Statistical Analysis

1. METODOLOGI
PENELITIAN
PENGOLAHAN DATA DAN
ANALISIS STATISTIK

2. PENGOLAHAN DATA
 Umumnya data (variabel) diolah menjadi
variable lain (parameter) yang akan dianalisis
 Variabel yang diperoleh disampaikan dalam
bentuk Tabel atau Grafik/Diagram
 Variabel diolah secara statistik untuk menarik
kesimpulan

3. Jenis penyajian data
 Tabulasi data
 Visual display for discrete variables
 Visual display for continuous variables
 Visual displays for two or more continuous
variables

4. Tabulasi data
Hasil penetapan kadar
Tetrasiklin
Pengurutan hasil penetapan
kadar tetrasiklin
Capsul Mg Rank Mg
1 251 1 245
2 250 2 247
3 253 3 248
4 249 4 249
5 250 5 250
6 252 6 250
7 247 7 251
8 248 8 252
9 254 9 253
10 245 10 254

5. Visual display for discrete variables
Contoh Pie-chart
Fig.3. Response of patients to a new analgesic drug.
45%
35%
20%
Good response
Fair response
Poor response

6. Contoh Pie-chart
Fig.3. Response of patients to a new analgesic drug.
Good response
45%
Fair response
35%
Poor response
20%

7. Visual display for continuous variables
Classification according to class-intervals
Determining the size of class interval:
i = R/(1 + 3.3 log N)
Where
 i = size of class interval;
 R = Range (i.e., difference between the values of the
largest item and smallest item among the given
items);
 N = Number of items to be grouped.

8.  Histogram yang melibatkan semua nilai
 Frequency polygon
 Cumulative frequency polygon
16.1
62.4
80.8
88.3
91.7
57.0
81.9
87.0
90.4
92.5
3.0
23.8
40.5
47.9
50.1
2.3
7.3
15.1
23.4
28.5
0.0
20.0
40.0
60.0
80.0
100.0
2 4 6 8 10
Time (hours)
Cumulative
amount
excreted
(%)
Cefadroxil
Cephalexin
Cefuroxime
Cefixime
Cumulative amounts of unchanged drug excreted in urine during the first 10 hours
following the administration of each drug.

9. Visual displays for two or more
continuous variables
Diagram Garis/Grafik
DISSOLUTION DATA
F2 = 42.1, Generic < Innovator
BIOAVAILABILITY DATA
NOT BIOEQUIVALENT
Rata-rata 2 subjek
0
50
100
150
200
250
300
350
400
0 4 8 12 16 20 24
Waktu (jam)
Kadar
(ng/ml)
AMARYL
ANPIRIDE CF5
0
20
40
60
80
100
0 10 20 30
Time (minutes)
%
drug
dissolved
Generic
Amaryl 4-mg

10. PENARIKAN KESIMPULAN
 Keberadaan hubungan/korelasi
 Membandingkan nilai rataan (uji
kebermaknaan atau test of significance)
 Dll.

11. METODE STATISTIK
Ditentukan oleh:
 Jenis dan desain penelitian (korelasi,
pembuktian hipotesis, dll.)
 Tipe data

12. Tipe Data
Kategori
 Nominal
 Ordinal
Numerik
 Interval
 Rasio

13. Kategori
Nominal
 Suatu bentuk data numerik berupa hasil pengkategorian data
(kualitatif atau deskriftif) atau berupa pengkodean.
 Misalnya jenis kelamin laki laki dan perempuan diberi kategori 1
dan 2, atau pengkategorian dari suatu keadaan yang
dinumerisasi dalam bentuk angka.
 Nominal data are numerical in name only, because they do not
share any of the properties of the numbers we deal in ordinary
arithmetic.
 For instance if we record marital status as 1, 2, 3, or 4 (blm
menikah, menikah, janda cerai, janda ditinggal mati) as stated
above, we cannot write 4 > 2 or 3 < 4 and we cannot write 3 – 1
= 4 – 2, 1 + 3 = 4 or 4 ¸ 2 = 2.

14. Ordinal scales
In those situations when we cannot do anything except set up
inequalities, we refer to the data as ordinal data. For instance, if
one mineral can scratch another, it receives a higher hardness
number and on Mohs’ scale the numbers from 1 to 10 are
assigned respectively to talc, gypsum, calcite, fluorite, apatite,
feldspar, quartz, topaz, sapphire and diamond. With these
numbers we can write 5 > 2 or 6 < 9 as apatite is harder than
gypsum and feldspar is softer than sapphire, but we cannot write
for example 10 – 9 = 5 – 4, because the difference in hardness
between diamond and sapphire is actually much greater than
that between apatite and fluorite. It would also be meaningless
to say that topaz is twice as hard as fluorite simply because their
respective hardness numbers on Mohs’ scale are 8 and 4.

