MAKING MEANING OUT OF DATA Statistics for IB-SL Biology

MAKING MEANING OUT OF DATA

Statistics for IB-SL Biology

There are two types of data.

QuantitativeQualitative


Quantitative dataMeasured using a naturally occurring numerical

scale Examples

Chemical concentration Temperature Length Weight…etc.

If you give a group of students a taste test and they have to rank drinks in order of 1-10 as to which one they like, would this be quantitative data?


Qualitative dataInformation that relates to characteristics or

description (observable qualities)Information is often grouped by descriptive

categoryExamples

Species of plant Type of insect Shades of color Rank of flavor in taste testingQualitative data can be “scored” and evaluated numerically

Can you count EVERY ONE?!?!

Sampling Data

Don’t have enough time or resources to measure every individual in a population.

Choose and measure a representative sample from a population.

Need to have a good SAMPLE SIZE in order to “believe” your data. (statistically significant)

Sample Size –

How many can you measure?

Statistical analysis of a sample

Mean: is the average of data pointsRange: range is the measure of the spread

of dataStandard Deviation: is a measure of how

the individual observation of data set are dispersed or spread out around the mean

The standard deviation tells us how tightly the data points are clustered together.

When standard deviation is small—data points are clustered very close

When standard deviation is large—data points are spread out



We will use standard deviation to summarize the spread of values around the mean and to compare the means and spread of data between two or more sample

In a normal distribution, about 68% of all values lie within ±1 standard deviation of the mean.

This rises to about 95% for ±2 standard deviation from the mean


Confidence Intervals (CI) We will use a CI of 95%. How many standard deviations away from the mean is this? This 95% CI will be used to measure the “significance” of

the data. We are 95% confident that the mean will be found within

this interval. What do we call data that lies outside of this?



Let’s imagine a scenario… You are trying to find the average height of a 5th grade

student. You measure 15 students present in one 5th grade class. You calculate the mean to be 1.6 m and the confidence

interval to be +/- 0.5m. This +/- amount represents which value? You measure a second class of 5th grade students, and then a

third class of 5th graders, etc. 95% of the time the mean should be between which two values?


Your experiment leads you to a new question… Are 6th graders the same height as 5th graders? You should always assume the null hypothesis, or n0. This is that there is no significant difference between the

two variables. You use the same procedure to measure the height of 6th

graders. How will you know if there is enough of a difference

between the average heights of the two groups to truly be different?

Statistical significance: 95% of the data should not overlap

So, CI’s should not overlap. If they do, it is not statistically significant (not different).


To present your data for all IA’s, you MUST use MS Excel. CI’s will be represented on graphs through the use of error

bars. These error bars represent the spread of data around the

mean.


Classes158

160

162

164

166

168

170

161.6

168.266666666667

5th graders6th graders

Heig

ht

(cm

)


What can you conclude when error bars do overlap?

No surprises here. When error bars overlap, you can be sure the

difference between the two means is not statistically significant.

Why? Due to chance variations!


What can you conclude when error bars do not overlap?

When error bars do not overlap, you cannot be sure that the difference between two means is statistically significant.

The t-test is commonly used to compare these groups.

We WILL be learning about t-tests.


What if you are comparing more than two groups?

ANOVA is a statistical test commonly used for comparing multiple groups.

We will not be using ANOVA!

The t-test

The t-test determines whether the difference observed between the means of two samples is significant

The test works by considering the following: The size of the difference between the means of the

samples. The number of items in each sample. The amount of variation between the individual

values inside of each sample…this is known as…? The t-test always assumes what is called the null

hypothesis, or n0.This always states that there is no significant

different between the two pieces of data.

The t-test

When a t-test is performed it returns a “p” value.We want p< 0.05When p < 0.05 this means that less than 5% of

the time the CIs of the two groups will overlap.5%...why does this sound familiar?This means that the two groups ARE

statistically different. When p > 0.05, there is a greater chance the CIs

of the two groups will overlap.This means that the two groups ARE NOT

statistically different.The difference is due to natural randomness.

The t-test

Let’s go back to the height of the 5th and 6th graders…

Using a calculator or Excel, you determined the following value:

p = 0.117695155What question do you ask yourself? Is there a difference between the heights of the 5th

and 6th graders?

Correlation

Correlation is a measure of the association between two factors.

The strength of the association between two factors can be measured.

An association in which all the values closely follow the trend is described as being a strong correlation.

An association in which there is much variation, with many values being far from the trend, is described as being a weak correlation.

A value can be given to the strength of the correlation, r. r = +1 a complete positive correlation r = 0 no correlation r = -1 a complete negative correlation

Correlation

0 5 10 15 20 25

0

10

20

30

40

50

60

70

80

90

100R² = 0.695346381573607

Sunlight Intensity vs. Temperature

Sunlight (lux)

Te

mp

era

ture

(C

)

Correlation

Correlation

Documents

MAKING MEANING OUT OF DATA Statistics for IB-SL Biology