Hypotheses + Collecting DATA PDF

Preview

Summary

Download Hypotheses + Collecting DATA PDF

Description

HYPOTHESES + COLLECTING DATA Hypothesis testing steps 1. Develop a hypothesis 2. Decide on a null-hypothesis 3. Design your data collection (experiment) a. Including planning statistical test to use 4. Calculate a test statistic 5. Find the probability (-p-value) of that test statistic 6. State what the p-value means in the real world a. Refer back to your null hypothesis Hypotheses A hypothesis is not…  A proven fact  A wild guess or crackpot theory It is…  The best explanation for the observable facts  Testable  Discarded if it does not fit the facts Hypothesis example  You observe a person with a blue colour to their skin.  You know that blue skin is often caused by low blood oxygen levels.  You hypothesise that the person is hypoxic  Does that definitely mean that the person is oxygen deficient? Not certain that the blue colour is caused by hypoxia? You need to test your hypothesis! The problem with hypotheses  Hypotheses generally hold that there is a difference between groups, or a relationship between variables, or that there has been a change in something  It is often impossible to prove that sort of hypothesis  Therefore, we cannot test hypotheses statistically, so we need to do something else The Swan Hypothesis  You are a British bird watcher  You look at all the swans in Britain – mute swan, whooper swan, Bewicks swan  You hypothesise that all swans are white  How would you prove this hypothesis?  Not proved unless you observe ALL swans everywhere  Hypothesis is shown to be wrong by one observation of black swans in Australia The Null Hypothesis  We need a testable statement that can be falsified  This is called the null hypothesis (H0)  It is, essentially, the opposite of your hypothesis  In statistics, the original hypothesis is called the alternate hypothesis (H1) Testing the Null Hypothesis

  

Since we cannot prove that the alternate hypothesis (H1) is true We try to show that H0 is unlikely to be true If the H0 does not match the facts, we say that the H1 is supported

Null Hypothesis Example  You observe a person with a blue colour to their skin  Alternate hypothesis (H1): the person is hypoxic  Null hypothesis (H0): person has normal blood oxygen You test H0 and their oxygen level is very low Your H1 is supported by evidence Collecting Data Several steps involved in obtaining data Null hypothesis  population  sample  observation Each step controls the following step Data are a set of observations Data are raw material used to answer the questions Defining a population First, clearly define your area of interest  All epileptic males in VIC  All Eucalyptus trees in Toorak  All arthritis sufferers in the world That is your statistical population NOT THE SAME AS A POPULATION IN ECOLOGY OR POLITICS Defining a population and sample Population – any collection of individual units that are the subject of study Sample – any collection of individual units that are drawn from a population Whole Population studies If you can measure the whole population, you do not need statistics, you know the answer. Remember the swan hypothesis. Sampling a population Generally, too hard to measure whole populations Instead we take a sample Use sample to draw inferences about the population

Getting a Good Sample Samples must be representative…of the whole population Commonly achieved by random sampling Random means each sample of a given size has an equal chance of being selected from the population. Random sampling The human brain does not do random well Several methods available…  Random number table  Random number generator  Draw numbers from a hat  Coin toss  Rolling dice Biased sampling 1936 US Presidential election poll Poll list compiled from the phone book and Literary Digest subscribers list 10 million questionnaires sent out 2.4 million responses Polling prediction

Polling v Election Result

Samples of Convenience

Experimental units Samples consist of experimental units Units may be individual items…  One patient in a cohort  One fish in a school Or something bigger…  A hospital full of patients  A school of fish Non-independent data Experimental units must not affect each other  E.g. fish in a tank are NOT independent because they compete with each other for space and resources. BIAS sample Grammatical Note Note – Data is plural of datum – therefore…  “the data are”, not “the data is”  “the data were”, not “the data was” Observations Get data by measuring replicate experimental units Measurements are called observations Choose appropriate scale of measurement Measurements must be accurate and precise Precision related to units of measurement Why Replication More representative sample – includes more of the variability present Partially counters a measurement error

