Statistical Analysis

I have all this data. Now what does it mean?

Is your data Quantitative or Qualitative?

Continuous quantitative – measurement scale divisible into partial units Ex-Distance in kilometers

Discrete quantitative - measurement scale with whole integers onlyEx- number of wolves born in given year

Quantitative data can be subdivided into:Ratio - with equal divisible intervals & absolute zero Interval - does not have absolute zero

Qualitative Nominal - objects are named or can’t be ranked Example- Gender (male/female)

Qualitative Ordinal - objects are placed into categories that can be ranked

Example- activity of an animal on a scale of 1 to 5

Decide which type of data you have__________________

Describing dataCentral tendency (How different 2 sets of Data is) Mode - value that occurs most often Median - middle value when ranked

highest to lowest Mean - mathematical average

Variation (How spread out the data is) For quantitative data –Range

http://www.mathsisfun.com/data/standard-deviation.html

For qualitative data -Frequency distribution Frequency Distribution example link

Statistics Software

… is not going to do your job for you.

It is:

not going to tell you what test to select

not going to tell you if the test you selected is the right one

not going to tell you how to interpret the test results.

Making decisions about descriptive statistics & Graphs

Decide which type of data you have, parameters you will need to calculate and on your Excel chart, enter the formula for each of the parameters.

Quantitative Data Qualitative

Parameters Ratio data Interval data Nominal data Ordinal data

Type of data data collected using a scale with equal intervals and with an absolute zero (distance, velocity)

using a scale with equal intervals but no absolute zero (temp0C, pH)

objects are placed into categories that cannot be ranked (male/female or brown, black, red hair)

objects are placed into categories that can be ranked (Moh’s hardness scale or color ranked 1- 10)

Central tendency Mean Mean Mode Median

Variation RangeStandard

deviationVariance

RangeStandard

deviationVariance

Frequency Distribution

Frequency Distribution

Degrees of freedom

Total # of samples -2(ex. 15+15-2 = 28)

Total # of samples -2(ex. 15+15-2 = 28)

(#rows –1) x (#columns-1)

(#rows –1) x (#columns-1)

Level of significance

0.025 0.025 0.05 0.05

Inferential Statistics Is the data statistically significant?

Statistical Tests

The t-test (or Analysis of Variance): two or more groups to compare measurements of each group.

The Chi-square test: counts that can be placed into yes or no categories, or categories such as quadrants.

The Pearson R Correlation: to test how the values of one event or object relates to the values of another event or object

How to select statistical test?Is Dependent Variable (DV)

continuous, ordinal, or nominal?

Null Hypothesis (μ) …..states that there is no difference between

the mean of your control group and the mean of your experimental group. Therefore any observed difference between the two sample means occurred by chance and is not significant.

If you can reject your null hypothesis then there is a significant difference between your control and experimental groups. Hence accept the alternative (original hypothesis).

Write your null hypothesis _____________________________

Probability - ChanceCould the difference between the groups

due to random chance /error?Probability of error or p-value < 0.05 means that

the error in the research is 5/100 or below 0.05

(95% results have no error)

P<0.05

Less than 5% chance is considered to be OK.

Reject Null hypothesis

Accept your alternative (original) hypothesis

P>0.05

Greater than 5% then the data is not significant.

Must accept Null hypothesis

Level of significance () and Degree of freedom (df)

Level of significance () - It communicates probability of error in rejecting Null hypothesisp-value < 0.05 means that the probability of error in the research is 5/100 (95% results with no error)

Degree of freedom (df) - It is number of independent observations in a sample.

t-test df = (n1-1) + (n2-1)Chi-square df = (#rows – 1) (#columns – 1)Pearson R correlation df = (n-2) subtract 2 from the number of comparisons made.

T test Chi square tables.doc

Accept or Reject the null hypothesis

Find the table value for the t-test and the Chi-square test

(using calculated degrees of freedom and the Level of Significance of 0.05 = 95%)

Compare calculated value to table value.

Calculated value < table value Null hypothesis is NOT rejected

Calculated value > or = table valueNull hypothesis is rejected.