1. DATA ANALYSIS
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2. Descriptive Statistics Inferential Statistics
Data Analysis
Qualitative Data
Words
Typology
Quantitative Data
Descriptive Statistics
Mode
Mean
Median
Inferential Statistics
t-test
Correlation
ANOVA
Regression

3. Qualitative Data - Words
Recording Data:
Transcripts from taped Interview
Field-notes of Observation
Diaries
Photographs
Documents

4. Qualitative Data - Typologies
Types of errors
Errors in Addition
Errors in Omission
etc.
Social variables:
Gender
Ages
Occupations
Ethnic groups

5. Reminders:
The data appear in words rather than in numbers.
The data may have been collected in a various ways:
Observation
Interviews
Extracts from documents
Tape recordings
Numbers used have no arithmetic values.
Numbers may be used for coding the data.
e.g.: Male (1), Female (2), Teachers (3), Bankers (4), Policemen (5)
Qualitative data exist dominantly in descriptive studies

6. 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

7. Quantitative Data – Descriptive Statistics
MEASURE
OF CENTRAL
TENDENCY
MODE
(the most frequently
occurring scores)
MEDIAN
(the middle
score)
MEAN (the average of all scores)

8. Measures of Central Tendency
26/04/2017
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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9. Measures of variability
26/04/2017
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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10. Range Range = X highest – X lowest
26/04/2017
Range
Range = X highest – X lowest
E.g. The youngest student is 17 and the oldest is 42,
Range = 42 – 17 = 25
The 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 / 2
Q3 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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11. Variance To see how close the scores are to the average for the test.
26/04/2017
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:
Compute the mean: X
Subtract the mean from each score to obtain the individual deviation scores x = X – X.
Square each individual deviation and add: ∑ x²
Divide by N – 1: ∑ x²/ N - 1
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12. 26/04/2017
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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13. QUANTITATIVE DATA –Inferential Statistics
26/04/2017
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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14. Visual representation of correlation: Scatter diagram
26/04/2017
Visual representation of correlation: Scatter diagram Y Y Y X X
High positive r X
High negative r
Lower positive r Y Y Y X X X
Nonlinear r
Lower negative r
No r
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15. Correlation coefficients:
26/04/2017
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.
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16. 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