STATISTICS WORKSHOP PART 1

STATISTICS WORKSHOP PART 1

BIO318 | TA: Madeline Schuster

Adapted version of presentation by Kyla Ercit, Sam Mahabir, Bryan Hughson, Jon Schneider & Jessica Browne

Important DatesOct. 14th● Fall Reading Week à NO CLASS

Oct. 21st● Statistics exercise using Excel *need to download ● Tree Cricket assignment DUE at 6 pm

Oct. 28th● Bibliography assignment DUE at 6pm● Statistics exercise DUE at 6 pm● Meet to discuss journal clubs and proposal presentations● Can also ask last minute questions on statistics exercise

November 4th● Journal Club 1 Due

Our Data So Far

• Qualitative:– Both goose and tree cricket lab were descriptive in

nature

• Quantitative:– Cricket aggression lab

• We haven’t summarized and displayed quantitative data yet…

Stats Time!

Why Do We Need Stats?

• Organize and display raw data

• Make comparisons and interpret findings

• Draw scientifically relevant conclusions

Why do we need stats?Food consumed (g)

apples oranges10 145 15

12 137 168 19

13 315 1017 144 166 5

10 2010 1510 145 15

12 137 168 19

13 3

Why do we need stats?

0

2

4

6

8

10

12

14

16

Apples Oranges

Mea

n co

nsum

ptio

n (g

)

Food options

Is there a difference?

0

2

4

6

8

10

12

14

16

Apples Oranges

mea

n co

nsum

ptio

n (g

)

Food options

P- value

• The likelihood that the data you observed were due to chance

• We typically accept anything less than 5% (p < 0.05)à α = 0.05

• Sometimes α needs to be decreased– This decreases the likelihood of false positive,

or Type 1 error

Is there a statistical difference?

0

2

4

6

8

10

12

14

16

Apples Oranges

Mea

n co

nsum

ptio

n (g

)

Food options

p= 0.098

Steps to Good Statistics

1) Identify your question

2) Identify your variables

3) Look at the structure of your data

4) Figure out the proper test of significance

5) Interpret and present your results







Identify the Question

• Consider the type of data you have (ie: averages, counts, co-varying factors, discrete data, continuous data, etc.)

• What am I asking statistically:– A difference in means between two treatments?– A difference in proportions/occurrence between two

treatments?– A relationship between two variables?

• How does B change as A increases?


• Example:– Do cockroaches on diet A gain more weight than

cockroaches on diet B?

• The Statistical Question:– Is there a difference in mean weight between

cockroaches on diet A vs. cockroaches on diet B?• Difference in means


• Example:– Do lions eat more prey in summer compared to

winter months?

• The Statistical Question:– Is there a difference in the sum of prey consumed

in summer compared to winter?• Difference in proportion/occurrence


• Example:– Does food consumption by fruit flies increase with

the amount of light they are exposed to?

• The Statistical Question:– Is there are relationship between light level and

food consumption?• correlation between 2 variables







Identify the Variables• Which variable is:– Dependent à what you measure in the experiment,

presumably what is affected.• Response variable• Often a measure of behavioral response

– Independent à variable you have manipulated for your experiment• Explanatory variable• This is your “treatment”

• How many of each kind of variable do you have?

Identify the Variables• Which variable is:– Dependent à what you measure in the experiment,


– Independent à variable you have manipulated for your experiment• Explanatory/ Predictor variable• This is your “treatment”


Identify the Variables

• Which variable is:– Dependent à what you measure in the experiment,


– Independent à variable you have manipulated for your experiment• Explanatory/ Predictor variable• This is your “treatment”

Identify the Variables• Are your variables:

– Categorical à limited fixed number of values with no ordering• Male or Female / Diet A or B / type of pet owned• Discrete

– Quantitative à measured on a numeric scale• Number of children / shoe size / number of pets owned• Continuous




– Quantitative à measured on a numeric scale• Number of children / shoe size / number of pets owned• Continuous




– Quantitative à measured on a numeric scale• Number of children / shoe size / number of pets owned/

mass of protein consumed• Continuous


Paired vs Unpaired data• Pairedà• Data collected from the same subjects at different points

in time• Eg. Collecting blood samples from 20 patients with breast

cancer before treatment AND after treatment

• Unpairedà• Data collected from different, independent subjects• Eg. Collecting blood samples in 100 patients with breast

cancer vs 100 healthy patients







Structure of Your Data

• Examining and visualizing your data to:– Spot trends and outliers– Determine whether your data is parametric or

nonparametric

• Can include descriptive statistics: – Mean, Range, Variance, Standard Error

• Best way to look at structure is to plot it!


0

2

4

6

8

10

12

14

16

Apples Oranges

mea

n co

nsum

ptio

n (g

)

Food options

Structure of Your Data:

Relative light intensity

Mas

s of

pro

tein

eat

en

Relative light intensity

Mas

s of

pro

tein

eat

en

Structure of Your Data:

Is your data parametric or non-parametric?

