statistical analysis ib topic 1. why study statistics? scientists use the scientific method when...

25
Statistical Analysis IB Topic 1

Upload: archibald-arnold

Post on 05-Jan-2016

224 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Statistical Analysis

IB Topic 1

Page 2: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Why study statistics? Scientists use the scientific method when

designing experiments Observations and experiments result in

the collection of measurable data Statistics is a branch of mathematics

which allows us to sample small portions and draw conclusions about the larger population

Page 3: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Words to know and love … Mean

Average of data points Sum divided by the total

Range Measures the spread of data Difference between the largest and smallest Very large or small values are called outliers

Page 4: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

More words … Standard deviation (SD)

A measure of how data are dispersed or spread around the mean

Determined by mathematical formula (which you do NOT need to know)

Use your calculator or online program Error bars

Graphical representation of the variability of data Error bars can show either the range of data OR the SD Look at Figures 1.1 and 1.2 in your packet

Page 5: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Standard Deviation In normal distribution, about 68% of all

values lie within +/- 1 SD of the mean This rises to about 95% for +/- 2 SD from

the mean The SD tells us how tightly the data points

are clustered around the mean Clustered together = small SD Spread out = large SD

Page 6: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Graphical Interpretation

Page 7: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Why is this useful? SD tells you how many extremes are in the

data

Questions: What is the shape of the graph of a normal

distribution of data points? If there are 100 bean plants represented by the

bell curve, how many will be within one standard deviation of the mean?

Page 8: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Comparing the means and spread of data between two or more samples Open your packet to page 6 and look at

the data table for the bean plants First, calculate the mean Look at the data – how would you describe

the values for both sets of data? How can we quantify your observations

about the variability of the data? Find the standard deviation Use your calculator

Don’t worry about the equation (unless you want to)

Page 9: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Options … TI 83, 84

http://www.saintmarys.edu/~cpeltier/calcforstat/StatTI-83.html

TI 86 http://www.saintmarys.edu/~cpeltier/calcforsta

t/StatTI-86.html Online calculator

http://www.graphpad.com/quickcalcs/ttest1.cfm

Page 10: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Back to the bean plants SD in sunlight = 17.68 cm SD in shade = 47.02 cm Looking at the means alone, it appears

there is no difference between the two sets of data

However, the high SD of the plants grown in the shade tells us what? How confident can we be in the data? What conclusions can we draw about just

looking at the mean?

Page 11: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Question… If all the data values are equal, such as 7, 7,

7, 7, what is the standard deviation of this set of four data points?

Page 12: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Answer 0, if all values are the same, there’s no

deviation from the mean

Page 13: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Question If the daily temperatures of a city A range from

10 *C to 30*C for one month, the mean temperature may be 20*C. Another city B may also have a mean temperature of 20*C for the same month. However, the range of city B is only 15*C to 25*C.

Which city has a temperature with a higher standard deviation?

Which city can give a more accurate prediction of weather and why?

Page 14: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Answer City A has a higher standard deviation City B since is has a very narrow range of

temperature or a very low standard deviation

Page 15: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Significant difference and the t-test The t-test is used to determine whether or

not the difference between two sets of data is a significant (real) difference

We use a Table of t values (page 8) You do not need to memorize this! This is a tool scientists use

Page 16: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

How to navigate the table Probability (p)

Bottom of the table (p) that chance alone could make a difference 0.50 = difference is due to chance 50% of the

time This is not a significant difference Statisticians are never 100% certain, but like to be at

least 95% certain

Degrees of freedom Sum of sample sizes of each of the two groups

minus two

Page 17: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Practice Looking at the table … If the degree of freedom is 9, and the

given value of t is 2.60, the table indicates that the t value is just greater that 2.26.

Looking at the bottom of the table, probability that chance alone could produce the result is only 5% This means there is a 95% chance that the

difference is significant

Page 18: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Worked example 1.5 What are the degrees of freedom used to

determine the probability that the differences between the two groups are due to chance?

Using the given t value of 2.00 with your calculated degrees of freedom, what is the probability that chance alone can produce a difference in the heights of these girls?

How confident are we that the British girls are taller than the US girls based on this sample size?

Page 19: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Answers 98

50+50-2 5% 95% confident

Page 20: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Correlation and Causation Observing something can suggest correlation

Experiments provide a test which shows cause

Observations without an experiment can only show a correlation.

Page 21: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Question For years we have known that there is a

high positive correlation between smoking and lung cancer. Does this high positive correlation prove that smoking causes lung cancer?

How can the cause of lung cancer be determined?

Page 22: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Africanized Honey Bees (AHB) Are there any volunteers who can

summarize the relationship between correlation and causation using this example?

Page 23: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Cormorants Example of using a mathematical

correlation test The value of r = correlation

+1 (complete positive correlation) to 0 (no correlation) to -1 (complete negative correlation)

Page 24: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Exit slip Tear and share paper Name, date, period upper right hand

corner Title: Exit Slip

Page 25: Statistical Analysis IB Topic 1. Why study statistics?  Scientists use the scientific method when designing experiments  Observations and experiments

Exit Slip 1. What is standard deviation used for? 2. What is an error bar?