Pseudoreplication – didn’t talk about in lecture  When replicates are not independent but we treat them as if they are

Scales of Measurement  4 scales of measurement:

Nominal Scale Classifies objects or events into categories Categories are:  Mutually exclusive  NOT ordered  ‘Equal’ or ‘not equal’ (no other relationship)  e.g. coin toss – either heads or tails; there’s two categories and one isn’t better than the other. Nominal Scale Example  Ducks may be classified by gender  Categories are mutually exclusive and not ranked o May be male OR female by NOT both o

Ordinal Scale Classifies and ranks experimental units measured  Does NOT indicate absolute values  Does NOT assume equal intervals between numbers  Does NOT describe relationships between individuals in different classifications Ordinal Scale Example

No relationship between the classes…  (small – extra small) NOT EQUAL (large-medium)  Medium is not 3 times bigger than Extra small  There doesn’t have to be even intervals Interval Scale Classifies and ranks measured variables Also recognises fixed interval between units Interval known so can add and subtract measures No absolute zero (i.e. negative values possible) so cannot multiply or divide Interval Scale Example Temperature  Fixed interval; can add and subtract o 10˚ and 20˚ differ by 10˚  each gap is the same size o 40˚ and 60˚ differ by 20˚  each gap is the same size  No absolute zero, cannot divide o 0˚C does not = no heat energy present o 30˚C is not 3 times hotter than 10˚C Ratio Scale Classifies and ranks and has fixed interval Has an absolute zero Can add, subtract, multiply or divide Ratio Scale Example Measures of mass, length, time, etc.  Fixed interval; can add and subtract o 2kg + 2kg = 4kg  Absolute zero possible, can multiply or o 0kg indicates no mass present o 2kg is twice as heavy as 1kg Interval + Ratio scale data treated much the same way

Scale Information Levels

Converting between Scales  not possible to convert variables to a higher scale o i.e. nominal  ordinal  interval  ratio o NOT POSSIBLE  It is possible to convert variables to simpler forms o i.e. ratio  interval  ordinal  nominal  BUT…you lose information Converting Scales Example

Accuracy and Precision Meaningful analysis impossible without BOTH  Accuracy = closeness of a measured (or computed) value to its true value  Precision = closeness to each other of repeated measurements of the same quantity

Not accurate, but precise.  Instrument sensitive but biased or incorrectly adjusted

Accurate, then not accurate and not precise  Instrument poor quality  Sloppy use

Precision and Measurement Units  For counts of objects (e.g. number of eggs in nest), we are usually sure of the precision of observations  This is not true of continuous variables (e.g. height) o Never exact o Only precise within limits o Limited by units on instrument and by user  We can choose an appropriate level of precision How precise should we be?  Would you measure the width of a lake in millimetres?  Sokal and Rohlf (1995) suggest an appropriate degree of precision as 30 to 300 unit steps between largest and smallest observations  i.e. 30 < (largest – smallest) < 300 Measurement Scale Example  study of growth in squirrels  measures to nearest gram  largest = 110g  smallest = 14g  appropriate: 110-14 = 96 units (within 30-300) Putting it all together  you have been asked to assess the mean height of all of the trees in a forest  there is not enough time to measure all of the trees 1. population = all trees in the forest 2. sample a. Size (n) = depends on time available b. Selection = random (to avoid bias) 3. Experimental unit = individual trees

4. Scale of measurement = ratio scale 5. Measurement method = many options What measurement scale should we use to achieve appropriate precision? Are metres appropriate? Remember Sokal & Rohlf’s 30-300 rule Assume tallest tree is 35m, the shortest is 2m Appropriate: 35 – 2 = 33 units (within 30-300) SUMMARY QUESTIONS  What is a null hypothesis?  What is a population?  What is a sample?  How do we get a good sample?  What are the different scales of measurement?  What does the 30-300 rule say?...