15. Numerik
Interval scales,
 When in addition to setting up inequalities we can also form differences, we refer
to the data as interval data. Suppose we are given the following temperature
readings (in degrees Fahrenheit): 58°, 63°, 70°, 95°, 110°, 126° and 135°. In this
case, we can write 100° > 70° or 95° < 135° which simply means that 110° is
warmer than 70° and that 95° is cooler than 135°. We can also write for example
95° – 70° = 135° – 110°, since equal temperature differences are equal in the
sense that the same amount of heat is required to raise the temperature of an
object from 70° to 95° or from 110° to 135°.
 On the other hand, it would not mean much if we said that 126° is twice as hot
as 63°, even though 126°/ 63° = 2. To show the reason, we have only to change
to the centigrade scale, where the first temperature becomes 5/9 (126 – 32) =
52°, the second temperature becomes 5/9 (63 –32) = 17° and the first figure is
now more than three times the second. This difficulty arises from the fact that
Fahrenheit and Centigrade scales both have artificial origins (zeros) i.e., the
number 0 of neither scale is indicative of the absence of whatever quantity we
are trying to measure.
 Interval scales can have an arbitrary zero, but it is not possible to determine for
them what may be called an absolute zero or the unique origin

16. Ratio scales,
 When in addition to setting up inequalities and forming
differences we can also form quotients (i.e., when we can
perform all the customary operations of mathematics), we
refer to such data as ratio data. In this sense, ratio data
includes all the usual measurement (or determinations) of
length, height, money amounts, weight, volume, area,
pressures etc
 Ratio scales have an absolute or true zero of
measurement. The term ‘absolute zero’ is not as precise
as it was once believed to be. We can conceive of an
absolute zero of length and similarly we can conceive of
an absolute zero of time.

17. Scale types with their properties according to Stanley Smith Stevens
Logical/
math
operations
Nominal Ordinal Interval Ratio
X
/
Ӿ Ӿ Ӿ √
+
-
Ӿ Ӿ √ √
<
>
Ӿ √ √ √
=
#
√ √ √ √
Contoh Jenis
kelamin
Kesehatan, Tanggal
Altitude
Umur

18. ANALISIS STATISTIK
 Deskriftif
 Inferensial (simpulan)
- Parametrik
- Non-parametrik

19. ANALISIS DESKRIPTIF

20. Inferential

21. Objective of research study

25. Analisis keberadaan hubungan
 Analisis korelasi-regresi (untuk data kontinyu)
 Analisis korelasi peringkat (untuk data
peringkat)

26. In modern times, with the availability of computer facilities, there has been a
rapid development of multivariate analysis which may be defined as “all
statistical methods which simultaneously analyse more than two variables on a
sample of observations”3. Usually the following analyses* are involved when we
make a reference of multivariate analysis:
(a) Multiple regression analysis: This analysis is adopted when the researcher
has one dependent variable which is presumed to be a function of two or
more independent variables. The objective of this analysis is to make a
prediction about the dependent variable based on its covariance with all the
concerned independent variables.
(b) Multiple discriminant analysis: This analysis is appropriate when the
researcher has a single dependent variable that cannot be measured, but
can be classified into two or more groups on the basis of some attribute. The
object of this analysis happens to be to predict an entity’s possibility of
belonging to a particular group based on several predictor variables.
(c) Multivariate analysis of variance (or multi-ANOVA): This analysis is an
extension of two way ANOVA, wherein the ratio of among group variance to
within group variance is worked out on a set of variables.
(d) Canonical analysis: This analysis can be used in case of both measurable
and non-measurable variables for the purpose of simultaneously predicting a
set of dependent variables from their joint covariance with a set of
independent variables.

27. Membandingkan nilai rataan
 Uji parametrik
- t-test atau uji hipotesis
- Analisis variansi (ANOVA)
 Uji non-parametrik (bebas distribusi)
- Uji tanda/Sign test
- Wilcoxon signed rank test,
- Wilcoxon rank sum test,
- Kruskal-Wallis test,
- Friedman test
 Uji untuk data hitung: Uji Khi-kuadrat

