1. PXGZ6102 BASIC STATISTICS FOR RESEARCH IN EDUCATION
Chap 2 - Descriptive and Inferential Statistics (Introduction)
- Level of Measurement,
- Measures of Central Tendency

2. Descriptive & Inferential Statistics
Descriptive statistics can be used to summarize the data, either numerically or graphically, to describe the sample.
Basic examples: mean and standard deviation.
Graphical summarizations:various kinds of charts and graphs.

3. Descriptive Statistics
Involves transformation of the raw data into a form that will make them easy to understand and interpret.
Describing responses or observations is a form of analysis
The calculation of averages, frequency distributions, and percentages distributions is the most common form of summarizing data.
Descriptive Statistics is used when no inferences are made about the population based on the sample

4. Inferential Statistics
Inferential statistics is used to model patterns in the data, accounting for randomness and drawing inferences about the larger population.
These inferences may take the form of answers to yes/no questions (hypothesis testing), estimates of numerical characteristics (estimation), descriptions of association (correlation), or modeling of relationships (regression). Other modeling techniques include ANOVA

5. Scales /levels of measurements of variables
Nominal (categorical) –
Ordinal
Interval
Ratio

6. Nominal (categorical) Scale
Simple Classification in Categories without any order or reference to quantity e.g.
Variable Classification
Gender Male (1) and Female (2)
Race Malay, Chinese, Indians
Football Jersey No 10, 7, 3 etc.
Your IC No.

7. Ordinal Scale Has order or rank ordering, e.g. called LIKERT SCALE
Reflects relative position not distance (quantity)
Strongly agree,
Agree,
Undecided,
Disagree,
Strongly disagree

8. Interval Scale Do not have true 0 points.
Has order as well as equal distance or interval between judgements (Social Sciences) e.g. IQ score of 95 is better than IQ 85 by 10 IQ points
E.g. Fahrenheit Scale

9. Ratio Scale
Have true 0 points. Has high order, equal distance between judgements, a true zero value (Physical Sciences) e.g.age,
no. of children, 9 ohm is 3 times 3 ohm and 6 ohm is 3 times 2 ohm

10. Descriptive Statistics for different levels/types of measurement
Types of Measurement Type of descriptive analyses
Nominal Mode
Ordinal Median
Interval Mean
Ratio Mean

11. Types of Measurement Scales and their Statistical Analyses
Tests
Characteristics
Type of Data
Simple Classification in Categories without any order e.g Boy / Girl
Happy / Not Happy
Muslim / Buddhist / Hindu
Non-
parametric
Association
Nominal
Chi-square
Ordinal
Has order or rank ordering
e.g. Strongly agree, agree,
undecided, disagree, strongly
disagree
(LIKERT SCALE)
RELATIONSHIP:
Spearman’s rho
COMPARISON:
Mann-Whitney
Wilcoxon
Non-
parametric

12. Types of Measurement Scales and their Statistical Analyses
Tests
Characteristics
Type of Data
Do not have true 0 points. Has order as well as equal distance or interval between judgements (Social Sciences) e.g. IQ score of 95 is better than IQ 85 by 10 IQ points
Parametric
COMPARISON:
t-tests
ANOVA
RELATIONSHIP:
Pearson r
Interval
Ratio
Have true 0 points. Has high
order, equal distance between
judgements, a true zero value
(Physical Sciences) e.g.age, no.
of children, 9 ohm is 3 times 3
ohm and 6 ohm is 3 times 2
ohm But IQ 120 is more
comparable to IQ 100 than to IQ
144, although ratio
IQ 120 /100 = 144 /120 = 1.2
Parametric
COMPARISON:
t-tests
ANOVA
RELATIONSHIP:
Pearson r

14. Types of Measurement Scales and their Statistical Analyses
Higher order of measurement --> lower order e.g. Interval ---> ordinal, nominal
But not ordinal, nominal ----> interval

15. Measures of Central Tendency
Mode
Median
Mean

16. Median, Mod and Mean
Median is the score at the center of the series when the scores are arranged in increasing order. Example:
30, 45, 48, 48, 54, 55, 60, 62, 68
The median is 54
30, 45, 48, 48, 54, 55, 60, 62, 68, 78
The median is ( )/2 = 54.5

17. Mode Mode is the most common score 30, 45, 48, 48, 54, 55, 60, 62, 68
The mode is 48

18. Upper and lower Quartile
Upper quartile is the score obtained by the top 25% of the students
Lower quartile is the score obtained by the bottom 25% of the students

19. Interquartile Range
Is the range between the lower quartile and the upper quartile

21. Exercise 2

22. Calculating Mean using Frequency distribution x xf f 7 6 5 4 3 2 1 1 3 2 5 4 7 18 10 20 12 2 1
n = Σf = 17
Σxf= 70
Σxf= 70
= 4.12
Mean, X =
Σf = 17

23. Measures of Variability
Range -
Variance
Standard Deviation

24. Range Refers to the overall span of the scores Eg. 18, 34, 44, 56, 78
The range is 78 – 18 = 60

25. Mean Deviation Is the degree to which scores deviate from the mean
Shows the variability of a distribution
Eg. Shoes sizes in Ali’s home: 11,12,13,14,15,16,17 the mean is 14
In Ahmad’s home: 5,8,11,14,17,20, 23 the mean is also 14
But the distribution in Ahmad’s home is greater

26. Calculation of Mean Deviation (MD)
Ali
Scores Mean (x - mean) |X – mean|
N = |x – Mean| =12
Σ |x – Mean| 12
MD = = = 1.71 n

27. End of Chap 2