Definition and Description of Statistics
Not what you're looking for?
Define / describe in your own words the following terms and give an example of each.
a. F distribution
b. F statistic
c. Chi-square distribution
d. T distribution
e. Dependent samples
f. Independent samples
g. Degrees of freedom
h. T statistic
i. Paired difference
Purchase this Solution
Solution Summary
The definition and description of statistic terms are discussed.
Solution Preview
Define / describe in your own words the following terms and give an example of each.
a. F distribution
b. F statistic
c. Chi-square distribution
d. T distribution
e. Dependent samples
f. Independent samples
g. Degrees of freedom
h. T statistic
i. Paired difference
Solution:
a. F distribution:
The F distribution is defined by F =[ U/n1]/[V/n2], where U and V are independent chi square variables with n1 and n2 degrees of freedom respectively. Thus if independent random samples of size n1 and n2 respectively are taken from normal populations with variances 1^2 and 2^2 then
S1²/1²/S2²/2² F n1-1,n2-1
b. F statistic:
Here are the steps required to compute an f statistic:
• Select a random sample of size n1 from a normal population, having a standard deviation equal to σ1.
• Select an independent random sample of size n2 from a normal population, having a standard deviation equal to σ2.
• The f statistic is the ratio of s12/σ12 and s22/σ22.
The following equivalent equations are commonly used to compute an f statistic:
f = [ s12/σ12 ] / [ s22/σ22 ]
f = [ s12 * σ22 ] / [ s22 * σ12 ]
f = [ Χ21 / v1 ] / [ Χ22 / v2 ]
f = [ Χ21 * v2 ] / [ Χ22 * v1 ]
where σ1 is the standard deviation of population 1, s1 is the standard deviation of the sample drawn from population 1, σ2 is the standard deviation of population 2, s2 is the standard deviation of the sample drawn from population 2, Χ21 is the chi-square statistic for the sample drawn from population 1, v1 is the degrees of freedom for Χ21, Χ22 is the chi-square statistic for the sample drawn from population 2, and v2 is the degrees of freedom for Χ22 . Note that degrees of freedom v1 = n1 - 1, and degrees of freedom v2 = n2 - 1 .
Suppose you randomly select 7 women from a population of women, and 12 men from a population of men. The table below shows the ...
Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.