Quantitative Analysis in Language Research

Carlo Magno, PhDcrlmgn@yahoo.com

Outcomes

State research questions and hypothesis anchored on a language theory

Decide on the statistical analysis to be used given research cases.

Create an outline of a research that will be conducted using quantitative Analysis

How do we arrive with good research questions?

BASIC

Read the prevailing literature

Test the theory Restate the theory

APPLIED

Observe the immediate need

Address the need Solution to the

problem

How do we arrive with good research questions?

Research Question

Read Reviews

Find theory/mo

del

Gaps? What’s new

Statistics in the HEIUndergraduate Statistics

Masters Statistics

Doctorate Statistics

•Computation and Interpretation of data•Descriptive and Inferential

•Review on Computation and Interpretation•Descriptive and Inferential statistics•Statistical Literacy – understanding statistics as used in journal articles

•Using statistics to test theories generated.•Multivariate data analysis

Outline

Considerations in the selection of statistics to use.

List of statistics Examples in using the statistics

Read the article on CORI

Increasing Reading Comprehension and Engagement Through Concept-Oriented Reading Instruction. By: Guthrie, John T., Wigfield, Allan, Barbosa, Pedro, Perencevich, Kathleen C., Taboada, Ana, Davis, Marcia H., Scafiddi, Nicole T., Tonks, Stephen, Journal of Educational Psychology, 00220663, 2004, Vol. 96, Issue 3.

Abstract Based on an engagement perspective of reading

development, we investigated the extent to which an instructional framework of combining motivation support and strategy instruction (Concept-Oriented Reading Instruction—CORI) influenced reading outcomes for third-grade children. In CORI, five motivational practices were integrated with six cognitive strategies for reading comprehension. In the first study, we compared this framework to an instructional framework emphasizing Strategy Instruction (SI), but not including motivation support. In the second study, we compared CORI to SI and to a traditional instruction group (TI), and used additional measures of major constructs. In both studies, class-level analyses showed that students in CORI classrooms were higher than SI and/or TI students on measures of reading comprehension, reading motivation, and reading strategies.

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 data 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 DataA 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 Data

Nominal

Ordinal

Interval

Ratio

Levels of Data

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?

Levels of Data

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 Data

Sometimes numbers are used to designate category membership

Example: Country of Origin1 = 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

Levels of Data

Ordinal Data - 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.

20

Ordinal Data 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

21

Levels of DataInterval 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!

22

Levels of Data

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 2 23

Levels of Data

• 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.

Levels of Data

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) Nominal b) Ordinal c) Interval d) Ratio

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 level of data of productivity?

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

Select the highest appropriate level of data:

Bicycle models:

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

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

Select the highest appropriate level of data:

Educational Level:

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

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

Select the highest appropriate level of data:

Number of questions asked during a class lecture

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

Select the highest level of data:

Categories on a Likert-type scale measuring attitudes:

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

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

Identify the level of data 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 data 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 data 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 UsedDesign Parametric Non-ParametricOne 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-ParametricOne 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

Identify the inferential statisticsCase A: The number of students were

counted categorized for those who prefer to take the science and humanities track. Males and females were counted for each track as well. The researcher wanted to compare the number of students categorized by gender and tracks.

Identify the inferential statisticsCase BThe attitude towards learning a

foreign language were determined using a 10 item questionnaire using a Lickert scale. The Filipinos, Chinese, and Japanese stduents were compared on their attitude towards learning a foreign langauge.

Identify the inferential statistics Case C Students were grouped for those whose

parents are native speakers (L1) of English and those whose English is L2. These two groups were requested to answer the an English Language Exposure scale with 10 items (4 point scale). Students with parents who speaks English in L1 and L2 were compared on their scores on the English Language Exposure.

Identify the inferential statistics Case D Students were asked to rank how

well they speak their local dialect. Students who studied grade school and high school in their province (where the dialect is spoken) and those that did not were compared on their rankings.

Identify the inferential statistics Case E Students were asked to watch

newscaster A then followed by newscaster B. The students were asked to rate the English proficiency of both newscaster A and B on a scale of 1 (not proficient) to 7 (very proficient). The ratings of newscaster A and B were compared.

Identify the inferential statistics Case F Students who passed and failed in a grammar test

were counted. Then students were given a special grammar class. The students were given a similar test again and those who passed and failed were counted. Those who initially passed then failed after the hypnosis were compared to those who initially failed and then passed after the special grammar class.

Before the special grammar classPass Fail

After Pass 29hypnosis Fail 15

Identify the inferential statisticsCase GThere were 30 students who

took a reading comprehension test (mean and SD were obtained). Their performance were compared with the mean score obtained from the test manual.

Identify the inferential statistics Case H Males and females are classified into

those with high and low verbal ability. These groups were compared on their self-efficacy (6 items, 4 point scale) and self-regulation (52 items, 4 point scale). Males with high and low ability and females with high and low ability were compared on the two scales.

