Statistics made simple - PowerPoint Presentation

Slide1

Statistics made simple

Modified from Dr. Tammy Frank’s presentation, NOVASlide2

Why do we need statistics?

Example:Chemical may increase growth of animalWill be tested on houseflyA colony of 20,000 houseflies are divided into 2 groupsGroup 1 gets chemical in foodGroup 2 gets a placebo in same food

What comes next?Slide3

2 weeks later – take random sample of 25 house flies from each group, measure wingspan

What are the results?Slide4

Housefly results

25 houseflies from each groupGroup 1 (with chemical) – 7.5mm wingspanGroup 2 (without) – 7.2mm wingspanWhat does this mean?Are group 1 flies really bigger?

Some might say yes, some might say no

Did you, by chance, happen to pick some larger flies from group 2?

Was there sampling error or bias?Slide5

One way to be sure is to measure all 20,000 flies……not feasible

So what do we do?Slide6

Statistics

You say the flies are bigger, I say notStatistics provide rules to help us find outStatistics will help tell us if these are significant (real) differencesIs there bias? Where bigger ones in group 2 picked by chance?Statistics will tell us what the chances are that the results are due to sampling bias or random chanceSlide7

Significant Difference

Real differenceDue to chemical, not chanceIf test shows probability of getting results by chance or random error is <5%, we accept claim that chemical produced larger flyIf test shows that the probability of getting results by chance or random error is >5%, we reject claim that chemical produced larger flySlide8

5% is arbitrary cut-off point that is generally accepted

However, if the cost of making an incorrect decision is very high, there will be higher cut-off like 1%such as research with cancer drugs, etc.Probability value is the p-valueMeasure of probability that the pattern we see in our data is due to sampling error or random chanceSlide9

Scientific Method

Remember that we cannot “prove” anything. We can only accept or reject a hypothesisA theory is the closest that a biologist can come to “proving” a hypothesisSupported and validated by data and scientific communitySlide10

Null and Alternative Hypotheses

For any experiment/survey/study, there must be a null hypothesis and an alternative hypothesisSet up so that one of them must be true, and one must be falseNull hypothesis (H0): = or ≤ or ≥Example:

The average weight of hermit crab group A is the same as that of hermit crab group B (=)

OR

The average weight of hermit crab group A is the same or greater than that of hermit crab group B (≥)

OR

The average weight of hermit crab group A is the same or less thank that of hermit crab group B (≤)Slide11

If null is true, then alternative must be false

Ho: average weight of hermit crab group A = average weight of group BHA: average weight of hermit crab group A ≠ average weight of group BSlide12

Two-tailed hypotheses

Use if you have no expectationsYou are trying to find out if weights are different but have no reason for them to beHo: average weight of hermit crab group A = average weight of group BH

A

:

average weight of hermit crab group A ≠ average weight of group BSlide13

One-tailed hypothesis

Use if you have an expectation of the outcome, based on previous studies or informationFor example, previous studies have demonstrated that Group A area has more hermit crab food that Group BHo: average weight of hermit crab group A ≤ average weight of group B

H

A

:

average weight of hermit crab group A › average weight of group B

Alternative hypothesis corresponds to what you expectSlide14

Always reject or accept the null hypothesis, never reject the alternativeIf you accept or support the null, then don’t mention the alternative

If you reject the null, then accept or support the alternativeWe never prove a hypothesisWe just gain a measure of how confident we are with our hypothesisSlide15

p-value

The measure of the probability that the pattern we see in our data is due to random chance or sampling error0.05 is the value most commonly usedIf p-value is ›0.05 (high p-value), accept nullWeight is not significantly differentIf p-value is ≤0.05 (low p-value), reject null and accept alternative

Weight is significantly differentSlide16

Important terms:

x = measurement value∑ = sum ofn = sample sizedf = degrees of freedom = n – 1X = mean or average = ∑x/n

√ s

2

= Standard deviation = average distance from mean

s

2

= Variance = mean of sum of squares

∑(x – X)

2

/

df

Tells you how much your values varied from mean

Large variance means there is large spread in data, small variance means data points are closer to meanSlide17

What test do you use to get p?

Depends on what type of data you are collectingMeasurement variable or nominal variables?Slide18

Measurement variables

Something that can be counted or measuredInvolves numbersExamples: length, weight, quantityWhat are examples of tests that can be used?Slide19

t-test

Used to determine if two sets of data have the same meanPaired t-test – when measurements are linkedPatient before and after using drugThe null would state there is no differenceUnpaired t-test – when you have before and after within 2 different groups

Patients with drug (group 1) and patients without drug (group 2)Slide20

What do you do when there are more than 2 sets of data?

ANOVA – analysis of varianceNull would state that the means are equalExample would be if you had 5 groups of patients taking drugs at different dosages per groupSingle factor ANOVAOnly vary one parameter – drug dosageTwo factor ANOVA with or without replication

Vary dosage and time of daySlide21

Nominal variables

Usually involves categoriesA nominal variable is often a word or percentageExamples: color, sex, genotypesWhat are examples of

tests that can be used?Slide22

Goodness of fitness test

Chi-square