Quantitative techniques in research

Quantitative Techniques in Research: Statistic in One day

Carlo Magno, PhD

Lasallian Institute for Development and Educational Research

Objectives Decide on what statistics to use given a set of

data Use appropriate statistics in studies that will

be conducted (long term). Use statistica to conduct some statistical

analysis

Outline Considerations in the selection of statistics to

use. List of statistics Examples in using the statistics

Read the article on CORI

Processing What was the aim of the study? What is the independent variable in the first

study? What is the dependent variable it the first

study? How many groups were used in the first

study? How many levels of IV was used in the first

study? How was the DV measured? How was the data analyzed? What statistics

was used? Why do you think this is the appropriate

analysis? What is the difference between study 1 and 2?

Would the analysis change?

When we analyzed the use of the statistics in the study by Guthrie et al., what information did we determine first?

What determines the use of statistics?

Variables Involved

• Independent• Dependent

How many groups?•Design

• Comparison• Correlating• Effect

Levels of Measurement of the variables (IV

and DV)

Identify the IV, DV, and design Case 1: A study compared males and females.

More specifically, the study wanted to determine who is higher in verbal ability between the two groups. A test on verbal ability is given for the two groups and the mean scores were compared.

Case 2: The effect of Project-Based Learning (PBL) on the grades of students was studied among college students. It was hypothesized that students will achieve more in the PBL as compared to a group who received pure lecture. The grades of the students were compared at the end of the term.

Identify the IV, DV, and design Case 3: Writing anxiety, writing

metacognition, and topic knowledge was used to predict students writing proficiency. Students essays were scored which served as indicator for their writing proficiency. Scales were used to determine writing anxiety, writing metacognition, and topic knowledge.

Case 4: Neophyte and experienced principals, coordinators, and directors were compared on their degree of transformational leadership. A scale measuring transformational leadership was administered to the administrators across 200 school in NCR.

Identify the IV, DV, and design Case 4: Filipino and Korean high school students

were compared on their oral proficiency (TOEFL), vocabulary, and reading comprehension in English (English test).

Case 5: The effect of case study method on students critical thinking was studied. The Watson Glaser Critical Thinking Appraisal (WGCTA) was administered as a pretest then the case study method was implemented for the rest of the term. Towards the end of the term, the WGCTA was administered again.

Case 6: The frequencies of SV agreement errors were counted among high school students in the public and private. The comparison was also done among high and low ability students in these two schools.

Levels of Measurement

A B C D

Type of schoolEthnicityGenderSocio-economic status

Favorite movie from like to least likeRanking of best science fiction storiesPerceived highest to lowest reputable universities in terms of research

English AbilityMath abilityAchievement in ScienceMotivationStressSelf-esteemSelf-efficacytemperature

Height of childrenWeight of first gradersLength of travelWidth of the tableBrightness of light

Levels of Measurement

Nominal

Ordinal

Interval

Ratio

Levels of measurement Three important properties:

Magnitude--property of “moreness”. Higher score refers to more of something.

Equal intervals--is the difference between any two adjacent numbers referring to the same amount of difference on the attribute?

Absolute zero--does the scale have a zero point that refers to having none of that attribute?

Types of Measurement Scales

Nominal Scales - there must be distinct classes but these classes have no quantitative properties. Therefore, no comparison can be made in terms of one category being higher than the other.

For example - there are two classes for the variable gender -- males and females. There are no quantitative properties for this variable or these classes and, therefore, gender is a nominal variable.

Other Examples:country of originbiological sex (male or female)animal or non-animalmarried vs. single

Nominal Scale Sometimes numbers are used to designate category

membership

Example: Country of Origin

1 = United States 3 = Canada2 = Mexico 4 = Other

However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaning

Types of Measurement Scales

Ordinal Scales - there are distinct classes but these classes have a natural ordering or ranking. The differences can be ordered on the basis of magnitude.

For example - final position of horses in a thoroughbred race is an ordinal variable. The horses finish first, second, third, fourth, and so on. The difference between first and second is not necessarily equivalent to the difference between second and third, or between third and fourth.

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Ordinal Scales

Does not assume that the intervals between numbers are equal

Example:finishing place in a race (first place, second place)

1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours

1st place 2nd place 3rd place 4th place

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Types of Measurement Scales (cont.)

Interval Scales - it is possible to compare differences in magnitude, but importantly the zero point does not have a natural meaning. It captures the properties of nominal and ordinal scales -- used by most psychological tests.

