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# Quantitative analysis in language research

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This slide contains different statistics applied in language research

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### Quantitative analysis in language research

1. 1. Carlo Magno, PhD crlmgn@yahoo.com
2. 2.  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 quantitativeAnalysis
3. 3. BASIC  Read the prevailing literature  Test the theory  Restate the theory APPLIED  Observe the immediate need  Address the need  Solution to the problem
4. 4. Research Question Read Reviews Find theory/model Gaps? What’s new
5. 5. Undergraduate 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
6. 6.  Considerations in the selection of statistics to use.  List of statistics  Examples in using the statistics
7. 7.  Increasing Reading Comprehension and EngagementThrough Concept-Oriented Reading Instruction. By: Guthrie, JohnT., Wigfield,Allan, Barbosa, Pedro, Perencevich, KathleenC.,Taboada, Ana, Davis, Marcia H., Scafiddi, NicoleT.,Tonks, Stephen, Journal of Educational Psychology, 00220663, 2004,Vol. 96, Issue 3.
8. 8.  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/orTI students on measures of reading comprehension, reading motivation, and reading strategies.
9. 9.  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?
10. 10.  When we analyzed the use of the statistics in the study by Guthrie et al., what information did we determine first?
11. 11. Variables Involved •Independent •Dependent How many groups? •Design •Comparison •Correlating •Effect Levels of data of the variables (IV and DV)
12. 12.  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.
13. 13.  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.
14. 14.  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.
15. 15. A B C D Type of school Ethnicity Gender Socio-economic status Favorite movie from like to least like Ranking of best science fiction stories Perceived highest to lowest reputable universities in terms of research EnglishAbility Math ability Achievement in Science Motivation Stress Self-esteem Self-efficacy temperature Height of children Weight of first graders Length of travel Width of the table Brightness of light
16. 16. Nominal Ordinal Interval Ratio
17. 17.  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?
18. 18. 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 origin biological sex (male or female) animal or non-animal married vs. single
19. 19.  Sometimes numbers are used to designate category membership  Example: Country of Origin 1 = United States 3 = Canada 2 = Mexico 4 = Other  However, in this case, it is important to keep in mind that the numbers do not have intrinsic meaning
20. 20. 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
21. 21.  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
22. 22. Levels of Data 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! 22
23. 23. 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 none a person who has had 4 relationships has had twice as many as someone who has had 2 23
24. 24. 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.
25. 25.  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)
26. 26. 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
27. 27. In the previous example, what is the measurement scale of letter grade on the final exam? a) Nominal b) Ordinal c) Interval d) Ratio
28. 28. 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
29. 29. In the previous example, what is the level of data of productivity? a) Nominal b) Ordinal c) Interval d) Ratio
30. 30. Select the highest appropriate level of data: Bicycle models: 1= Road 2 =Touring 3 = Mountain 4 = Hybrid 5 = Comfort 6 = Cruiser a) Nominal b) Ordinal c) Interval d) Ratio
31. 31. Select the highest appropriate level of data: Educational Level: 1 = Some High school 2 =High school Diploma 3 = Undergraduate Degree 4 = Masters Degree 5 = Doctorate Degree a) Nominal b) Ordinal c) Interval d) Ratio
32. 32. Select the highest appropriate level of data: Number of questions asked during a class lecture a) Nominal b) Ordinal c) Interval d) Ratio
33. 33. Select the highest level of data: Categories on a Likert-type scale measuring attitudes: 1 = Strongly Disagree 2 = Disagree 3 = Neutral 4 = Agree 5 = Strongly Agree a) Nominal b) Ordinal c) Interval d) Ratio
34. 34.  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.
35. 35.  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.
36. 36.  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.
37. 37. Parametric 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
38. 38. Design Parametric Non-Parametric One sample -the mean of one sample is compared with a standard No. of comparisons: nominal DV: 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: nominal DV: interval/ratio No. of comparisons: nominal DV: nominal/ordinal Two independent groups -studying two distinct samples/groups Groups/IV: nominal DV: interval/ratio Groups/IV: nominal DV: nominal/ordinal Comparing multiple groups (independent or dependent groups) Groups/IV: nominal DV: interval/ratio Groups/IV: nominal DV: nominal Relating one variable to another
39. 39. Design Parametric Non-Parametric One sample -the mean of one sample is compared with a standard z-test t-test One-way chi-square Kolmogorov 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 test Wilcoxon signed ranks test Two independent groups -studying two distinct samples/groups t-test for 2 independent samples Two-way chi-square Mann Whitney U test Comparing multiple groups (independent or dependent groups) Analysis ofVariance (ANOVA) 1 IV, 1 DV: one way ANOVA 2 IV, 1 DV: two way ANOVA 1 more IV, 2 or more DV: MANOVA Kruskal wallis test Relating one variable to another Pearson r Spearman rho
40. 40.  Case 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.
41. 41.  Case B  The 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.
42. 42.  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.
43. 43.  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.
44. 44.  Case E  Students were asked to watch newscasterA then followed by newscaster B. The students were asked to rate the English proficiency of both newscasterA and B on a scale of 1 (not proficient) to 7 (very proficient). The ratings of newscasterA and B were compared.
45. 45.  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 class Pass Fail After Pass 29 hypnosis Fail 15
46. 46.  Case G  There 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.
47. 47.  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.
48. 48.  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.
49. 49.  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.
50. 50.  It was hypothesized in a study that students ability in school is related to perfectionism. College students were tested using the OTIS Lenon School AblityTest (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?
51. 51. OLSAT (X) Perfectionism (Y) 100 99 95 98 90 94 85 87 82 84 80 81 75 78 70 73 65 68 50 60
52. 52. Scatterplot: X vs. Y Y = 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
53. 53.  There is a straight line relationship between variables X andY  When X increases,Y also increases-positive relationship  When X increases,Y decreases or vice versa – negative relationship
54. 54.  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
55. 55. Writing proficiency Errors in Grammar 100 35 95 40 90 45 85 50 75 55 70 60 65 64 60 70 55 76 50 80
56. 56. Scatterplot: Y vs. X X = 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
57. 57.  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
58. 58.  A correlation coefficient is computed for a bivariate distribution using a statistical formula Correlation CoefficientValue 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
59. 59.  How much ofY’s is explained/accounted for by X  Proportion explained  Square of the correlation coefficient value
60. 60.  Students ranked their degree of importance on learning a foreign language and working overseas. Learning a foreign language Working overseas 14 13 11 12 10 9 10 8 14 10 13 14
61. 61. Struggling Independent Have books at home 30 20 No books at home 10 40 Reading Level Availability of books
62. 62.  7 Filipino college students have taken theTest 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
63. 63. 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 21.11 Wrong punctuation 46 21.11 Fragment 8 21.11 Wrong article 16 21.11 Run-on sentence 27 21.11 Wrong verb 9 21.11 Total=190
64. 64. fo fe Asst. Instructor 25 15.6 Instructor 10 15.6 Ass. Prof 31 15.6 Prof 7 15.6 Full Prof 5 15.6 ft/∑ fo = 78
65. 65.  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.
66. 66. LPQ pre test LPQ post test 24 2 28 30 32 37 18 22 24 29 36 40 40 38 37 41 24 29 20 28
67. 67.  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?
68. 68. Student No. English Accent Filipino Accent 1 12 12 2 14 16 3 15 14 4 12 11 5 16 14 6 15 18 7 13 16 8 10 11