Problem Description and Data

The problem is to determine whether 3 methods of teaching a statistics course differ in effectiveness as measured by students' scores on the final examination.

Method 1. The lecturer neither works out nor assigns problems.

Method 2. The lecturer works out and assigns problems.

Method 3. The lecturer works out and assign problems. Students are also required to
carry out a
projects
that entail the use of the techniques as they are being covered in class.

The research questions are: Does a significant difference exist between the mean
scores (µ_{j}) from the three sub-populations (j = 1,2,3)? If indeed it
does, which sub-population/teaching method/treatment will produce the highest
possible score, on the average?

The same professor teaches 3 different section of students, using one of the 3 methods in
each class. All of the students are sophomores at the same university and are randomly
assigned to the 3 sections. There are only 12 students in the experiment, 4 in each of the
3 different section. This problem is adapted from Hamburg, et al, 1994, p. 400.

The data matrix for the students' score sin the final examination is as follows:

Student |
Method 1 |
Method 2 |
Method 3 |

1 |
16 | 19 | 24 |

2 | 21 | 20 | 21 |

3 | 18 | 21 | 22 |

4 | 13 | 20 | 25 |

Total | 68 | 80 | 92 |

Method
Score

1
16

1
21

1
18

1
13

2 19

2
20

2
21

2
20

3
24

3
21

3
22

3 25

In SPSS/win, you must enter the data into columns by **Factor (teaching Method)** and **Response (Score)**
even though the data matrix is a 3 by 4 table. Note that by viewing a student score as
depending on the specific teaching method employed, **Factor** is conceivably the **Independent
variable (IV) **with **Factor levels/Treatments** as values; while **Response** is
the **Dependent Variable (DV)** with student scores as the values. The dichotomy between
the DV and the IV will become more apparent when we examine the **Regression Analysis**
method.

Use the following **commands** to declare the variable names and their labels:

Double-click on **var** in column one to open the **Define Variable** window;
type *method* in the **Variable Name** box. Open the **Type** window and set **Decimal
Places** to zero ( i.e.; type 0 to replace the default value of 2). Then open the **Labels**
window and type *Teaching Method* in the **Variable Label** box. Click on **Continue**
option then **Okay** to return to the data entry screen.

To define the variable *score,* double-click on **var** in the second column.
Repeat the above steps; type *Final Exam Score* in the **Variable label** box.

Note: Because the *values* are quantitative, the variable **Type** is
automatically set to **Numeric**.

Execute the ANOVA command sequence as described in the **previous page **(provide link).

Select **FILE/PRINT** or the **Printer Icon** to send your output to the local
printer.

**Discussion of the Outputs and Testing Procedure **

:

N | Mean | Std. Deviation | Std. Error | 95% Confidence Interval for Mean | Minimum | Maximum | ||||
---|---|---|---|---|---|---|---|---|---|---|

Lower Bound | Upper Bound |
|||||||||

Final Exam Score | Teaching Method | 1 | 4 | 17.00 | 3.37 | 1.68 | 11.64 | 22.36 | 13 | 21 |

2 | 4 | 20.00 | .82 | .41 | 18.70 | 21.30 | 19 | 21 | ||

3 | 4 | 23.00 | 1.83 | .91 | 20.09 | 25.91 | 21 | 25 | ||

Total | 12 | 20.00 | 3.28 | .95 | 17.92 | 22.08 | 13 | 25 |

Sum of Squares | df | Mean Square | F | Sig. | ||
---|---|---|---|---|---|---|

Final Exam Score | Between Groups | 72.000 | 2 | 36.000 | 7.043 | .014 |

Within Groups | 46.000 | 9 | 5.111 | |||

Total | 118.000 | 11 |

SPSS/win produces both the **Descriptive Statistics** table and the **ANOVA**
table. As demonstrated in class, the descriptive table provides the necessary
input/information for the individual formulas in the key identity relation** TSS =
BSS + WSS** upon which the ANOVA table is based. The ANOVA table per se summarizes
all the essential statistics that are needed to actually do the test. These include the **BSS
= 72** and the associated degrees of freedom **(v _{1}) = 2**;
the

:

The null hypothesis

**Copyright© 1996, Ebenge Usip, all rights reserved.
Last revised:
Thursday, July 11, 2013.**