Dr Kari Lock Morgan Synthesis and Review for Exam 2 EXAM 2 Inclass on Monday 119 Covers everything we have done in class or lab so far Chapters 1 6 in book except not 26 but with emphasis on Chapters 4 6 ID: 428320
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Slide1
STAT 250Dr. Kari Lock Morgan
Synthesis and Review for Exam 2Slide2
EXAM 2In-class on Monday, 11/9Covers everything we have done in class or lab so
far (Chapters 1 – 6
in book, except not 2.6), but with emphasis on Chapters 4 – 6
Bring a non-cell phone calculator
Bring two one-sided pages of notes (8 ½ x 11 paper) (or one two-sided page of notes)
Review reading and optional review problems posted on
WileyPlus
(doing lots of problems is the best way to study!)Slide3
Exam Topics: Ch 1-3 Chapter 1: Data Collection
Data (cases, variables, etc.)
Sampling
Observational studies and confounding
Randomized experiments
Chapter 2: Descriptive Statistics (except not 2.6)
Summary statistics for one or two variable(s)
Graphical displays for one or two variable(s)
Conditional
probability
Chapter 3: Confidence Intervals
Sampling distributions
Confidence intervals
Margin of error
Standard error and 95% confidence intervals
Bootstrapping
Percentile method for any level of confidenceSlide4
Exam Topics: Ch 4-6 Chapter 4: Hypothesis Testing
Stating hypotheses
Randomization distribution
p-value
T
est conclusions (generic and in context)
Errors
Multiple testing, publication bias, replication of results
Connecting intervals and tests
Chapter 5: Normal Distribution
Hypothesis tests using the normal distribution
Confidence intervals using the normal distribution
Chapter
6
: Inference for Means and Proportions
Central Limit Theorem
Standard error formulas
N(0,1) and t-distribution
Analyzing paired
vs
unpaired data
Sample size for desired margin of error (proportion only)Slide5
Question of the Day
Do lizards learn to behaviorally avoid invasive fire ants?
Topic, data, and following slides are from Tracy
Langkilde
, Associate Professor of Biology at Penn State
(
Langkilde
Lab
)Slide6
Red Imported Fire AntSolenopsis
invicta
: “World’s worst ant pest”
Native to South America, but expansive invasive range, including much of southern US
Disperse rapidly
Predicted to go global
Aggressive
Impose novel selective
pressures on native species
Similar habitats as
fence lizardsSlide7
Fire ants eat lizardsSlide8
Lizards eat fire antsSlide9
Exposure to venom causes immediate and delayed mortality
Langkilde and
Freidenfelds
2010 Wildlife Res
Control
Stung
Fed
Time (weeks)
% SurvivalSlide10
Lizards and Fire AntsThe study took lizards, exposed them to fire ants, and observed their reactionsLizards were either from an area invaded with fire ants (southern Alabama, invaded for >70 years) or not yet invaded (eastern Arkansas)
Researchers recorded the lizards’ time to flee (in seconds) and the number of twitches (number of times lizard did a body twitch within 60 seconds)
Langkilde
, T. (2009).
Invasive fire ants alter behavior and morphology of native lizards
,
Ecology
,
90
(1): 208-217. Slide11
Video from Data CollectionSlide12
ParameterTo see if uninvaded lizards take longer to flee than invaded lizards, which parameter would be most appropriate?
Single mean
Difference in means
Single proportion
Difference in proportions
CorrelationSlide13
HypothesesTo see if uninvaded lizards take longer to flee than invaded lizards,
state the relevant hypotheses.
H
0
:
μ
ui
>
μ
i
,
H
a
: μui =
μ
i
H
0
:
μ
ui
=
μ
i
,
Ha: μui
≥ μi H0: μui = μi, H
a: μui > μi H0: μui ≥ μ
i, Ha: μui = μi H0: μ
ui = μi, Ha:
μui < μiSlide14
VisualizationTo see if uninvaded lizards take longer to flee than invaded lizards,
which type of graph would be most appropriate?
Bar chart
Segmented bar chart
Histogram
Side-by-side boxplots
ScatterplotSlide15
Standardized Statistic
Calculate the relevant standardized statistic.Slide16
DistributionWhich distribution should you compare this statistic to?
Standard Normal
t with 40
df
t with 39
df
t with 79
df
t with 80
dfSlide17
SignificantAre the results statistically significant?
Yes
NoSlide18
ConclusionThe appropriate generic conclusion is
Reject H
0
Do not reject H
0
Reject H
a
Do not reject H
aSlide19
Conclusion in ContextWrite a conclusion in context.Slide20
Causal Conclusion?Can we conclude that the presence of invasive fire ants in their habitat causes lizards to adapt their behavior?
Yes
NoSlide21
Number of TwitchesNext, we’ll investigate whether number of twitches is higher for invaded lizards than for uninvaded lizardsSlide22
Randomization TestThe p-value is closest to…
0.0005
b)
0.001
c)
0.05
d)
0.1
e)
0.4Slide23
ConclusionThe appropriate conclusions are
Reject H
0
. We have evidence that invaded lizards twitch more than
uninvaded
lizards.
Do not reject H
0.
We have evidence that invaded lizards twitch more than
uninvaded
lizards
.
Reject H
0
. We do not have evidence that invaded lizards twitch more than uninvaded lizards
.
Do not Reject
H
0
. We do not have evidence that invaded lizards twitch more than
uninvaded
lizards.Slide24
ErrorIf we did make an error in this test, which type of error would we have made?
Type I
Type II
Either one
Neither oneSlide25
ErrorHow could we have reduced the chances of making a Type I error?
Decrease α
Increase
α
Increase
n
Decrease
n
Either increase α or increase
nSlide26
ErrorHow could we have reduced the chances of making a Type II error?
Decrease α
Increase
α
Increase
n
Decrease
n
Either increase α or increase
nSlide27
Number of Twitches and Time to FleeIs there an association between number of twitches and time to flee?Which type of graph would be most relevant?
Bar chart
Segmented bar chart
Histogram
Side-by-side boxplots
ScatterplotSlide28
Number of Twitches and Time to FleeIs there an association between number of twitches and time to flee?
Which statistic would be most relevant?
Single mean
Difference in means
Single proportion
Difference in proportions
CorrelationSlide29
Confidence IntervalIf we were to create a bootstrap distribution to generate a confidence interval for the correlation between number of twitches and time to flee, where would the distribution be centered?
0
-0.341
ρSlide30
TestIf we were to create a randomization distribution to test for an association between number of twitches and time to flee, where would the distribution be centered?
0
-0.341
ρSlide31
Intervals and TestsA 95% confidence interval for the true correlation between number of twitches and time to flee is (-0.50, -0.17). Using α = 0.05, if we were testing for an association between the two variables, we would
…
Reject H
0
Not reject H
0
Impossible to tellSlide32
To DoSTUDY FOR EXAM 2! (Monday, 11/9)