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CHAPTER III

RESEARCH METHODOLOGY

A. The Research Method

The objective of this study is to explain the appropriateness of the

final test item used by the tenth grade students at SMA Negeri 5 Surakarta in
the second semester. Regarding the purpose of the research, the writer uses
the descriptive method with the quantitative approach in conducting the
research.
A brief definition of the descriptive study is provided by Fraenkel et al
(2012:13), they state that descriptive studies describe the situation as fully and
carefully as possible.
Johnson and Christensen (2012:302) mentioned that descriptive
research provides an accurate description or picture of a situation or
phenomenon’s status or characteristics. In addition, this research focuses on
describing of the variables in a given situation or phenomenon.
Creswell (2003:153) mentioned that quantitative methodology needs
data gathering information to be quantified and statistically treated to support
“alternative claims of knowledge”. Quantitative research often includes data
collection, usually numerical, and the researcher uses mathematical models as
methodology to analyze data. Researcher often uses investigation techniques
to ensure compliance with statistical data collection methodologies.
Based on the explanation above, the writer selects the descriptive
method with quantitative approach as the research method.

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B. Research Time and Location

This study was conducted in academic year of 2017/2018. The study

was conducted at SMA Negeri 5 Surakarta which is located in Jl. Letjen
Sutoyo 18 Surakarta on December 2017.

C. The Research Subject

To minimize the ambiguity which can arise throughout research, the

writer must define population, sample, and sampling technique.

1. Population
Johnson and Christensen (2000:158) said that a population is the
collection of all components or a big group in other names to which the
researcher wants to generalize their sample outcomes.
As per Creswell (2012:142) population has the same characteristics.
Similar to Creswell’s definition, Fraenkel et al (2012:93) defined an interest
population is typically a group of people (students, teachers, or other
individuals) with those same characteristics.
Throughout this study, the population was English final test items for
the first semester for tenth grade students and English final test result or
responses.
2. Sample
Creswell (2012:142) said a sample is a target population subgroup the
researcher plans to analyze to generalize the target of population. Ideally, the
writer should pick individuals representing the entire population
Fraenkel et al (2012: 93) stated that the research study sample is the
group that obtained information. The sample is taken in order to overcome the
time, financial, and energy insufficiency. Using all subjects or entire
populations in this research was complicated. Although only part of the

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population, the sample should be representative. The sample for this research
was one set of English the test items and test results taken from 100 tenth
grade students of SMA Negeri 5 Surakarta from class X A 1, X A 2, X S 4,
and X S 5.
3. Sampling Technique

Based on Johnson and Christensen (2000:156) sampling is the drawing

process of a sample form the population. Creswell (2012:154) states that of
sampling strictly chooses individuals from the population comprising that
population.
There are many techniques in selecting sample. As stated by Fraenkel,
Wallen, and Hyun (2012: 97), instead of randomly assigning 100 students
from a 3,000-ninth graders population in 100 classes, the researcher may
decide to choose 25 classes randomly from the 100-class population and then
randomly select 4 students from each. It is far less time-consuming than other
100 classes. Simply, the sample was selected from the pre-existing groups.
Groups are selected and the study uses individuals in those groups.
This research applies two-stage cluster random sampling technique.
Creswell (2012:143) said that the writer choose respondents (or units, such as
schools) for the sample in the random sampling so that any individual is
equally likely to be selected from the population. The simple random
sampling aims for pick individuals to be sampled, representing the population.
In this study, researcher took response and score from 25 students from each
class. There were a hundred samples from four different groups.
In determining the response sheet for each 25 students, the researcher
took the procedure called lottery method. This method is an objective
selection. The writer had write down the number order of students answer
sheet on a piece of paper, and then roll the pieces of paper and drop ten rolls
of papers one after one.
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D. Data Collection Technique

The technique in this study is documentary. This method is commonly

defined as a way or technique used to collect data by taking the existing data
or document. Creswell (2012: 154) sees documents as representative accurate
data composed of numerical, individual data available in public files. These
sets of information include degree reports, school attendance records, and
census information. The document that used for this study is the documents or
related information data including summative English tests and answer sheets
for students.

The writer will use the following steps to collect data:

a. Collecting the English final test sheets each major in SMAN 5 Surakarta.

b. Collecting the answer key of tenth-grade English final test in SMAN 5

Surakarta.

c. Collecting English final test score for each major in SMAN 5 Surakarta.

E. Data Analysis Methodology

In line with the study intent, the writer chooses item analysis the
data analysis technique. The formula of item analysis proposed by Linn and
Gronlund and will be used in the analysis:

1. Computing Item Difficulty

To find the test item’s difficulty level, the following formula is

considered acceptable in the research.

