University:
Brigham Young University
Course:
CPSE496R | Academic Internship: Special Education
Academic year:

2024
Views:

382

Pages:

6
Author:

Adaline W.

SUMMARY OF REGRESSION ANALYSIS MATERIAL 1. What is meant by analysis of variance? Answer : Analysis of variance is an analysis used to compare two or more variants together. Variance analysis is included in comparative analysis (comparison test) 2. What is meant by variance and covariance? Also explain the difference between these two terms! Answer : Variance and covariance are two measures used in statistics. Variance is a measure of the spread of data, and covariance indicates the rate of change of two random variables simultaneously. Covariance is a measure of the correlation between two or more random variables while variance is a special case of covariance where Y=X, in other words variance is a measure of the correlation between two equal random variables. The difference between variance and covariance is that variance is a measure of the spread/dispersion in a population while covariance is considered a measure of the variation of two random variables or the strength of correlation. Covariance is normalized into the correlation coefficient (divided by the product of the standard deviations of two random variables) and variance is normalized into the standard deviation (by taking the square root). In statistics, there are many forms of continuous theoretical distribution including the normal, t, and F distributions. Write down the differences between these three types of distribution in the following matrix table: Dist Normal (Dist Z) Fungtion Dist t Dist F Used as a reference for Used for statistical To test the averages of three calculating several testing with relatively or more populations at once phenomena that are often small sample sizes to determine whether the encountered in everyday averages are the same or life. For example, not. calculating blood pressure, calculating errors and translating IQ values. Value table Calcul ation F(x) = 1 𝑒 formul a 𝜎√2𝜋 1 𝑥−𝜇 2 − ( ) 2 𝜎 t= 𝑥−𝜇 𝑠 1(𝑣1−2) √𝑛 − 1 𝑓(𝐹) = 𝐾 𝐹2 {1+𝑣 1𝐹 𝑣2 }1/2(𝑣1+𝑣2) 1. Complete case 3 on the attached material Case 3 Two statistical test results are known for groups of female and male students. Researchers want to know whether the variance in scores of female students is higher than that of male students. Below are the scores from the statistics exam. Completion steps 1. State Ho and Ha “female students statistics test scores vary more than male students test scores” Ho = 𝜎2per ≤ 𝜎2lak Ha = 𝜎2per > 𝜎2lak 2. Determine the significance level. Significance level = 5% 3. Create a rule for rejecting Ho. Reject Ho if Fcount > Ftable 4. Calculate F and find the Ftable No X1 X2 X12 X22 1 3 4 9 16 2 4 5 16 25 3 5 5 25 25 4 5 6 25 36 5 6 6 36 36 6 6 6 36 36 7 7 6 49 36 8 7 7 49 49 Look for Fcount 9 8 7 64 49 Fcount = (var X1) / (var X2) 10 8 8 64 64 11 9 8 81 64 12 9 8 81 64 13 9 Total 86 value Look for Ftable N1 = 13 : df1 = 13-1 = 12 N2 = 12 : df2 = 12-1 = 11 Ftable = 2,79 = 𝟑,𝟗𝟐𝟑 = 2,311 𝟏,𝟔𝟗𝟕 81 76 616 500 2 Σ𝑋12−(Σ𝑋1) 𝑛 Var X1 = S12 = 𝑛−1 (86 616− 2 ) = 1 3 13−1 616−7.396 13 = 12 = 616−568,92 12 = 47,08 = 3,923 12 Σ𝑋22−(Σ 𝑋2)2 Var X2 = S22 = 𝑛 𝑛−1 (76 500− 2 ) = 1 2 12−1 500−5.776 12 = 11 = 500−481,33 11 = 18,67 = 1,697 11 Make conclusions It can be concluded that Fcount < Ftable 2.311 < 2.79, then Ho is accepted.