Transcript Statistical Analysis

Statistical Analysis
I have all this data.
Now what does it mean?
Height (cm)
Plant Height vs. Amount Watered
20
18
16
14
12
10
8
6
4
2
0
10 mL
25 mL
50 mL
1
Amount Watered
Can you say that a bean plant will grow taller with
50 mL of water instead of 25 mL?
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 only
Ex- number of wolves born in
given year
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
Quantitative data can be subdivided
into:
Ratio - with equal divisible
intervals & absolute zero
Interval - does not have
absolute zero
Decide which type of data you have__________________
Describing data
Central 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,
Standard Deviation σ , Variance σ2
http://www.mathsisfun.com/data/standard-deviation.html

For qualitative data - Frequency distribution
chi square by paul anderson
Frequency Distribution
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
Quantitative Data
Parameters
Ratio data
Type of data
data collected using
a scale with equal
intervals and with
an absolute zero
(distance, velocity)
Central tendency
Mean
Interval data
using a scale with
equal intervals but
no absolute zero
(temp0C, pH)
Mean
Qualitative
Nominal data
Ordinal data
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)
Mode
Median
Variation
Range
Standard
deviation
Variance
Range
Standard
deviation
Variance
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
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.
Inferential Statistics
Is the data statistically significant?
NOT due to random chance or error or uncontrolled variable
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?
Dependent
Variable
(DV)
continuous
Continuous IV
T-test or
ANOVA
Nominal IV
T-test or
ANOVA
Ordinal IV
T-test
Scatter plot
Bar graph of
means
Bar graph of
means
Dependent
Variable
(DV)
Ordinal
Continuous IV
Nominal IV
Ordinal IV
Chi-square
Mann-Whitney’s
test
Spearman’s test
Scatter plot
Or Histogram
Bar of means
Scatter plot
Dependent
Variable (DV)
Nominal
Continuous IV
Nominal IV
T-test or F-test
Paired-Mcnemar’s
Unpaired-Chi-square
Bar graph of
means
Bar graph of
proportions
Ordinal IV
Spearman’s test
Scatter plot
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
statistically 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 - Chance
Could 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 hypothesis
p-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 t-test and Chi-square test
(using calculated degrees of freedom and Level of Significance of
0.05 = 95%)
Compare calculated value to table value.
Calculated value < table value means P>0.05
Null hypothesis is accepted
Calculated value > or = table value means P<0.05
Null hypothesis is rejected.
s/w does it for you, and will show you p-value
If P<0.05 then reject Null & accept alternative hypothesis