Observations

• DI Water

• 40% Ethanol

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Statement of Problem• Why does the pigment look faded with 40% ethanol?

Hypotheses• Ha1 Ethanol enters the cell and breaks down the pigment.

• Ha2 Ethanol breaks down the cell membrane releasing contents of the cell including the pigment.

Methods• Control = chopped onions added to water.

• Treatment = chopped onions added to 40% ethanol.

• Measure amount of pigment in two solutions with spectrometer.

SpectrometerMeasures light intensity of different wavelengths (colors)

Sensor

Predictions

• If Ha1, then the control solution will have the same or more pigment than the treatment.

• If Ha2, then the control solution will have less pigment than the treatment.

Ha1 Ethanol enters the cell and breaks down the pigment.Ha2 Ethanol breaks down the cell membrane releasing contents of the cell including the pigment.

Measures of Central Tendency

3 4 4 5 6 7 7 7 7 8 8

Mean = (sum)/n = 66/11 = 6

Median = center value = 7*If n is even, median = avg. of

the two middle numbersex. 1 4 4 6 9 15

median = 5

Indices

Mathematical manipulations of the data to assist with interpretation

Ex. Diet Studies typically record:N = numerical percentageM = mass percentageF = frequency of occurrence

Index of Relative Importance = (N+M)*F

Another example: Shannon Weaver’s Index of Diversity

Graphs

Continuous independent variables

t

Graphs

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

fish present fish removed

prop

ortio

n aq

uatic

pre

y

Discrete independent variablesBar graphs need error bars

Cascades frog stomach contents at fish-containing and fishless lakes

Graphs•X-axis is the independent variable•Y- axis is the dependent variable•Need titles or legends•Bar graphs need error bars, usually +/- SE

SE=Standard Error

Onto stats…

Statistics for this labProcedure #2 Bar graphs need to have error barsError bars will represent the standard error (SE)3 4 4 5 6 7

7 7 7 8 8Dataset A Mean = 66/11 = 6

-200 -58 -20 -15 4 7 7 40 43 70 188

Dataset B Mean = 66/11 = 6

What’s the difference?SEA = 0.52 SEB =

28.18

Standard ErrorSE represents the amount of variation within a sample

SE = (standard deviation) / (sqrt(N))

N is the sample sizeStandard deviation:

T-tests & Statistical HypothesesHo: Treatment (alcohol)

absorption = control (water) absorption.Ha: Treatment absorption ≠ control absorption.

T-tests use means and standard errors to determine whether two discrete groups are significantly different.

T-testsP value Probability(type I error)Level of significance = P

“Statistically significant”

Type I error: rejecting a true null hypothesis

Type II error: accepting a false null hypothesis

Generally, scientists try to minimize the probability of making a type I error.

T-testsHo: Treatment (alcohol) absorption = control (water) absorption.Ha: Treatment absorption ≠ control absorption.

ex. if P=0.48 48% chance that we are wrong to reject Ho. Thus, we do not reject Ho.

P<0.05 acceptable for most things

ex. If P=0.03, we would reject Ho and accept Ha.