• This will determine which type of statistical test you should use (parametric or non-parametric)

• Parametric tests have strict assumptions, but tend to be more powerful

Data are parametric when:– Independence: Data are independent– Homogeneity of variances: Data from multiple groups

have the same variance– Normality: Data have a normal distribution

Homogeneity of variances

0

2

4

6

8

10

12

14

16

Apples Oranges

mea

n co

nsum

ptio

n (g

)

Food options

Homogeneity of Variances

Examine data spread using boxplots

NormalityFood consumed (g)apples oranges

10 145 15

12 137 168 19

13 315 1017 144 166 5

10 2010 1510 145 15

12 137 168 19

13 315 1017 14

g consumed

coun

t

Normality

Can be visualized with a histogram

Bins


Normal Data = Parametric Tests Non-Normal Data = Non-Parametric Tests







Are you comparing means?

Let’s try an example

0

2

4

6

8

10

12

14

16

Apples Oranges

mea

n co

nsum

ptio

n (g

)

Food options

Based on my examinations: • Data are normally

distributed• Variances are

equal • N = 15

independent data collections

One-tailed vs two-tailed

• Specifies the direction in the statistical test

• Two-tailed: tests two directions of significance– E.g is the mean of x significantly higher OR lower

than mean of y?– More common

• One-tailed: tests one direction of significance– E.g is the mean of x significantly lower than mean

of y?

Run your Test!

• Programs to Consider:– Excel *what we will focus on– R *most common in biology– Minitab– SAS– SPSS







Interpret Results• P value:– probability that the pattern we observed was simply due

to chance– if p <0.05 (5%), there is a statistically significant difference à our pattern is not due to chance

• Other important results:– Correlation coefficients (r values)– Trendlines – Degrees of freedom (has to do with statistical power) – Mean differences – Variation, error, or confidence intervals

Display data

• Present your data in a way that shows the important trends – Potentially multiple ways to display data – this may be the figure you used to look at the

structure or it may be different

• Ensure figures or tables are clear and easy to interpret – Figure caption, axis labels, legend, etc.

Google is your friend

• There is lots of useful information about statistics – theory, code, step-by step explanations, forums, classes, example problems, etc.

• If you are unsure, first do an internet search -this is most like a real research environment

• There are different ways to do things, not just one right answer

Let’s Apply This –Cricket Aggression Time

Steps to Good Statistics1) Identify your question





• Question:– What is the effect of female presence on male-male

aggression in the Field Cricket?

• Hypothesis:– Female presence affects the aggressive behaviors of

male crickets

• Prediction:– Males will show a greater number and duration of

aggressive behaviours when a female is present

Cricket Aggression

• What are we asking statistically:– What is the difference in the occurrence of aggressive

behaviors between two treatments– What is the difference in song duration of males

when females are present vs. when they are absent

• What are we comparing? – Mean? Total counts? – Why?

Identify Your Question

• Dependent Variable?– Aggressive male behaviors• Discrete or Continuous?

• Independent Variable?– Presence or absence of a female• Discrete or Continuous?

Identify Your Variables


• Independent Variable?– Presence or absence of a female• Discrete or Continuous?



• Independent Variable?– Presence or absence of a female


Examine data structure

With Female Without Female

Number of Judders in each treatment group

Plot means and observe trends

0

40

80

120

160

200

duration call w/ female duration calls w/out female

Error Bars!Standard error

Cricket Aggression Lab

• You will write up a full lab report with emphasis on Results

• Add your data to class data from last years cricket aggression lab and ANALYZE the results • Display data• Identify and describe any trends• Consider how you would test this statistically


Mark Breakdown: • Introduction (8 marks)• Hypotheses & predictions (2 marks)• Results (20 marks)• Discussion (10 marks)• References (5 marks)

Total: 45 marks**10 double spaced pages


• Introduction (8 marks)This will be brief – Introduce general behavior we are studying– Introduce the study system and discussing why it is

ideal for addressing the general behavior– Explanation of reason behind this experiment, and

how it relates to prior work. – BRIEFLY describing what we did in our experiment


• Hypotheses (2 marks)– Hypotheses– Predictions– *Make sure you encompass all behaviors


• Results (20 marks) – For each behavior: • Show a descriptive graph • Choose an appropriate statistical test• Briefly justify your reasoning behind the statistical test

choice

– Summarize results and highlight any trends – Do not draw conclusions in this section!


• Discussion (10 marks)– More in-depth discussion behind results– Other information you feel is relevant– Concluding take away/statement– Reference integration

• References (5 marks)– Formatting according to the journal of Animal

Behavior– Variety and quality of references

Next week

• Statistics workshop part 2: Stats exercise

• Handouts and data files can be downloaded on Weebly à you will complete 2

• We will start with an Excel tutorial, but you can complete the exercise in any program of your choice

Using Microsoft Excel

• If you haven’t already:-Install the Excel add-in “Data Analysis ToolPak”

Using Microsoft Excel

Documents

STATISTICS WORKSHOP PART 1