Designates an equal-interval ordering - The distance between, for example, a 1 and a 2 is the same as the distance between a 4 and a 5

Example - Celsius temperature is an interval variable. It is meaningful to say that 25 degrees Celsius is 3 degrees hotter than 22 degrees Celsius, and that 17 degrees Celsius is the same amount hotter (3 degrees) than 14 degrees Celsius. Notice, however, that 0 degrees Celsius does not have a natural meaning. That is, 0 degrees Celsius does not mean the absence of heat!

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Ratio Scales - captures the properties of the other types of scales, but also contains a true zero, which represents the absence of the quality being measured.

For example - heart beats per minute has a very natural zero point. Zero means no heart beats. Weight (in grams) is also a ratio variable. Again, the zero value is meaningful, zero grams means the absence of weight.

Example: the number of intimate relationships a person has had

0 quite literally means nonea person who has had 4 relationships has had twice as many as someone who has had 219


• Each of these scales have different properties (i.e., difference, magnitude, equal intervals, or a true zero point) and allows for different interpretations.

• The scales are listed in hierarchical order. Nominal scales have the fewest measurement properties and ratio having the most properties including the properties of all the scales beneath it on the hierarchy.

• The goal is to be able to identify the type of measurement scale, and to understand proper use and interpretation of the scale.

Types of scales Nominal scales--qualitative, not

quantitative distinction (no absolute zero, not equal intervals, not magnitude)

Ordinal scales--ranking individuals (magnitude, but not equal intervals or absolute zero)

Interval scales--scales that have magnitude and equal intervals but not absolute zero

Ratio scales--have magnitude, equal intervals, and absolute zero (so can compute ratios)

Test Your Knowledge:

A professor is interested in the relationship between the number of times students are absent from class and the letter grade that students receive on the final exam. He records the number of absences for each student, as well as the letter grade (A,B,C,D,F) each student earns on the final exam. In this example, what is the measurement scale for number of absences?

a) Nominal b) Ordinal c) Interval d) Ratio

In the previous example, what is the measurement scale of letter grade on the final exam?


A researcher is interested in studying the effect of room temperature in degrees Fahrenheit on productivity of automobile assembly workers. She controls the temperature of the three manufacturing facilities, such that employees in one facility work in a room temperature of 60 degrees, employees in another facility work in a room temperature of 65 degrees, and the last group works in a room temperature of 70 degrees. The productivity of each group is indicated by the number of automobiles produced each day. In this example, what is the measurement scale of room temperature?

a) Nominal b) Ordinal c) Interval d)Ratio

In the previous example, what is the measurement scale of productivity?


Select the highest appropriate level of measurement:

Bicycle models:

1= Road2 = Touring3 = Mountain4 = Hybrid5 = Comfort6 = Cruiser



Educational Level:

1 = Some High school2 =High school Diploma3 = Undergraduate Degree4 = Masters Degree5 = Doctorate Degree



Number of questions asked during a class lecture


Select the highest level of measurement:

Categories on a Likert-type scale measuring attitudes:

1 = Strongly Disagree2 = Disagree3 = Neutral4 = Agree5 = Strongly Agree


Identify the level of measurement Case 1: A study compared males and females

on their verbal ability. More specifically, the study wanted to determine who is higher in verbal ability between the two groups. A test on verbal ability is given for the two groups and the mean scores were compared.

Case 2: The effect of Project-Based Learning (PBL) on the grades of students was studied among college students. It was hypothesized that students will achieve more in the PBL as compared to a group who received pure lecture. The grades of the students were compared at the end of the term.

Identify the level of measurement Case 3: Writing anxiety, writing

metacognition, and topic knowledge was used to predict students writing proficiency. Students essays were scored which served as indicator for their writing proficiency. Scales were used to determine writing anxiety, writing metacognition, and topic knowledge.

Case 4: Neophyte and experienced principals, coordinators, and directors were compared on their degree of transformational leadership. A scale measuring transformational leadership was administered to the administrators across 200 school in NCR.

Identify the level of measurement Case 4: Filipino and Korean high school students were

compared on their oral proficiency (TOEFL), vocabulary, and reading comprehension in English (English test).

Case 5: The effect of case study method on students critical thinking was studied. The Watson Glaser Critical Thinking Appraisal (WGCTA) was administered as a pretest then the case study method was implemented for the rest of the term. Towards the end of the term, the WGCTA was administered again.

Case 6: The frequencies of SV agreement errors in an essay were counted among high school students in the public and private. The comparison was also done among high and low ability students in these two schools.

