Transcribed Image Text:Iranian researchers studied factors affecting patients' likelihood of wearing orthodontic appliances, noting that
orthodontics is perhaps the area of health care with the highest need for patient cooperation (Behenam & Pooya,
2007). Among their analyses, they compared students in primary school, junior high school, and high school. The
data that follow have almost exactly the same means as they found in their study, but with far smaller samples.
The score for each student is his or her daily hours of wearing the orthodontic appliance.
Groups
nk
Primary school: 16, 13, 18
Junior high school: 8, 13, 14, 12
High school: 20, 15, 16, 18
Primary school
15.67
6.33
Junior high school
11.75
6.92
High school
17.25
4.92
State research and null hypotheses in words & symbols:
The F-distribution shows values of F you would get if you repeatedly drew 3+ samples from one particular population and
calculated the ratio of between-groups to within-groups variance.
dfpetween =
dfwithin
dftotal =
Determine the critical value and mark it on the
distribution to the right.
Ferit (dfpetween dfwithin) =
5%
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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