RAMESH DEBUR

Hypothesis testing

The Way Back

Formulate a research QuestionDevelop a research MethodologyCollected DataSorted Data

The Way Forward

IntroductionGENERATE A HYPOTHESIS

NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS

Significance The p Value

Errors TYPE 1 TYPE 2

ACCEPT OR REJECT HYPOTHESISINFERENCE & PRESENTATION OF THE DATA

Hypothesis Testing

Scientific Hypothesis testing – A Deductive method of accepting or rejecting a hypothetical

statement

Definition

A hypothesis consists either of a suggested explanation for a phenomenonEg: Gastric Juices produces Hunger

or A reasoned proposal suggesting a possible correlation between multiple phenomena

Eg: People who smoke more cigarettes are at a higher risk of developing lung

cancer

Therefore…..

Hypothesis testing implies either accepting or rejecting a certain statement.

Generating a Hypothesis In Scientific Research the hypothesis is an offshoot of the research question

Eg: Do people who smoke more cigarettes increase their risk of developing Lung Cancer

The Logic of Hypothesis Testing

All hypothesis are false until proven true The farther away from falsification the truer is the hypothesis

A Hypothesis is NEVER a Fact. We accept a hypothesis as true until it is falsified

Eg: Columbus wants to discover a route to India Columbus Discovers America Every body he sees are called Indian – Hypothesis Later learns they are not Indian – Hypothesis falsified

The NULL Hypothesis

The exact opposite of the perceived effect or change

Eg: Gastric Juices DOES NOT cause Hunger Smoking DOES NOT Increase the risk of Developing Lung Cancer

The Alternate Hypothesis

The Exact opposite of the NULL Hypothesis

Called alternate because the falsification is the primary logic of hypothesis testing Gastric Juices DOES NOT cause Hunger Smoking DOES NOT Increase the risk of Developing Lung Cancer

Easier to Falsify things than prove facts?????

Disproving Null Vs Proving the Alternate

Null Alternate

THE NEXT QUESTION

WHEN DO WE REJECT THE NULL HYPOTHESIS

ANSWER : WHEN THE CHANCES OF IT BEING TRUE ARE VERY SLIM ( NON SIGNIFICANT)

PROBABILITY TESTING

Probability (prob·a·bil·i·ty)

Similar to Chance:Derived from the Noun Probable What is a probability : The chance of a event occurring at any given time

The likelihood of an event having a particular outcome

Eg: Flipping a coinAll probability is between 0 and 1

Flip a coin

Likelihood of getting only 1 head in 1 flip = 0.5 2 flips = 0.34 4flips = 0.24 10 = 0.01 100=0.00001

Likelihood of getting atleast 1 head in 1 flip = 0.5 2 flips = 0.66 4flips = 0.76 10 = 0.99 100=0.999999

Probability as related to hypothesis testing

The p value

The likelihood that the data collected is equal to or more extreme than the null hypothesis (logic: The Null hypothesis is the extreme value of an experiment)

Alternatively: The probability that the expected outcome occurred purely by chance

Significance - Definition

The significance level of a test is the probability that the test statistic will reject the null hypothesis when the [hypothesis] is true.

IN REAL TERMS

Get Test statistic (outcome of research )

Null hypothesis – test statistic if > chance : accept test and reject null

If ≤ chance : reject testGenerally the significance is kept at 0.05 or 1 chance in 100 or 0.001( 1 in 1000)

Errors of Hypothesis testing

Stastical Decision

True state of the Null Hypothesis

True HO False HO

Reject HO Type 1 ( α) Correct

Do Not Reject HO Correct Type II (β)

α is also called as the significance value and is determined by the investigator

A type 1 error is considered much more serious than a type 2 error

Why? EG. A new drug is introduced into the market which can potentially cure hypertension but can also cause sudden death. Evaluate the chances of sudden death by the drug

Statistical Decision

True state of the Null Hypothesis

True HO NO Death False HO Death

Reject HO Type 1 ( α) (Accept drug)

Correct (Reject drug)

Do Not Reject HO Correct (Accept Drug)

Type II (β) (Reject Drug)