28. Membandingkan dua nilai rataan
Goup A Group B
70 60
60 56
59 55
56 53
56 48
54 45
52 45
51 44
44 42
44 38
n 10 10
Mean 54,6 49,8
Variance 53,4 61,8
Standar deviation 7,3 7,9
Contoh nilai ujian dari dua
kelompok yang berbeda
p
X z
n


p = 0,05
Group A = 50,1 – 59,1
Group B = 44,91 - 54,69

29. The total population may be too to be tested or the testing may be destructive. In
such cases, the variance must be estimated from data obtained from samples.
The appropriate test in this case is Student’s t-test
Disintegration Time
(Minutes) of Hard-Shell
Capsules
Containing Two
Formulations, A and B
Form. A Form B
11,1 9,2
10,3 10,3
13 11,2
14,3 11,3
11,2 1,5
14,7 9,5
n 6 6
Mean 12,43 10,33
Variance 3,36 0,74
Standar deviation 1,83 0,86
Statistical tests such as Student’s
t involve comparison of a value of
t calculated from the data with a
tabulated value. If the calculated
value exceeds the tabulated
value, then a significant difference
between the means of the two
groups has been detected.

30. The calculated value of t is also altered by changing the number of
replicates. If the number of degrees of freedom is increased, the calculated
value of t will rise, and a significant difference between the means is again
more likely to be detected.
Changes in the Calculated and Tabulated Values of t with Increased
Replication
Jumlah
pengukuran
T hitung Derajat
kebebasan
Two tail test One tail test
P=0,05 P=0,01 P=0,05 P=0,01
6 2,540 10 2,228 3,169 1,812 2,764
12 3,593 22 2,074 2,819 1,717 2,508
18 4,400 34 2,042 2,750 1,679 2,457
24 5,081 46 2,021 2,704 1,684 2,423

31. TREATMENT OF OUTLYING DATA POINTS
Identification of Outlying Data Points Using Hampel’s Rule
Group B Deviasi dari
median
Deviasi yang
diabsolutkan
Deviasi absolut yang
dinormalkan
66 19,5 19,5 2,42
56 9,5 9,5 1,18
55 8,5 8,5 1,06
53 6,5 6,5 0,81
48 1,5 1,5 0,49
45 -1,5 1,5 0,19
45 -1,5 1,5 0,19
44 -2,5 2,5 0,31
42 -4,5 4,5 0,56
0 -46,5 46,5 5,78
Median 46,5 5,5 Any result greater
than 3.5 is
considered an
outlier
MAD (1,483x5,5)
8,16

32. COMPARISON OF MEANS BETWEEN MORE THAN
TWO GROUPS OF DATA
ANOVA (contoh kekerasan tablet)
1. ONE-WAY ANALYSIS OF VARIANCE (One factor is deliberately
changed (e.g., Batch A, B, or C), yang membedakan antar group hanya
formula saja)
2. TWO-WAY ANALYSIS OF VARIANCE (misal kekerasan tablet
yang disebabkan oleh perbedaan formula dan alat yang digunakan)

33. One-way analysis of variance
Batch A Batch B Batch C
5,2 5,5 3,8
5,9 4,5 4,8
6,0 6,6 5,1
4,4 4,2 4,2
7,0 5,6 3,3
5,4 4,5 3,5
4,4 4,4 4,0
5,6 4,8 1,7
5,6 5,3 5,9
5,1 3,8 4,8
N 10 10 10
Mean 54,6 49,2 41,11
Total 5,46 4,92 4,11
Grand total 144,9
Variance 0,59 0,69 1,34
Standard deviation 0,77 0,83 1,16

34. 1. Calculate the total and the mean of every column.
2. Calculate the grand total.
3. Calculate the (grand total)2/(number of observations) = (144.9)2/30 =
699.87. This term is used several times in this calculation. It is often called
the correction term and denoted by the letter C.
4. Calculate the sum of (every result)2 = (5.2)2+ (5.9)2+ . . . + (4.8)2= 732.71.
5. Subtract C from the result of Step 4 = 732.71 − 699.87 = 32.84. This gives
the value of the term (Sx2− (Sx)2/n) and is known as the total sum of
squares.
6. Calculate the sums of squares between means = [(54.6)2/10 + (49.2)2/10 +
(41.1)2/10] −C= (298.12 + 242.06 + 168.92) − 699.87 = 9.23.
7. Calculate the difference between the total sum of squares and the sum of
squares between means = 32.84 − 9.23 = 23.61. This is known as the
residual sum of squares.
8. The degrees of freedom for the whole experiment are (3 × 10) − 1 = 29.
There are three groups of tablets and hence three means. There are
hence (3 − 1) 2 degrees of freedom here. Thus, the residual sum of
squares has (29 − 2) 27 degrees of freedom.

35. Source of Error Sum of
Squares
Degrees of
Freedom
Mean
Square
F
Between means 9.23 2 4.62 5.31
Within each group 23.61 27 0.87
Total 32.84 29