MARE 250 Dr. Jason Turner Introduction to Statistics

“After evaluating millions of pieces of data in the blink of an eye, the Gamble-Tron 2000 says the winner is...Cincinnati by 200 points!? Why, you worthless hunk of junk” – Professor John Frink Deals with the calculation of trends and differences from repeated collections of information Way to analyze quantitative observations consisting of numerical facts – DATA Statistics 101

“Well, sure, the Frinkiac-7 looks impressive, don't touch it, but I predict that within 100 years, computers will be twice as powerful, 10,000 times larger, and so expensive that only the five richest kings of Europe will own them.” – Professor John Frink Refers to the analysis and interpretation of data with a view toward objective evaluation of the reliability of the conclusions based on the data

Statistics 101 Allows us to make quantitative decisions regarding relationships within our datasets Answers questions like: Are they different? Is there a relationship? Can we predict Y using X?

Initial Observations Explanatory Model Hypothesis Null Hypothesis, Formulated with Experimental Test in Mind Experiment or Field Sampling Test DATA STATISTICS Statistics 101

Stats in Marine Science 1. Sample vs. Population 2. Parametric vs. Nonparametric stats 3. Measures of Central Tendency 4. Hypothesis testing/p values 5. Means Testing – testing for differences 6. Linear Associations – relationships 7. Assumptions – parametric vs. non 8. Means tests – t-test, ANOVA (1 way, 2 way), MANOVA 9. Correlation/Regression

Intro to Stats - Summary

Statistics 101 Allows us to make quantitative decisions regarding relationships within our datasets Answers questions like: Are they different? Is there a relationship? Can we predict Y using X?

Stats in Marine Science Two major types of statistics: Descriptive Statistics: consists of methods of organizing and summarizing information Inferential Statistics: consists of drawing and measuring the reliability of conclusions about a population based upon information obtained from a sample of the population

Stats in Marine Science Descriptive Statistics: consists of methods of organizing and summarizing information Used to summarize or “explain” your data Cannot examine or publish “raw data” Includes measures of central tendency and variation, also graphs and charts

Descriptive Statistics Length of Raccoon Butterflyfish (in mm) 10.0, 11.2, 10.5, 19.7, 70.7, 77.5, 20.2, 33.6, 44.7, 52.3, 55.0, 67.8, 70.3, 21.5, 18.2, 17.5, 34.6, 39.0, 40.2, 66.5, 70.2, 68.6, 10.0, 11.2, 10.5, 19.7, 70.7, 77.5, 20.2, 33.6, 44.7, 52.3, 55.0, 67.8, 70.3, 21.5, 18.2, 17.5, 34.6, 39.0, 40.2, 66.5, 70.2, 68.6

Descriptive Statistics Length of Raccoon Butterflyfish (in mm) Average (mean): 42.6 Median (middle): 40.2

Inferential Statistics Inferential Statistics: consists of drawing and measuring the reliability of conclusions about a population based upon information obtained from a sample of the population Why? Cannot survey an entire population Sample a portion of the population, analyze, and infer conclusions regarding the population

Inferential Statistics Population: collection of all individuals or items under consideration in a statistical study Sample: that part of the population from which information is obtained

Sample vs. Populations The primary objective of statistic analysis is to infer characteristics of a group of data by analyzing the characteristics of a smaller sampling group Populations – the entire collection of measurements about which one wishes to draw conclusions e.g. – If you wish to measure the age of all Yellow tang at Puako, then the population is all Yellow tang at Puako. “Dear Baby…Welcome to Dumpsville…Population – You.” – Homer Simpson

Populations of interest are often so large as to render the obtaining of all measurements unfeasible Samples – a subset of measurements which can be used to draw conclusions about the characteristics of the population from which the samples were taken Sample vs. Populations

Population Sample

Sample vs. Populations

The statistics calculated will vary from sample to sample for samples taken from the same population Therefore it is up to US to choose the best sample possible Therefore – note the following rules of sample procurement… “Then there is the man who drowned crossing a stream with an average depth of six inches.” - W.I.E. Gates Sample vs. Populations

3 Rules for Good Statistics 1.It is desirable to take an infinitely large number of samples from a population 2.It is desirable that a statistic obtained from any single sample from a population be very close to the value of the parameter being estimated 3.Multiple large samples can be taken from a population which become a better estimate that a single sample

Stats in Marine Science Two major types of statistics: Descriptive Statistics and Inferential Statistics Use Descriptive for all; Inferential for some

Stats in Marine Science Type of experiment can have an effect the statistics you will employ 2 basic types: Observational Study and a Designed Experiment

Stats in Marine Science Observational Study: researchers observe characteristics and take measurement - sample survey - would employ descriptive statistics Designed Experiment: researchers impose treatments and controls and then observe characteristics and take measurements

Stats in Marine Science Important Design Terms: Response Variable: the characteristic of the experimental outcome that is to be measured or observed Factor: a variable whose effect the response variable is of interest in the experiment

Stats in Marine Science Important Design Terms: Level: the possible values of a factor Treatment: Each experimental condition; levels of single factors or combination of levels for large, multifactor experiments

Stats in Marine Science Response – variable of interest; variable you collect - #Fish, %Coral cover, temperature, salinity, etc Factor – variable by which response is divided; categorical - location, Date, Gender, Species Level – components of factor; - Location (Puako, Hilo Bay), Date (Jan, Feb), Gender (♂, ♀)

Stats in Marine Science Response – Raccoon Butterflyfish Length Factor – Location Levels - Richardson’s, Puako Butterflyfish Lengths Richardsons Butterflyfish Lengths Puako

Variables and Data Variables: a characteristic that varies from one person or thing to another Qualitative Variable: – nonnumerical valued variable; sex, eye color, marital status Quantitative Variable: – numerical variable; height, weight, counts

Variables and Data Types of Quantitative Variables: Discrete: – quantitative variable whose values can be listed; # of something, counts Continuous: – a quantitative variable whose possible values form some interval of numbers; height, weight, length

Variables and Data Data Terms…. Observation: – individual piece of data; a data point Data Set: – collection of all observations for a particular variable Data are pleural….

Variables and Data Grouping Quantitative Data Classes: – categories for grouping data Frequency: – the number of observations that fall within a class Frequency Distribution: a listing of all classes and their frequencies

Variables and Data Grouping Quantitative Data Relative-Frequency: – the ratio of the frequency of a class to the total number of observations Relative-Frequency Distribution: – a listing of all classes and their relative frequencies