R
P  (100)
T

Where:
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P : percentage of pupils who answer correct item;

R : number of pupils who answer correct item

T : total numbers of pupils who attempt to answer the test item.

Difficulty level of an item is judged through the following range:

P Interpretation

< 0,30 Very difficult

0,30 – 0,70 Satisfactory

> 0,70 Very easy

Table 3.1

2. Computing Item Discriminating Power

Before computing the discriminating power, the first thing to

do is to categorize pupils into three groups, they are lower, middle, and
upper. Upper and lower groups are used in computing, while the mid-third
are discarded. In other words, the difference between the percentage of the
top scoring (upper group) 27% and bottom (lower group) scoring 27% of
students who get the correct item in its discrimination index while the
middle group 46% is discarded. Those percentages are as stated by
Madsen (1983: 180).The formula for calculating an index of
discriminating power is as follows:

D  (RU  RL) /(.5T )

Where:

D: item discriminating power

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RU: pupils from upper group who answer correct item

RL: pupils from lower group who answer correct item

.5T: number of pupils in two group.

Maximum index value is +1.00 and the minimum value -1.00.

Every negative value means that the test item discriminates in the wrong
direction and is unsatisfactory. Positive values indicate that, while it may
not be satisfactory, the test item discriminates in the expected direction.
Every D values above +0.40 can be considered to be very good, any
between +0.40 and +0.20 is considered acceptable and an item between
+0.20 and zero is considered bad.

The discriminating power is assessed by the following range

proposed by Ebel and Frisbie (1991: 232)

D Interpretation

0.70< D< 1.00 Excellent/Very Good

0.40< D < + 0.70 Reasonably Good

+0.20<D< +0.40 Satisfactory/Marginal items

0.00< D < +0,20 Poor

Negative Very poor

Table 3.2

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3. Effectiveness of the Distractor

In multiple-choice item, we also need to effectiveness of the

distractors. As said by Nunnally and Bernstein (1994 as cited in
Abdulghani et al. 2014), a distractor can be considered to be well
functioned if at least 5% selected by the test takers.

4. Validity and Reliability

a. Analysis of validity
As per Creswell (2012: 630) validity is the creation of sound
evidence show that the intended test interpretation (of the definition or
construction that the test is supposed to measure) suits the proposed test
intent. This proof is focused on research material, responses procedures,
internal structure, relationships to other variables, and testing results.
In this research, the researcher used criterion-related validity
(validity coefficient to decide if the test items are valid or not). The
researcher used the Pearson Product-Moment formula to find the
coefficient validity. The formula follows:
𝑟 𝑁/ ∑𝑋𝑌−(∑𝑋)(∑𝑌)
𝑥𝑦 =
√{𝑁/∑𝑋2 −(∑𝑋)2}{√𝑁/∑𝑌2−(∑𝑌) 2}

rxy = coefficient index

x = the score of each item
y = the total score
N = the total number of the respondent
∑ = the sum of the score
(Miller et al 2009: 508)

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Rxy Interpretation
0.0 - 0.20 No correlation
>0.20-0.40 Low correlation
>0.40-0.70 Moderate correlation
>0.70 – 0.90 High correlation
>0.90 – 1.00 Excellent correlation
Table 3. 3

Guilford (1950 in sudjana, 193:2015)

b) Internal validity
- Point biserial
𝑀𝑝−𝑀𝑡 𝑝
𝑟𝑝𝑏𝑖 = √𝑞
𝑆𝐷𝑡

Mt = Mean of total score

Mp = mean of total right answer
SDt = Deviation standard
p = the number of pupils who answer correct item
q = the number of pupils who answer incorrect item

c. Analysis of reliability

The formula to estimate test reliability is Kuder–Richardson

Formula 20 (KR-20). According to Brown (2005: 185) formula KR-20 is
by far the most precise and adaptable formula to calculate reliability. The
formula is:

k ∑𝑝𝑖𝑞𝑖
𝐾𝑅20 = ( ) (1 − )
𝑘−1 𝑆𝑡2

(Ebel and Frisbie 1991: 83)

The formula to calculate variance is as follows:

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(∑𝑦2)
∑𝑦2 −
𝑆𝑡2 = 𝑛
𝑛

Where:

St2 = the variance y = the total score

∑ = the sum of n = the number of respondent

The result can be interpreted on following standard that stated by Hair et

al (2016 as cited in Nawi et al, 2020):
Cronbach Alpa Reliability Level
<0.6 Poor
>0.6 – 0.7 Moderate
>0.7 - 0.8 Good
>0.8 - 0.9 Very Good

>0.9 Excellent

Table 3.4

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