This document provides an overview of quantitative descriptive research and statistics. It defines levels of measurement as nominal, ordinal, interval, and ratio scales. Descriptive statistics are used to summarize data through measures of central tendency like mean, median, and mode as well as measures of variability like standard deviation. Nominal data is described through frequencies and percentages. Ordinal and interval data can also be described graphically through stem-and-leaf plots and evaluations of distributions, skewness, and kurtosis. Reliability of measures is determined through methods like split-half analysis and Cronbach's alpha.

1. Measurements
Statistics
An overview

2. Lesson Objectives
 Review
 Quantitative descriptive research/ Survey
 Level of measurements
 Descriptive Statistics

3.  Define objectives
 Define resources available
 Identify study population
 Identify variables to study
 Develop instrument (questionnaire)
 Create sampling frame
 Select sample
 Pilot data collection
 Collect data
 Analyse data
 Communicate results
 Use results
Looking at descriptive
survey

4. Levels of measurements
 Quantitative and Qualitative
variables
 Quantitative variables are measured on an
ordinal, interval, ratio scale and nominal scale.
 If five-year old subjects were asked to name
their favorite color, then the variable would be
qualitative. If the time it took them to respond
were measured, then the variable would be
quantitative

5. Ordinal
 Measurements with ordinal scales are ordered in the
sense that higher numbers represent higher values.
 The intervals between the numbers are not
necessarily equal. For example, on a five-point rating
scale measuring attitudes toward gun control, the
difference between a rating of 2 and a rating of 3 may
not represent the same difference as the difference
between a rating of 4 and a rating of 5.
 There is no "true" zero point for ordinal scales since
the zero point is chosen arbitrarily. The lowest point
on the rating scale is usually chosen to be 1. It could
just as well have been 0 or -5.

6. Interval scale
 On interval measurement scales, one unit on the
scale represents the same magnitude on the trait or
characteristic being measured across the whole
range of the scale.
 For example, if anxiety were measured on an
interval scale, then a difference between a score
of 10 and a score of 11 would represent the same
difference in anxiety as would a difference
between a score of 50 and a score of 51.

7. Interval scale
 Interval scales do not have a "true" zero point,
however, and therefore it is not possible to make
statements about how many times higher one score
is than another. For the anxiety scale, it would not be
valid to say that a person with a score of 30 was
twice as anxious as a person with a score of 15.
 A good example of an interval scale is the
Fahrenheit scale for temperature. Equal
differences on this scale represent equal
differences in temperature, but a temperature of
30 degrees is not twice as warm as one of 15
degrees

8. Ratio scale
 Ratio scales are like interval scales except
they have true zero points. A good example is
the Kelvin scale of temperature. This scale
has an absolute zero. Thus, a temperature of
300 Kelvin is twice as high as a temperature
of 150 Kelvin

9. Nominal scale
 Nominal measurement consists of assigning items to
groups or categories.
 No quantitative information is conveyed and no
ordering of the items is implied.
 Nominal scales are therefore qualitative rather than
quantitative.
 Religious preference, race, and sex are all
examples of nominal scales.
 Frequency distributions are usually used to analyze
data measured on a nominal scale. The main statistic
computed is the mode. Variables measured on a
nominal scale are often referred to as categorical or
qualitative variables.

10. Categorizing data
 Discrete data: finite options (e.g., labels)
 Gender
 Female 1
 Male 2
 Discrete: nominal, ordinal, interval
 Continuous data: infinite options
 Test scores 12 18 23.5
 Continuous: ratio
 Discrete data is generally only whole numbers, whilst
continuous data can have many decimals

11. Descriptive vs.
Inferential Statistics

12. Descriptive vs. Inferential
Statistics
 Descriptive
 Used to summarize a
collection of data in a
clear and
understandable way
 Inferential
 Used to draw
inferences about a
population from a
sample
 “generalize to a larger
population”
 Common methods
used
 Estimation
 Hypothesis testing

