Suppose a researcher wants to see whether teaching students to read using a computer game gives better results than teaching with a tried-and-true phonics method. She randomly selects 20 students and puts them into 10 pairs according to their reading readiness level, age, IQ, and so on. She randomly selects one student from each pair to learn to read via the computer game, and the other learns to read using the phonics method. At the end of the study, each student takes the same reading test. The data are shown in the following table. Student Pair 1 2 3 4 5 6 7 8 9 10 Reading Score under Computer Method 85 80 95 87 78 82 57 69 73 99 Reading Score under phonics method 80 80 88 90 72 79 50 73 78 95 Test whether there is a significant difference between the computer method and the phonics method. If there is a significant difference, which particular method is better?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- Suppose a researcher wants to see whether teaching students to read using a computer game gives better results than teaching with a tried-and-true phonics method. She randomly selects 20 students and puts them into 10 pairs according to their reading readiness level, age, IQ, and so on. She randomly selects one student from each pair to learn to read via the computer game, and the other learns to read using the phonics method. At the end of the study, each student takes the same reading test. The data are shown in the following table.
|
Student Pair |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Reading Score under Computer Method |
85 |
80 |
95 |
87 |
78 |
82 |
57 |
69 |
73 |
99 |
|
Reading Score under phonics method |
80 |
80 |
88 |
90 |
72 |
79 |
50 |
73 |
78 |
95 |
Test whether there is a significant difference between the computer method and the phonics method. If there is a significant difference, which particular method is better?
- A school psychologist is interested in whether or not teachers affect the anxiety scores among students taking the Statistics exam. The data below are the standardized anxiety test scores for students with the three different teachers.
|
Teacher’s Name |
||
|
Ms. San Pedro |
Ms. San Juan |
Ms. San Jose |
|
8 |
23 |
22 |
|
10 |
14 |
18 |
|
12 |
12 |
14 |
|
11 |
8 |
22 |
|
13 |
15 |
22 |
|
15 |
16 |
10 |
|
16 |
14 |
11 |
|
17 |
19 |
9 |
|
9 |
10 |
|
|
10 |
|
|
|
13 |
|
|
Perform an analysis of variance at the 0.05 level of significance.
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