comparison between 2 or more populations based on samples drawn from those populations. The results of test for a relationship between variables. Ex: t-tests

History of Statistics

Ancient Greek: The Philosophers- they came up with ideas but had no quantitative analyses.
17th Century: Graunt- studied affairs of the state and began the stepping stones for statistics. Petty- Economist who studied probability and created the census technique. Pascal- Studied probability through gambling.
17th-18th Century: Bernoulli-studied probability and risk.
18th Century: Laplace- created the normal curve and studied regression. Gauss- created the bell-shaped curve.
19th Century: Quetelet- applied statistics to human behavior (criminals) in order to predict criminal behavior through physical properties. Galton- (Darwin's Cousin) looked at relationships of parents and their offspring. Applied genetic base for size (height).
Early 20th Century: Pearson- Father of Statistics. Created first statistic journal Biometrika. Formed the first academic department for statistics. Gossett (Student)- student of Pearson's. Studied brewing and created the first student-t test to compare means. Fisher- developed ANOVA to compare 3 or more means.
Later 20th Century: Wilcoxon-biochemist who developed the wilcoxon test. Kruskal, Wallis- economist who developed the non-paramedic equivalent of the ANOVA. Spearman- a psychologist who developed a non-parametric equivalent of the correlation coefficient. Kendall- the first real statistician, developed another non-parametric equivalent. Tukey- Statistician, developed multiple comparisons procedure. Dunnett- biochemist, developed multiple comparisons procedure to compare the control groups. Keuls- agronomist who developed multiple comparisons procedure.
Computer Technology: ENIAC- used during WWII to position guns. Easier to use than calculating by hand.