13. Descriptive
Statistics

14. Mean and standard
deviation
 Central Tendency
 Measures the location of the middle or the
center of the
 Mean - Average
 Median: Centre of the distribution
 Mode : Most frequently occurring score in a
distribution
 Standard Deviation
 Measure of spread

15. Levels and measures
Measures of Central Tendency
XXXRatio
XXXInterval
XXOrdinal
XNominal
MeanMedianMode

16. LEVELS OF
MEASUREMENT
Link

17. Describing nominal data
 Nominal data consist of labels
 e. g 1 = no, 2 = yes
 Describe frequencies
 Most frequent
 Least frequent
 Percentages
 Bar graphs

18. Frequencies
 No. of individuals obtaining each score on a
variable
 Frequency tables
 Graphically ( bar chart, pie chart)
 Also %

19. Displaying data for gender

20. Mode
 Most common score
 Suitable for all types of data including
nominal
 Example:
 Test scores: 16, 18, 19, 18, 22, 20, 28, 18

21. Describing ordinal data
 Data shows order e.g ranks
 Descriptives
 frequencies, mode
 Median
 Min, max
 Display
 Bar graph
 Stem and leaf

22. Example: Stem and Leaf
Plot
Stem & Leaf Plot
Frequency Stem & Leaf
1.00 4 . 0
3.00 5 . 057
8.00 6 . 00002558
2.00 7 . 05
3.00 8 . 005
1.00 9 . 0
1.00 10 . 0
1.00 Extremes (>=110)
Stem width: 10.00
Each leaf: 1 case(s)
 Underused.
 Powerful
 Efficient – e.g., they contain
all the data succintly –
others could use the data in
a stem & leaf plot to do
further analysis
 Visual and mathematical: As
well as containing all the data,
the stem & leaf plot presents a
powerful, recognizable visual of
the data, akin to a bar graph.

23. Example
 The data: Math test scores out of 50 points: 35, 36,
38, 40, 42, 42, 44, 45, 45, 47, 48, 49, 50, 50, 50.
 Separate each number into a stem and a leaf. Since
these are two digit numbers, the tens digit is the stem
and the units digit is the leaf.
 The number 38 would be represented as
 Stem3 Leaf 8
 Group the numbers with the same stems. List the
stems in numerical order. (If your leaf values are not
in increasing order, order them now.)
 Title the graph
 To find the median in a stem-and-leaf plot, count off
half the total number of leaves.

24. Describing interval data
 Interval data are discrete but also treated as
ratio/continuous
 Descriptives
 Mode
 Median
 Min, max
 Mean if treated as continuous

25. Distribution
 Describing
 Mean
 Average, central tendency
 Deviation
 Variance
 Standard deviation
 Dispersion
 If the bell-shaped curve is steep, the standard deviation
is small.
 When the data are spread apart and the bell curve is
relatively flat, you have a relatively large standard
deviation

26. Distribution
 Describing
 Skewness
 a measure of symmetry, or more precisely, the
lack of symmetry
 Lean, tail
 +ve : tail at the right

27. Distribution
 Describing
 Kurtosis
 Flatness/peakedness of distribution
 + ve : peaked
 data sets with high kurtosis tend to have a distinct
peak near the mean, decline rather rapidly, and
have heavy tails.
 data sets with low kurtosis tend to have a flat top
near the mean rather than a sharp peak

28. Approx. same skewness,
different kurtosis

29. Describing Ratio Data
 Can talk meaningfully about ratio data
 Measures - central tendency, dispersion

30. Describing Ratio Data
 Displaying frequency

31. LET’S LOOK AT DATA
Sleepiness

32. Determining Reliability
 Reliability
 Reliability is defined as the ability of a measuring
instrument to measure the concept in a consistent
manner
 To determine
 Split half analysis- answers on the first half of the
questionnaire are compared to the second half of
the questionnaire
 If there is a high correlation – internally
consistent / reliable

33. Determining Reliability
Coefficient
 Cronbach’s Alpha α
 Examines average inter item correlation of the
items in the questionnaire
 If all items measuring the exact same thing, α
= 1
 α = 0.7 or more – reliable
 Use SPSS

34. Inferential Statistics
Next