Feb 23, 2016
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.