Statistics UsedParametric Non-Parametric

•Enables researchers to make assumptions about the population•Large sample size is requires (N>30)•Used for interval and ratio scales

•Difficult to make assumptions about the population•Large sample size is not a requirement•Used for nominal and ordinal scales

Statistics Used

Design Parametric Non-Parametric

One sample-the mean of one sample is compared with a standard

No. of comparisons: nominalDV: interval/ratio

One sample, categories are nominal/ordinal

One sample repeated measures (dependent groups)-One sample is studies but more measured twice (2 set of data)- e. g. pre and post test design

No. of comparisons: nominalDV: interval/ratio

No. of comparisons: nominalDV: nominal/ordinal

Two independent groups-studying two distinct samples/groups

Groups/IV: nominalDV: interval/ratio

Groups/IV: nominalDV: nominal/ordinal

Comparing multiple groups (independent or dependent groups)

Groups/IV: nominalDV: interval/ratio

Groups/IV: nominalDV: nominal

Relating one variable to another

Statistics UsedDesign Parametric Non-Parametric

One sample-the mean of one sample is compared with a standard

z-testt-test

One-way chi-squareKolmogorov smirnov

One sample repeated measures (dependent groups)-One sample is studies but more measured twice (2 set of data)- e. g. pre and post test design

t-test for 2 dependent samples

McNemar change testWilcoxon signed ranks test

Two independent groups-studying two distinct samples/groups

t-test for 2 independent samples

Two-way chi-squareMann Whitney U test

Comparing multiple groups (independent or dependent groups)

Analysis of Variance (ANOVA)1 IV, 1 DV: one way ANOVA 2 IV, 1 DV: two way ANOVA1 more IV, 2 or more DV: MANOVA

Kruskal wallis test

Relating one variable to another

Pearson r Spearman rhoPhi coefficient

Case 1 It was hypothesized in a study that students

ability in school is related to procrastination. College students were tested using the OTIS Lenon School Ablity Test (OLSAT) and the perfectionism scale by Frost was administered to the same group.

How many variables are studied? What are the levels of measurement of the

variables? What is the purpose of the study? What statistics will be used?

Data

OLSAT (X) Procrastination (Y)

100 99

95 98

90 94

85 87

82 84

80 81

75 78

70 73

65 68

50 60

Regression Line between OLSAT and perfectionism

Scatterplot: X vs. Y

Y = 14.379 + .85633 * XCorrelation: r = .98966

40 50 60 70 80 90 100 110

X

55

60

65

70

75

80

85

90

95

100

105

Y

95% confidence

Linear Regression There is a straight line relationship between

variables X and Y When X increases, Y also increases-positive

relationship When X increases, Y decreases or vice versa –

negative relationship

Correlational Techniques Pearson Product-Moment correlation – (r) used

for interval/ratio sets of variables Spearman Rank-order correlation – two sets of

data are ordinal Phi coefficient – each of the variables is a

dichotomy

OLSAT Perfectionism

100 35

95 40

90 45

85 50

75 55

70 60

65 64

60 70

55 76

50 80

Relationship between Laziness and Perseverance

Scatterplot: Y vs. X

X = 139.94 - 1.138 * YCorrelation: r = -.9959

30 40 50 60 70 80 90

Y

40

50

60

70

80

90

100

110

X

95% confidence

Magnitude of the Relationship

Positive relationship – as one variable increases the other variable also increases

Ex. academic grades and intelligence Negative relationship – as one variable

increases, the other decreases or vice versa

Ex. procrastination and motivation Absence of relationship between variables –

denoted by .00 Show computation in statistica

Strength of Relationship

A correlation coefficient is computed for a bivariate distribution using a statistical formula

Correlation Coefficient Value Interpretation

0.80 – 1.00 Very strong relationship

0.6 – 0.79 Strong relationship

0.40 – 0.59 Substantial/marked relationship

0.2 – 0.39 Low relationship

0.00 – 0.19 Negligible relationship

Variance How much of Y’s is explained/accounted for by

X Proportion explained Square of the correlation coefficient value

Case 2: Spearman rho Students ranked their degree of importance

on poverty alleviation poverty and health policy.

Poverty alleviation policy

Health policy

14 13

11 12

10 9

10 8

14 10

13 14

Case 3: Phi coefficient

High Low

Own choice 30 20

Others choice 10 40

Teaching Satisfaction

Becoming a teacher

Case 4: One sample t-test 7 Filipino college students have taken the Test

for English as a Second Language (TESL). The researcher wanted to determine if their scores are far from the standard norm among speakers of ESL. The standard norm in the manual is 40.5 with a standard error of 4.54. 42

