Please turn in your signed syllabus.
We will be going to get textbooks shortly after class
starts.
Homework:
• Reading Guide – Chapter 2: The Chemical Context
of Life. – Finish by Monday. Due the day of the
Chapter 2 Test.
Science Practice 2: The student can use
mathematics appropriately.
Science Practice 5: The student can perform
data analysis and evaluation of evidence.
The Irongate Foundry, Ltd., has kept records of on-thejob accidents for many years. Accidents are reported
according to which hour of an 8-hour shift they
happen. The following table shows their accident
report.
The union at the foundry
wants to know whether
accidents are more likely to
take place during one hour of
the shift rather than another.
They are asking you what you
think.
Chi-square
Chi-square is a statistical test
commonly used to compare
observed data with data we
would expect to obtain according
to a specific hypothesis.
The χ2 test provides a measure of
the difference between the
observed and expected values (χ2
value) and the probability that
the differences are due to chance
alone (the P value)
χ2 assumptions
• Have counts of categorical data & we expect each
category to happen at least once.
• Sample size – to insure that the sample size is
large enough we should expect at least five in
each category.
• Observations are mutually exclusive and
independent.
• The chi-square test is always testing what
scientists call the null hypothesis, which states
that there is no significant difference between
the expected and observed result.
• H0: The observed counts are not statistically
different from the expected counts.
• Ha: The observed counts are statistically different
from the expected counts.
• H0:
The number of accidents during each shift are
equal.
Three steps to performing the chisquared test
1. Calculate the chi-squared value
2. Calculate the degrees of freedom
3. Compare the chi-square value with a scale of
values given by a standard probability.
Equation
O is the observed value
E is the expected value
Shift
1
2
3
4
5
6
7
8 Total
Observed 19 17 15 24 20 26 22 25 168
Expected
(o-e)2
e
Shift
1
2
3
4
5
6
7
8 Total
Observed 19 17 15 24 20 26 22 25 168
Expected
21 21
21
21
21
(o-e)2
e
0.19 0.76
1.72
0.43
0.048 1.19
Χ2 = 5.148
21
21
21
0.048 0.762
21
2. Calculate the degrees of freedom
The degrees of freedom is equal to the number
of classes minus one.
In the Irongate example there are 7 degrees of
freedom because there are 8 shifts. (8-1=7)
• Remember that the chi-square is testing the null
hypothesis.
• H0: The observed counts are not statistically
different from the expected counts.
• Generally speaking, we can reject the null
hypothesis if there is a 95% probability that the
difference between the observed and the
expected is not due to chance. (p value of 0.05)
Χ2 = 5.148
df = 7
Critical value = 14.07
Accept the null hypothesis.
There is not a statistical difference in the number of accidents that
occurred during each shift.
•
•
•
•
•
•
13% brown
14% yellow
13% red
24% blue
20% orange
16% green