Statistical analysisStatistical analysis

Types of AnalysisTypes of Analysis

Mean

Range

Standard Deviation

Error Bars

MeanMean

the average of data points (central tendency)

how to calculate: add numbers together and divide by the number of data points

ex: data: 10, 11, 12, 9, 8, and 7 cm

(10+11+12+9+8+7) = 57 / 6 numbers = 9.5

RangeRange

the difference between the largest and smallest observed values

how to calculate: subtract the smallest value from the largest

ex: 12 - 7 = 5 cm

(very small or very large values--outliers--will affect the range)

Standard DeviationStandard Deviation

a measure of how the individual observations of a data set are spread out around the mean

IB will permit you to use a graphing calculator

how to calculate...how to calculate...

data set: data: 10, 11, 12, 9, 8, and 7 cm

1. find the mean: 9.5

2. subtract the mean from each data point (ex. 10 - 9.5 = 0.5) 0.5, 1.5, 2.5, -0.5, -1.5, -2.5

3. square the deviations found above: 0.25, 2.25, 6.25, 0.25, 2.25, 6.25

4. sum the squares of deviations: 0.25 + 2.25 + 6.25 + 0.25 + 2.25 + 6.25 = 17.5

5. divide by one less than the number of figures: 17.5 / 5 = 3.5

6. take the square root of this number: sq. root of 3.5 = 1.87

in a normal distribution, about 68% of the data lies within 1 standard deviation (in either direction) and 95% lies with in 2

Error barsError bars

a graphical representation of the variability of data

can be used to show either the range or the standard deviation on a graph

Complete the following data Complete the following data table to find the mean and table to find the mean and

the rangethe rangeSeedling Height After 21 Days (cm)

Plant Number Maple Oak Birch1 5.0 7.1 5.8

2 5.2 7.2 5.8

3 4.9 7.4 5.5

4 4.8 6.9 5.4

5 4.5 6.8 5.7

6 5.3 7.0 5.9

7 5.1 7.4 5.4

8 4.8 7.1 5.7

Mean

Range

Now find the standard Now find the standard deviation for each set of deviation for each set of

valuesvaluesSeedling Height After 21 Days (cm)

Maple Oak Birch

Mean

RangeStandard Deviation

Create a bar graph (label title, axes, units) to show the range as an error

bar for each species of tree.

One More SD PracticeOne More SD PracticeResidents of upstate New York are accustomed to large amounts of snow with snowfalls often exceeding 6 centimeters in one day. In one city, such snowfalls were recorded for two seasons and are as follows (in centimeters):

8.6, 9.5, 14.1, 11.5, 7.0, 8.4, 9.0, 6.7, 21.5, 7.7, 6.8, 6.1, 8.5, 14.4, 6.1, 8.0, 9.2, 7.1

Find the mean, range, and standard deviation for this data.

What are the mean and the population standard deviation for this data, to the nearest hundredth?

The t-testThe t-test

Used to determine if a difference between two data sets is considered significant

Were your results significant? Or were differences due to chance?

Look up t value on chart to find the probability (p) that chance alone could produce that difference

if p = .50, then there is a 50% probability that your results are due to chance

if p = .05, there is only a 5% probability

the smaller the p value, the less likely it is that your results are from random chance

to find p, you must know the t-value and the degrees of freedom (we will learn how to do this on Excel)

degrees of freedom = the sum of the sample sizes of each of the two groups minus two

then look up on t value table

your result should fall within p=0.05 to be significant

Correlation Vs. Correlation Vs. CausationCausation

Correlation- an observational trend made without an experiment (ex. many people who smoke get lung cancer)

Causation- must be proved by an experiment (experiments showed that chemicals in cigarettes damage lung tissue and can cause cancer)

to determine correlation, you can calculate the value r (use calculator)

r varies from completely positive correlation (+1) to no correlation (0) to completely negative correlation (-1)

correlation is still not cause!!