Identify the inferential statistics Case I Students answered a scale measuring

their language learning strategies composed of cognitive, affective, social, and metacogntive strategies. At the end of the term, their grades in English were obtained. It is hypothesized that cognitive, affective, social, and metacogntive strategies will predict students English grades.

Identify the inferential statistics Case J Students level of proficiency in

writing an essay (rate using a rubric) and students knowledge of content (using a test) were determined. The researcher hypothesized that when students knowledge of content increases, their proficiency in writing an essay also increases.

Case 1 It was hypothesized in a study that students

ability in school is related to perfectionism. 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?

DataOLSAT (X) Perfectionism (Y)

100 9995 9890 9485 8782 8480 8175 7870 7365 6850 60

Regression Line between OLSAT and perfectionism

Scatterplot: X vs. YY = 14.379 + .85633 * X

Correlation: 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

Writing proficiency Errors in Grammar100 3595 4090 4585 5075 5570 6065 6460 7055 7650 80

Relationship between writing proficiency and errors in grammar

Scatterplot: Y vs. XX = 139.94 - 1.138 * Y

Correlation: 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 formulaCorrelation Coefficient Value Interpretation0.80 – 1.00 Very strong relationship0.6 – 0.79 Strong relationship0.40 – 0.59 Substantial/marked relationship0.2 – 0.39 Low relationship0.00 – 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 learning

a foreign language and working overseas.

Learning a foreign language

Working overseas

14 1311 1210 910 814 1013 14

Case 3: Phi coefficient

Struggling IndependentHave books at home

30 20

No books at home

10 40

Reading Level

Availability of books

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.

42454645434647

Case 5: one way chi-square

Errors 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 21.11Wrong punctuation

46 21.11

Fragment 8 21.11Wrong article 16 21.11Run-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

project-based learning in an English class would develop students deep approach to learning English. 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 situations in English they were asked to respond thorugh speaking and writing. After the instruction, the LPQ was again administered to the same 10 students.

Case 7: t-test for 2 dependent samples

LPQ pre test LPQ post test24 228 3032 3718 2224 2936 4040 3837 4124 2920 28

Case 8: Wilcoxon signed ranks test One group of students were asked to

rank the English proficiency of a person speaking with an English accent. In another occasion, the same students watched another speaker with a Filipino accent. Is there a difference in the 2 sets of rankings?

Case 8: Wilcoxon signed ranks test

Student No. English Accent

Filipino Accent

1 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

word work strategy can be a intervention to help studnets become readers. A reading test was given and students who are readers and non readers were identified. The students have undergone word work strategy and after session they were again given an identical reading test. The students who are readers and non readers were again identified.

Before word work strategyReaders Non

readersAfter word work strategy

Non readers

7 10

Readers 15 20

Case 10: t-test for 2 independent samples The effect of exposure to a scientific report on

students technical writing skill was investigated among 30 senior high school STEM students. The 15 participants in the experiment group were given a model of a good scientific paper before they wrote their own investigative project. The other 15 participants in the control group were just given guidelines how to write without an example. After the procedure, both groups submitted their report for the investigative report. The report was rated using a rubric.

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= 781 = 12 2 = 5.2

Case 11: Mann-Whitney U test In the study, 8 students who attended an English remedial class

and 7 who immediately attended a regular class in English were asked to rank their confidence in speaking English using a ranking scale. Test whether they differ in their rankings.

Attended a remedial class

Went to a regular English

class40 1037 7535 4037 3251 2538 6242 549

Case 12: Chi-square Three corpora was studied: Philippine English,

Singaporean English, and Malaysian English. Three modals were counted in each of the corpora.

Corpus Modalscould would should Total

Philippine English

3 7 1 11

Singapore English

2 3 6 11

MalaysianEnglish

1 2 5 8

Total 6 12 12 30

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

comprehension techniques were investigated on the reading comprehension of literature students. The techniques has three levels: questioning, context clue, and guided practice. These techniques were used as a teaching strategy in a lesson in a literatire class for three sections. Each of the strategy was used for each class. 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 items about a text read.

Case 13: One-Way ANOVA

Control Questioning Guided practice

Context clue

8 14 19 159 13 18 156 12 19 147 15 19 152 15 17 134 14 18 144 13 18 13

English Proficiency

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 English grades.

Regression Summary for Dependent Variable: GRades (data for multiple regression) R= .68021315 R²= .46268992 Adjusted R²= .46163998 F(4,2047)=440.68 p

b* Std.Err. - of b* b Std.Err.

- of b t(2047) p-valueIntercept 0.45 0.06 6.89 0.00goal_set 0.19** 0.02 0.17 0.01 8.80 0.00self_ev 0.21** 0.02 0.23 0.02 8.88 0.00seek_ast 0.15** 0.02 0.17 0.02 6.74 0.00env_struc 0.28** 0.02 0.26 0.02 13.32 0.00

Path Analysis

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