DATA ANALYSIS

Indawan Syahri

Data Analy

sis

Qualitative Data

Words

Typology

Quantitative Data

Descriptive

Statistics

ModeMea

n

Median

Inferential

Statisticst-

testCorrelati

on ANOVA

Regression

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Qualitative Data - Words

1. Recording Data:1. Transcripts from taped

Interview 2. Field-notes of Observation

2. Diaries3. Photographs4. Documents

Qualitative Data - Typologies• Types of errors

– Errors in Addition– Errors in Omission– etc.

• Social variables:– Gender– Ages– Occupations– Ethnic groups– etc.

REMINDERS:

1. The data appear in words rather than in numbers.

2. The data may have been collected in a various ways:

Observation Interviews Extracts from documents Tape recordings

3. Numbers used have no arithmetic values.4. Numbers may be used for coding the data.

e.g.: Male (1), Female (2), Teachers (3), Bankers (4), Policemen (5)

3. Qualitative data exist dominantly in descriptive studies

Stages in Qualitative Data Analysis

• Observation• Interviews• Document• Recording

Data Collection

• Selecting • Focusing• Simplifying• Abstracting• Transforming

Data Reduction • Matrices

• Graphs• Networks• Charts

Data Display

• Give meanings

• Confirming• Verifying

Conclusion Drawing

Quantitative Data – Descriptive Statistics

MEASURE OF CENTRAL TENDENCY

MODE(the most frequently

occurring scores)

MEDIAN(the middle

score)

MEAN (the average of all

scores)

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Measures of Central Tendency

Central tendency is used to talk about the central point

in the distribution of value in the data.

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Measures of variability• In order to describe the distribution of

interval data, the measure of central tendency will not suffice.

• To describe the data more accurately, we have to measure the degree of variability of the data of the data from the measure of central tendency.

• There are 3 ways to show the data are spread out from the point, i.e. range, variance, and standard deviation.

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Range• Range = X highest – X lowest• E.g. The youngest student is 17 and the oldest is

42,Range = 42 – 17 = 25The age range in this class is 25.

• If range is so unstable, some researchers prefer to stabilize it by using the semi-interquartile range (SIQR)SIQR = Q3 – Q1 / 2Q3 is the score at the 75th percentile and Q1 is the

score at the 25th percentile.• E.g., the score of the toefl score at the 75th

percentile is 560 and 470 is the score at the 25th percentile. SIQR is 560 – 470 / 2 = 45

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Variance• To see how close the scores are to the average

for the test.• E.g., if the mean score on the exam was 93.5

and a student got 89, the deviation of the score from the mean is 4.5.

• If we want a measure that takes the distribution of all scores into account, it is variance.

• To compute variance, we begin with the deviation of the individual scores from the mean.

Stages:1. Compute the mean: X2. Subtract the mean from each score to

obtain the individual deviation scores x = X – X.

3. Square each individual deviation and add: ∑ x²

4. Divide by N – 1: ∑ x²/ N - 1

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Standard Deviation• Variance = standard deviation are to

give us a measure that show how much variability there is in the scores.

• They calculate the distance of every individual score from the mean.

• Standard deviation goes one step further, to take the square root of the variance.

S =√ ∑ (X –X)²/ N – 1 or s = √ ∑x² / N - 1

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QUANTITATIVE DATA –Inferential Statistics

• Correlation is that area of statistics which is concerned with the study of systematic relationships between two (or more) variables.

• It attempts to answer questions such as: • Do high values of variable X tend to go together

with high values of variable Y? (positive correlation)

• Do high values of X go with low values of Y? (negative correlation)

• Is there some more complex relationship between X and Y, or perhaps no relationship at all?

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Visual representation of correlation: Scatter diagram

X

Y

X

Y

X

Y

Y

X

High positive r High negative r Lower positive r

Lower negative r No r

YY

X XNonlinear r

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Correlation coefficients:• To supplement the information given by a scatter

diagram a correlation coefficient is normally calculated.

• The expressions for calculating such coefficients are so devised that a value of +1 is obtained for perfect positive correlation, a value of -1 for perfect negative correlation, a value of 0 for no correlation at all.

• For interval variables, the appropriate measure is the so-called Pearson product-moment correlation coefficient.

• For ordinal variables (scattergraghs are not really appropriate), they use the Spearman rank correlation coefficient.

• For nominal variables, they use the phi coefficient.

t-test• t-test is used to compare two means

of sets of scores:– Pre-test vs. posttest– Test scores in experimental group vs.

test scores in control group• It means to observe the differences

between the scores obtained by Group A and those obtained by Group B