Introduction to Statistics

1. INTRODUCTION
TO
STATISTICS
By: Daphne M. Legaspino

2. APPLIED STATISTICS
Descriptive
Statistics
Inferential
Statistics
Frequency
Distribution
Measures of
Central tendency
Measures of
position
Measures of
Variability
Correlation
Coefficient
Parametric
statistics
Non-Parametric
statistics
T-test
ANOVA
Sign Test
Kolmogrow-smirnov
Run Test
Mann-whitney
Median
Spearman Rank
Correlation
Friedman Test
Wilcoxon Test
McNemar Test
Chi-square
Krushkal Wallis Test

3. What is statistics?
Statistics is the study of how to
collect, organize, analyze, and
interpret numerical from data

4. Descriptive Statistics
Descriptive Statistics is that part
of statistics which quantitatively
describes the characteristics of a
particular dataset under study, with
the help of brief summary about the
sample

5. Example of Descriptive Statistics
Present the Philippine population by constructing a
graph indicating the total number of Filipinos counted
during the last census by age group and sex

6. Example of Inferential Statistics
A new milk formulation designed to improve the psychomotor
development of infants was tested on randomly selected infants.
Based on the results, it was concluded that the new milk formulation is
effective in improving the psychomotor development of infants.

7. Inferential Statistics
Larger Set
(N units/observations) Smaller Set
(n units/observations)
Inferences and
Generalizations

8. Use of Descriptive and Inferential Statistics in answering Common
Research Problems
1. What is the BMI of the students before and after the
intervention? Descriptive
2. What is the profile of the students in terms of gender and
age? Descriptive
3. What is the assessment of the participants on their extent
of compliance to R.A. 2026? Descriptive
4. Is there a significant difference on the performance of
students when they are grouped according to year level?
inferential
5. Do students significantly differ on their level of
acceptability of Gay Lingo when they are grouped
according to sex? Inferential
6. Is there a significant association between work
performance level and teaching position? inferential

9. Example

10. Inferential Statistics
Inferential Statistics is one of the
type of statistics in which a random
sample is drawn from the large
population, to make deductions
about the whole population, from
which the sample is taken

11. Example

12. Example

13. Example

14. Identify if Descriptive or
Inferential
Descriptive
Inferential
Descriptive

15. Identify if Descriptive or
Inferential
Inferential

16. Identify if Descriptive or
Inferential
Inferential

17. Descriptive
Statistics
It describes basic
feature of the
situation.
Chart, Graph and
Tables
Measures of
Central Tendency,
Measures of
Dispersion
Data set is small
Inferential
Statistics
It explains the
chances of
occurrence of an
event or activity
Probability scores
Hypothesis test
and Analysis of
Variance
Large dataset
VS

18. Individuals are the people or
objects included in the study.
A variable is a characteristic of
the individual to be measured or
observed.

19. A quantitative variable has a value or
numerical measurement for which operations
such as addition or averaging make sense.
A continuous variable can assume an infinite
number of values between any two specific
values. They are obtained by measuring often
includes fractions and decimals.
A discrete variable assumes values that can
be counted.

20. Identify if Discrete or
Continuous
Continuous
Discrete

21. Identify if Discrete or
Continuous
Continuous
Discrete

22. A qualitative variable describes an
individual by placing the individual into a
category or group, such as male or female.
A hypothesis testing is a decision-making
process for evaluating claims about a population,
based on information obtained from samples.

23. Identify if Quantitative or
Qualitative
Quantitative
Qualitative

24. Identify if Quantitative or
Qualitative
Quantitative
Quantitative

25. Identify if Quantitative or
Qualitative
Qualitative

26. • Variable • Type (QL or
QN)
Discrete /Continous
• Gender
• Years of teaching
• Height in meters
• Size of shirt (small, medium, large)
• Crime committed
• Number of crimes in a day
• Score in a test
QL
QL
QL
QN
QN
QN
QN
N/
A
Continuous
Continuous
Discrete
Discrete
N/
A
N/
A

27. The classification of variables can be
summarized as follows:
DATA
QUALITATIVE QUANTITATIVE
DISCRETE CONTINUOUS

28. In population data, the data are from every
individual of interest.
In sample data, the data are from only some
of the individuals interest.

29. Identify if Population or Sample
Sample
Population

30. Identify if Population or Sample
Sample
Population

31. Identify if Population or Sample
Sample

32. A parameter is a numerical measure that
describes an aspect of a population.
A statistic is a numerical measure that
describes an aspect of a sample.

33. Example 1
The Hawaii Department of Tropical Agriculture is
conducting a study of ready-to-go harvest pineapples in an
experimental field.
• The pineapples are the objects (individuals) of the study. If the
researchers are interested in the individual weights of pineapple in
the field, then the variable consists of weights. At this point, it is
important to specify units of measurement and degree of accuracy of
measurement. The weights could be measured to the nearest ounce
or gram. Weight is a quantitative variable because it is a numerical
measure. If the weights of all the ready-to-harvest pineapples in the
field are included in the data, then we have a population. The
average weight of all ready-to-harvest pineapples in the field is a
parameter.

34. Example
The Hawaii Department of Tropical Agriculture is
conducting a study of ready-to-go harvest pineapples in an
experimental field.
• Suppose the researchers also want data on taste. A panel of
tasters rates the pineapples according to the categories “poor”,
“acceptable”, and “good”. Only some of the pineapples are included in
the taste test. In this case, the variable is taste. This is a qualitative
or categorical variable. Because only some of the pineapples in the
field are included in the sturdy, we have a sample. The proportion of
pineapples in the sample with a taste rating of “good” is a statistic.