45

46

45

43

46

47

Case 5: one way chi-squareErrors found F Expected

frequency

Poor sentence construction

26 21.11

Wrong choice of word

32 21.11

Faulty parallelism

12 21.11

Wrong case 14 21.11

Wrong punctuation

46 21.11

Fragment 8 21.11

Wrong article 16 21.11

Run-on sentence

27 21.11

Wrong verb 9 21.11Total=190

Case 6: Kolmogorov smirnov

fo fe

Asst. Instructor25 15.6

Instructor10 15.6

Ass. Prof31 15.6

Prof7 15.6

Full Prof 5 15.6ft/∑ fo = 78

Case 7: t-test for 2 dependent samples A study investigated whether the effect of

problem-based teaching in mathematics would develop students deep approach to learning. The students were first given a pre test using the learning process questionnaire (LPQ) that measures deep approach to learning. The students are exposed to different problems in mathematics before learning concepts and algorithms. After the instruction, the LPQ was again administered to the same 10 students.

Case 7: t-test for 2 dependent samplesLPQ pre test LPQ post test

24 228 3032 3718 2224 2936 4040 3837 4124 2920 28

Case 8: Wilcoxon signed ranks test One group of pre-school students were asked

to rank a picture by giving the age of a very simple person in a picture without make-up. On a second occasion, the same person in the first picture was again shown but with elaborate clothes and with make-up. Is there a difference in the 2 sets of rankings?

Case 8: Wilcoxon signed ranks test

Student No. 1st Pic 2nd Pic1 12 122 14 163 15 144 12 115 16 146 15 187 13 168 10 11

Case 9: McNemar Change test An experiment was conducted to determine

whether hypnosis can be a clinical intervention to increase students test performance. A test was given and students who passed and failed were identified. The students have undergone hypnosis and after session they were again given an identical test. The students who passed and failed were again identified. Before hypnosis

Pass Fail

After hypnosis

Fail 7 10

Pass 15 20

Case 10: t-test for 2 independent samples The effect of picture-taste association on

memory recall was investigated among 30 volunteer college students. The 15 participants in the experiment group looked at 20 pictures matched with the food that they have to taste. The other 15 participants in the control group just looked at the pictures. After the procedure, both groups were tested in their memory where they have to enumerate in order the labels of the pictures they saw.

Case 10: t-test for 2 independent samples

Experimental group Control group9 4

14 911 39 6

12 413 214 59 511 413 511 613 612 414 715 8

∑x1 = 180 ∑x2= 78

1 = 12 2 = 5.2

Case 11: Mann-Whitney U test In the study, 8 single individuals and 7

married individuals were asked to rank their life satisfaction using a ranking scale. Test whether they differ in their rankings.Single Married

40 1037 7535 4037 3251 2538 6242 549

Case 12: Chi-square A survey was conducted among 29 prisoners

in manila city jail. They were asked crimes that they committed and their educational attainment through a checklist. The following data was tabulated

Crimes Committed

Educational Attainment

Elementary

HS College Total

Murder 3 7 1 11Homicide 2 3 6 11Robbery 1 2 5 8

Total 6 12 12 30

Case 13: One-Way ANOVA In an experiment, the effect of nonbehavioral

intervention techniques was investigated on the computational ability of fourth year high school students. The non-behavioral intervention techniques has three levels: bibliotherapy, small group interaction, and games. These techniques were used as a teaching strategy in a lesson in a math class for three sections. Each of the strategy was used for each section. One section did not receive any strategy which served as the control group. After undergoing the strategy, the students were tested where they answered a series of computation items.

Case 13: One-Way ANOVA

Control bibliotherapy

Small group

Games

8 14 19 15

9 13 18 15

6 12 19 14

7 15 19 15

2 15 17 13

4 14 18 14

4 13 18 13

Self-efficacy

Achievement

Effect of Achievement and Type of school on self-efficacy

Low Achievers

High Achievers

Type of school

Public school

Private School

Case 14: Two way ANOVA

Case 14: Two way ANOVA

low achiever high achiever

Public

10 159 165 176 155 16

Private

15 1914 2014 1913 1815 18

Case 15: MANOVA Public and Private schools were compared on

their self-monitoring and goal-setting Self-monitoring goal-settingPublic 10 9

10 89 77 78 57 5

6 4Private 18 17

19 1918 1917 1817 1818 17

18 18

Case 16: Multiple regression Goal-setting, self-evaluation, seeking

assistance, and environmental structuring were used to predict learning responsibility.

Workshop Work with a team Make an outline of a study that will make use

of quantitative analysis State the purpose of the study (research question) Possible hypothesis (if there is) Framework that supports the study Research Design Participants Instruments Procedure Data Analysis

Quantitative techniques in research

Business

design case

use of statistics

effect of case study

grades of students

college students

students essays

low ability students

nominal variable