Chi-Square Goodness of Fit Tests in Statistics
Chi-square goodness of fit tests
Chi-square goodness of fit
•
Core issue in statistics
:
When are you viewing just
random noise and when is there a real trend?
Chi-square goodness of fit
•
Core issue in statistics
:
When are you viewing just
random noise and when is there a real trend?
Chi-square goodness of fit
•
Core issue in statistics
:
When are you viewing just
random noise and when is there a real trend?
Chi-square goodness of fit
•
Core issue in statistics
:
When are you viewing just
random noise and when is there a real trend?
Chi-square goodness of fit
•
Your response variable is
count data
When to use a chi-square test
•
Your response falls into different
categories
•
You have a hypothesis for
the responses you
expect
•
You want to know if the difference
between
the responses you
observe
and the responses
you
expect
is significant or not
If
the test tells you your data is
not significantly
different
from what you expect, you
support
the hypothesis
How to interpret a chi-square test
If
the test tells you your data
is significantly
different
from what you expect, you
reject
the
hypothesis
No statistical test ever
proves
a hypothesis.
What is chi-square?
x
2
= Chi-square value
Σ = Sum of
x
2
= Σ
(Observed Value – Expected Value)
2
Expected Value
Example problem #1
Chi-square probability
table
Chi-square probability
table
Only 5% chance that the difference
between your obs and exp values comes
from chance alone
Your hypothesis can be rejected
Chi-square probability
table
50-60% chance differences are from random chance
Example problem 2
Female Song Worksheet
Bird song:
It’s not just for males anymore
Male house wrens sing to attract mates
and defend territories
Females sing a lot too!
Why?
Why do females sing?
H1: To help coordinate their behavior with their male
Prediction
Why do females sing?
H2: To solicit copulations from the male
Prediction
Why do females sing?
H3: To defend their nests against other house wrens
Prediction
Why do females sing?
Null hypothesis: Female song occurs randomly
Prediction
Explore the significance of Chi-square goodness of fit tests in statistics. Learn how to differentiate between random noise and actual trends, when to use a Chi-square test, and how to interpret the results. Dive into the core issues and examples associated with Chi-square tests along with a Chi-square probability table. Gain insights into calculating Chi-square values, understanding hypothesis testing, and making informed decisions based on test outcomes.
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Presentation Transcript
Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend?
Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend?
Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend?
Chi-square goodness of fit Core issue in statistics: When are you viewing just random noise and when is there a real trend?
When to use a chi-square test Your response variable is count data Your response falls into different categories You have a hypothesis for the responses you expect You want to know if the difference between the responses you observe and the responses you expect is significant or not
How to interpret a chi-square test If the test tells you your data is not significantly different from what you expect, you support the hypothesis If the test tells you your data is significantly different from what you expect, you reject the hypothesis No statistical test ever proves a hypothesis.
What is chi-square? x2 = Chi-square value = Sum of x2= (Observed Value Expected Value)2 Expected Value Observed Expected Obs-Exp (Obs-Exp)2(Obs-Exp)2 Exp Category 1 Category 2 .. X2 total Degrees of Freedom
Chi-square probability table 0.99 0.95 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.01 df 1 0.0001 0.003 0.015 0.064 0.148 0.275 0.455 0.708 1.07 1.64 2.71 3.84 6.63 2 0.020 0.103 0.211 0.446 0.713 1.02 1.39 1.83 2.41 3.22 4.61 5.99 9.21 3 0.115 0.352 0.584 1.00 1.42 1.87 2.37 2.95 3.67 4.64 6.25 7.81 11.3 4 0.297 0.711 1.06 1.65 2.19 2.75 3.36 4.04 4.88 5.99 7.78 9.49 13.3 5 0.554 1.15 1.61 2.34 3.00 3.66 4.35 5.13 6.06 7.29 9.24 11.1 15.1 6 0.872 1.64 2.20 3.07 3.83 4.57 5.35 6.21 7.23 8.56 10.6 12.6 16.8 7 1.24 2.17 2.83 3.82 4.67 5.49 6.35 7.28 8.38 9.80 12.0 14.1 18.5 8 1.65 2.73 3.49 4.59 5.53 6.42 7.34 8.35 9.52 11.0 13.4 15.5 20.1
Chi-square probability table 0.95 Only 5% chance that the difference between your obs and exp values comes from chance alone 0.99 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.01 df 1 0.0001 0.003 0.015 0.064 0.148 0.275 0.455 0.708 1.07 1.64 2.71 3.84 6.63 2 0.020 0.103 0.211 0.446 0.713 Your hypothesis can be rejected 1.02 1.39 1.83 2.41 3.22 4.61 5.99 9.21 3 0.115 0.352 0.584 1.00 1.42 1.87 2.37 2.95 3.67 4.64 6.25 7.81 11.3 4 0.297 0.711 1.06 1.65 2.19 2.75 3.36 4.04 4.88 5.99 7.78 9.49 13.3 5 0.554 1.15 1.61 2.34 3.00 3.66 4.35 5.13 6.06 7.29 9.24 11.1 15.1 6 0.872 1.64 2.20 3.07 3.83 4.57 5.35 6.21 7.23 8.56 10.6 12.6 16.8 7 1.24 2.17 2.83 3.82 4.67 5.49 6.35 7.28 8.38 9.80 12.0 14.1 18.5 8 1.65 2.73 3.49 4.59 5.53 6.42 7.34 8.35 9.52 11.0 13.4 15.5 20.1
Chi-square probability table 50-60% chance differences are from random chance 0.99 0.95 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.01 df 1 0.0001 0.003 0.015 0.064 0.148 0.275 0.455 0.708 1.07 1.64 2.71 3.84 6.63 2 0.020 0.103 0.211 0.446 0.713 1.02 1.39 1.83 2.41 3.22 4.61 5.99 9.21 3 0.115 0.352 0.584 1.00 1.42 1.87 2.37 2.95 3.67 4.64 6.25 7.81 11.3 4 0.297 0.711 1.06 1.65 2.19 2.75 3.36 4.04 4.88 5.99 7.78 9.49 13.3 5 0.554 1.15 1.61 2.34 3.00 3.66 4.35 5.13 6.06 7.29 9.24 11.1 15.1 6 0.872 1.64 2.20 3.07 3.83 4.57 5.35 6.21 7.23 8.56 10.6 12.6 16.8 7 1.24 2.17 2.83 3.82 4.67 5.49 6.35 7.28 8.38 9.80 12.0 14.1 18.5 8 1.65 2.73 3.49 4.59 5.53 6.42 7.34 8.35 9.52 11.0 13.4 15.5 20.1
Bird song: Its not just for males anymore Male house wrens sing to attract mates and defend territories Females sing a lot too! Why?
Why do females sing? H1: To help coordinate their behavior with their male Prediction
Why do females sing? H2: To solicit copulations from the male Prediction
Why do females sing? H3: To defend their nests against other house wrens Prediction
Why do females sing? Null hypothesis: Female song occurs randomly Prediction
