Technique of Analyzing the Data

E. Technique of Analyzing the Data

To test the hypothesis, data analysis is needed. Descriptive analysis and inferential analysis were used in this research. The descriptive analysis includes mean, median mode and standard deviation of the reading score.

Furthermore, the formulas of mean, median and more are described as follows:

(1) Mean

Tuckman (1978: 250) states that “the mean or average is computed by adding a list of scores and then dividing by the numbers of scores”. The algebraic formula used to determine the mean is :

Where

X = the mean ∑ = the sum of

raw score X = N = the number of cases (2) . Median Ary (1985: 153) expresses that “The median is defined as that point in a distribution of measures below which 50 percent of the cases lie (which means that the other 50 percent will be above this point)”. The median formula is employed :

Where Md

= the median N

= the number of cases in the distribution L = the lower limit of the interval within which the median lies cfb = the cumulative frequency in all intervals below the interval

containing the median containing the median

= the interval size Meanwhile, according to Mehrens (1978: 78), median (Mdn) is : “the point below which 50 percent of the scores lie. For an odd

number of scores, such as 25, the approximation to the median would

be the middlemost score, or the score below which and above which

12 scores lie (actually 12 ½ if one splits the middle score and considers half of it to be above the midpoint and half below). That is,

the median considered to be the 13 th score. For an even number of scores the median would be the point that lies halfway between the

two middlemost scores. “ (3) Mode

According to Ary (1985: 103), “the mode is that value in a distribution that occurs most frequently”. He adds that mode can be more than one in a distribution. This kind of distribution with two modes is called bimodal. Distributions with three or more modes are called trimodal or multimodal.

(4) Standard Deviation

( X  X ) Sx 

N Mehrens (1978: 79).

(5) Draw histogram / polygon to know where the polygon goes.

A histogram (sometimes referred to a bar graph) is a graph in which the frequencies are represented by bars. A frequency polygon is constructed from the grouped data. In constructing a histogram and a frequency polygon, a researcher needs to group the scores into a systematic order that is called as class interval.

There are some general guidelines for preparing class intervals:

1. The size of the class interval should be selected and cover the total range of observed scores.

2. The size of the class interval should be an odd number so that the midpoint of the interval is a whole number.

3. It is generally considered good style to start the class interval at a value that is a multiple of that interval (Mehrens, 1978: 70).

Guilford (1981: 28) says that it is naturally to start the intervals with the lowest score at multiples of the size of the interval. When the interval is 3, the score limits (the top and bottom scores for each interval) can be started with 9, 12, 15, 18, 21 etc.

Furthermore, the normality and homogeneity tests are needed to know the normality and the homogeneity of the data. The latest is multifactor analysis of variance 2 x 2. if Ho is rejected, the analysis will be continued to know which groups are different. The multifactor design is explained below:

Teaching

Group-Discussion Expository

Method

using Word Wall Teaching

High (B 1 )

Low (B 2 )

Table 7. The Design of Multifactor Analysis of Variance Note:

A 1 : Group-Discussion using Word Wall

A 2 : Expository Teaching Model

B 1 : Students with high interest

B 2 : Students with low interest

A 1 B 1 : Students with high interest taught through group-discussion.

A 1 B 2 : Students with low interest taught through group-discussion.

A 2 B 1 : Students with high interest taught through expository teaching model.

A 2 B 2 : Students with low interest taught through expository teaching model.

The research design shown in that table is matrix with 4 cells. Generally, the table is named as matrix AB consisting of: teaching methods (A) and level of interest (B). Furthermore, each of those two

variables has two factors, namely index A 1 refers to teaching through group-discussion, and index A 2 indicates teaching through expository teaching model. Meanwhile, index B 1 is students with high interest, and B 2 represents students with low interest. Therefore, A 1 B 1 shows students with high interest taught through group-discussion. A 1 B 2 refers to students with low interest taught through group-discussion. Furthermore, A 2 B 1 indicates students with high interest variables has two factors, namely index A 1 refers to teaching through group-discussion, and index A 2 indicates teaching through expository teaching model. Meanwhile, index B 1 is students with high interest, and B 2 represents students with low interest. Therefore, A 1 B 1 shows students with high interest taught through group-discussion. A 1 B 2 refers to students with low interest taught through group-discussion. Furthermore, A 2 B 1 indicates students with high interest

students with low interest taught through expository teaching model.

The data are analyzed using the formula as follows:

1. The total of sum squares:

2. The sum of squares between groups:

3. The sum of squares within groups:

4. The between-columns sum of squares:

5. The between-rows sum of squares:

6. The sum of squares interaction:

7. df for between – columns sum of squares = C – 1

df for between – rows sum of squares = R – 1

df for interaction (C – 1) (R – 1)

df for between – groups sum of squares = G – 1

df for within – columns sum of squares =  (n-1)

df for total sum of squares = N – 1 Note :

C = the number of columns R = the number of rows

G = the number of groups n = the number of subjects in one group N = the number of subjects in all groups

8. The q is found by dividing the difference between the means by the square root of the ratio of the within group variation and the sample size (http://people.richland.edu/james/lecture/m170/ch13-dif.html).

q=

2 or q = s w / n

MS error / n

where : j X and k X are means to be compared

MS error is the appropriate error term for testing the between-group effect

n is the number of observations from which each of X j and k X is calculated (Ferguson, 1989: 335).

a. Between column q =

Error vari ance/n

b. Between column (HI) q=

Error vari ance/n

c. Between column (LI) q= or q =

Error vari ance/n

Error vari ance/n

Tukey’s method is sometimes called Tukey’s honestly significant difference (HSD) method (Ferguson. 1989: 334). The use of Tukey test is to know which method is more effective or better.

Tukey’s method is sometimes called Tukey’s honestly significant difference (HSD).

The critical value is looked up in a table. It is a Table N of Bluman. There are actually several different tables, one for each level of significance. The number of samples, k, is used as an index along the top, and the degrees of freedom for the within group variance, v = N-k, are used as an index along the left side. The null hypothesis is rejected if the absolute value of the test statistic is greater than the critical value (just like the linear correlation coefficient critical values).

1. Tukey Test The finding of q is found by dividing the difference between the means by the square root of the ratio of the within group variation and the sample size.

x i  x j q=