Analyzing Data

Advanced BiologyMrs. Morgan

There are three kinds of lies - lies, damned lies and

statistics.  ~Benjamin Disraeli

Using Data

Statistics: The only science that enables different experts using the same figures

to draw different conclusions. - Evan Esar

After collecting data during lab investigations there are many ways to

organize and analyze it.

Presenting Data

• Always present data in charts and graphs as well as in words

• Example:– Table 1 shows the heart rate of

subjects before and after exercise. The average of subjects’ heart rates shows a rise of 10.2 beats per minute after exercise.

SubjectHR

Before ExerciseHR

After Exercise

1 60 84

2 76 80

3 62 90

4 78 110

5 70 92

6 66 92

7 70 88

8 74 80

9 78 100

10 68 88

Avg 70.2 80.4

Simple Data Analysis

Example

Data set: 2 4 5 7 10

Mean

(2+4+5+7+10)/5 = 5.6

Median

middle number = 5

Range

10 – 2 = 8

Median: the middle number in a series of measurements.

Range: the difference between the highest and lowest values in a series of measurements

Mean (average): sum of all measurements divided by the total # of measurements (duh…)

The Q-Test– Used to determine if a data point should be left out

of analysis calculations– Example: data set includes

45, 48, 52, 43, 89, 56, 48, 47, 44, 51, 50(One of these things is not like the others…)

A Q-test decides if the analysis of the data set should include the 89 or not

More Analysis

Q-Test

Q = gap

rangeGap: distance between the outlier and nearest data point

45, 48, 52, 43, 89, 56, 48, 47, 44, 51, 50

Q = (89-56) = 33

(89-43) = 46 = .717

So what do we do with this number?

It helps to put the data points in numerical order

Q-TestUse a Q-table for the expected Q value

N-1 Q-value

3 .94

4 .76

5 .64

6 .56

7 .51

8 .47

9 .44

10 .41

N = number of data points

N-1 = 10

If calculated Q value is greater than expected Q value - discard the data point

Qcalc = .717 > Qexp = .41

Discard point 89

The last and most useful type of analysis

The T-Test

• Determines if the averages of two sets of results are statistically different from each other, thus allowing for a confident conclusion to be made

• The chance that the results are due to coincidence must be below 5%

Say what?

Statistically different: t-test result is less than 0.05

What this means: if results are statistically different, there is less than a 5% chance the results are coincidence - therefore your hypothesis is more likely to be supported

Calculate a t-test value for 2 sets of data and compare it

to .05

Types of Data in a T-Test• Tails:

– One-tailed: experimenter has expected results (one group being higher/lower than another)

– Two-tailed: experimenter only assumes a difference in results

• Paired/Two-Sample– Paired: same group used in each experiment;

dependent (before and after)

– Two-Sample: two separate groups; independent (men v.women)

T-Test Formula

In words: the mean of the first set minus the mean of the second set over the square root of the variance of each group divided by the number of results in each group.

That’s a crap load of math – we’ll use PowerPoint

Using Microsoft Excel

Open the program and create a new workbook.

Under “View” choose to see the “Formula Builder”

T-Test using Microsoft Excel

Type your data in, using one column for each group of

results:

T-Test using Microsoft Excel

• To take a t-test, choose an empty cell and enter a “=“ which will bring up the formula builder.

• If “TTEST” isn’t on the list of functions, search for it at the top of the builder.

• Double click on “TTEST”

Fill in the required data:

• Each of the categories are described

• Array = group of data (highlight the column to select group – don’t include any headings)

• Tails = one or two tailed (1 or 2)

• Type = paired or two-sample (1 or 2) And the answer just appears…

T-Test using Microsoft Excel

Tips for a Better T-Test

• The more results you have, the better and more accurate the results.

• If you have several sets of results, perform t-tests for all of them versus each other.

• The columns of data can also be used to generate graphs if the lab calls for it.