35. Example 2
Television station ABIAS wants to know the
proportion of TV owners in Davao City who watch the
station’s new program at least once a week. The station
asked a group of 1000 TV owners in Davao City if watch
the program at least once a week.
(a) Identify the individuals of the study and the variable.
(b) Do the data comprise a sample? If so, what is the underlying
population?
(c) Is the variable qualitative or quantitative?
(d) Identify a quantitative variable that might be of interest.
(e) Is the proportion of viewers in the sample who watch the new
program at least once a week a statistic or a parameter?

36. Example 2
(a) Identify the individuals of the
study and the variable.
(b) Do the data comprise a sample? If so, what
is the underlying population?
(c) Is the variable qualitative or quantitative?
(d) Identify a quantitative variable that might
be of interest.
(e) Is the proportion of viewers in the sample
who watch the new program at least once
a week a statistic or a parameter?
The individuals are the 1000 TV owners
surveyed.
The variable is the response does, or does not
watch the new program at least once a week
The data comprise a sample of the population
of responses from all TV owners in Davao
City.
Qualitative
Age or income might be of interest.
Statistic- the proportion is computed from
sample data

37. SCALES or LEVELS OF MEASUREMENT

38. Levels of Measurement:
Nominal, Ordinal, Interval, Ratio
• Nominal – we can put the data into categories
• Ordinal – we can order the data from smallest to largest or
“worst” to “best”.
• Interval – ranks data, and precise differences between units of
measure do exist; however there is no
meaningful zero.
• Ratio – we can order the data, take differences, and also find
the
ratio between data values.

39. Qualitative-Nominal
Characterizes
Describes
Categorizes
Labels
Names

40. NOMINAL (label, characterize, categorize)
Q
L

41. Qualitative-Ordinal
Characterizes
Describes
Categorizes
Labels
Names
Can be arranged

42. NOMINAL (label, characterize, categorize)
ORDINAL (can be arranged in order)
Q
L

43. Quantitative-Interval

44. NOMINAL (label, characterize, categorize)
ORDINAL (can be arranged in order)
INTERVAL (with distance, no absolute zero (meanigful), no
origin)
Q
L
Q
N

45. Quantitative-Ratio

46. NOMINAL (label, characterize, categorize)
ORDINAL (can be arranged in order)
INTERVAL (with distance, no absolute zero, no origin))
RATIO(with distance, ratio, absolute zero, have origin))
Q
L
Q
N

47. DATA QUALITATIVE OR
QUANTITATIVE
DISCRETE OR
CONTINUOUS
Nominal, Ordinal
Interval, Ratio
Name -
Age in Years
Sex -
Tax Identification
Number
-
Number of
Trainings
Number of
Teardrops
Municipality Class -
Weight
Answers in a
Multiple Choice
Test
-
Scores in a Multiple
Choice Test
QL
QN
QL
QL
QN
QN
QL
QN
QL
QN
Discrete
Discrete
Discrete
Discrete
Continuous
Nominal
Nominal
Nominal
Nominal
Ratio
Ratio
Ratio
Ratio
Ratio
Ordinal

48. Examples of Measurement Scales
Nominal-level data Ordinal-level data Interval-level data Ratio-level data
Zip code Grade
(A,B,C,D,F)
NAT score Height
Gender
(male, female)
Judging
(first place, second place,
etc.)
IQ Weight
Eye color
(blue, brown, black, green, hazel)
Rating scale
(poor, good, excellent)
Temperature Time
Political affiliation Ranking of tennis players Salary
Religious affiliation Age
Major fields
(mathematics, Filipino, English, etc.)
Nationality

49. Safe Travel
Direction: Read the following information about the transportation industry and
answer the questions.
Transportation Safety
The table shows the number of job-related injuries for each of the transportation
industries for 1998.
Examples of Measurement Scales
Industry Number of Injuries
Railroad 4520
Intercity Bus 5100
Subway 6850
Trucking 7144
Airline 9950

50. Questions
1. What are the variables of the study?
2. Categorize each variable as quantitative or qualitative.
3. Categorize each quantitative variable as discrete or continuous.
4. Identify the level of measurement for each variable.
5. The railroad is shown as the safest transportation industry.
Does that mean railroads have fewer accidents than the other
industries? Explain.
6. What factors other than safety influence a person’s choice of
transportation?
7. From the information given, comment on the relationship
between variables.

51. Question Answer
The variables are industry and number of job-related injuries.
The type of industry is a qualitative variable, while the
number of job-related injuries is quantitative.
The number of job-related injuries is discrete.
The type of industry is nominal, and the number of job-related
injuries is ratio.
The railroads do show fewer job-related injuries; however,
there may be other things to consider. For example, railroads
employ fewer people than the other transportation industries
in the study.
A person’s choice of transportation might also be affected by
convenience issues, cost, service, etc.
Answers will vary. One possible answer is that the railroads
have the fewest job-related injuries, while the airline industry
has the most job-related injuries (more than twice those of
the railroad industry). The numbers of job-related injuries in
the subway and tracking industries are fairly comparable.
1. What are the variables of the study?
2. Categorize each variable as quantitative or
qualitative.
3. Categorize each quantitative variable as
discrete or continuous.
4. Identify the level of measurement for each
variable.
5. The railroad is shown as the safest transportation
industry. Does that mean railroads have fewer
accidents than the other industries? Explain.
6. What factors other than safety influence a
person’s choice of transportation?
7. From the information given, comment on
the relationship between variables.

52. Task/Qui
z

53. Task/Qui
z

54. Thank you!