Statistical Error

Statistical Error- 

Type I- Reject null hypothesis when null hypothesis is true (p<.05) 

Type II- do not reject a null hypothesis when the null hypothesis is false, uses beta to express power of test and its results 

Distribution and Deviations

Deviations- 

·     Asymmetric Deviation- Skewed distributions (right is positive, left is negative) 

·     Kurtic Deviation- 

platykurtic- flat, (closer to mean) and 

leptokurtic- peaked (more extreme) 

Normal Curve- area underneath the curve can be used to find probability of finding values greater than X1 

Elementary Data Analysis (EDA)

Measure of central tendency: 

·     Arithmetic mean/average 

·     Median- middle datum of sample – (50% above, 50% below) 

·     Mode- datum that occurs most often (frequency analysis) 

Measure of dispersion: 

·     Asses variation of data around median and mode 

-     Range 

-     Variance 

-     Coefficients of variance 

-     Standard deviation

-     Standard error

Range- numerical data between minimum and maximum 

Variance- measure of variation in data 

Standard Deviation- (SD) measure of spread of data around a mean 

Standard error- describe dispersion of sample mean around the population 

Coefficient of variation- compare amount of variation among data that differs- expressed as percentage 

Synthesis- population and samples (frequency distribution/ elementary statistics) 

Sample/ Probability

Population: Universe of events (ex- patients with aids, red wing birds) 

Rarely able to obtain data from every subject- the solution is samples 

Samples- subsets drawn from a population

Techniques- 

Random- every subject has same probability of being selected (Ex- table, coin flip, drawing straws) 

Systematic- predetermined method (Ex- every 3^rd, every 4^th) 

Convince - obtain under financial constraints

Probability-  the chance or likelihood that an event will occur

Theoretical- chances an event will occur (Ex- coin flip 50%) 

Empirical- based on data collection (Ex- HTHHTTHH) 

Frequency distribution- 

Exploratory Data analysis (EDA) 

-     Used to count frequency of occurrence of each datum in a sample population 

-     Search for trends/ patterns 

Displaying results- frequency distribution 

·     Pie Chart 

·     Bar Chart 

·     Histogram 

·     Relative Frequency – (pie chart/ stacked graph) 

Scientific Method

Scientific Method- 

·     Obtain background information 

·     Ask biological questions 

·     Develop testable hypothesis 

·     Design experiment 

·     Collect data 

·     Analyze data 

·     Interpret results 

·     Answer biological questions 

·     Present results   

Data/ Measurement

Metric- 

·     Volume (ml) 

·     Distance (m) 

·     Temperature (c) 

·     weight (grams) 

Types of Data- 

·     Ratio: True zero (weight, volume, length) 

·     Interval: arbitrary zero (temp, time of day, date) 

·     Ordinal: no number value (dark vs. light) 

·     Nominal: non- numeric (colors) 

Continuous- infinite number of values between two individuals (ex: 2.7, 7.701, 2.702) 

Discrete- integers (ex: 35 seals, 22 cells) 

Accuracy- measuring device (ex: nearest .1 g) 

Precision- researcher (how close they are to repeated measurement) 

Implied Range: value between data 

Rounding rules: If x> 5, then round 

History of Statistics

17^thCentury-

Graunt- Studied affairs of the state/ vital statistics of population 

Petty- economist, probability/ political/ insurance 

Pascal- Probability/ gambling 

Bernoulli- probability/ risks with vaccines 

18^thCentury-

Laplace/ Gauss- normal curve 

19^thCentury-

Auelelet- statistical analysis to human biology, social mechanics 

Galton- genetic regression/ variation 

20^thCentury- 

Pearson- (father of modern statistics) natural selection using correlation, first academic department, journal helped develop chi square analysis 

Gossett- developed student T test 

Fisher- developed ANOVA and importance of experimental design 

20^thCentury (later) 

Wilcoxon- studied pesticides, non-parametric equivalent of two sample tests

Kuskal, Wallis- non- parametric equivalent of the ANOVA 

Spearman- nonparametric equivalent of correlation coeffient 

Kendall- nonparametric equivalent of correlation coefficient 

Turkey- multiple comparisons procedure 

Dunnett- multiple comparisons procedure for control group 

Keuls- multiple comparisons procedure 

Computer tech- growth of investigation into new techniques