Mathmworld Statistics Research Proposal Requirements - Holy Angel University PDF

STAT I ST I C S R I A C R I S T I NA A. S I C AT ENGR. MA L Y A NG E L U NI VE R S I T Y HO MIDTERM REQUIREMENT (PROJECT): RESEARCH PROPOSAL W/ VIDEO PRESENTATION § WHILE WE HAVE ONLY BARELY TOUCHED THE SURFACE OF THIS VERY IMPORTANT AREA OF STUDY CALLED STAT...

STAT I ST I C S R I A C R I S T I NA A. S I C AT ENGR. MA L Y A NG E L U NI VE R S I T Y HO MIDTERM REQUIREMENT (PROJECT): RESEARCH PROPOSAL W/ VIDEO PRESENTATION § WHILE WE HAVE ONLY BARELY TOUCHED THE SURFACE OF THIS VERY IMPORTANT AREA OF STUDY CALLED STATISTICS, YOU ARE ENJOINED TO BEGIN THINKING ABOUT ITS USEFULNESS AND APPLICATION. FOR THIS REQUIREMENT, YOU ARE TO WORK TOGETHER IN A GROUP WITH MAXIMUM OF 4 MEMBERS. § YOUR TASK IS TO PREPARE A RESEARCH PROPOSAL FOR A STUDY THAT WILL: 1. CONTRIBUTE TO OR LEAD TO A SOLUTION OF A SOCIAL, ECONOMIC, OR CULTURAL (INCLUDING EDUCATIONAL) PROBLEM; 2.MAKE USE OF STATISTICAL METHODS FOR DATA PROCESSING AND ANALYSES.  RESEARCH PROPOSAL REQUIREMENT Your output is A DOCUMENT AND VIDEO PRESENTATION that details your proposed study. The outline of your OUTPUT is as follows: v PROPOSED RESEARCH TITLE (The title summarizes the main idea or ideas of your study. It should reflect the variables that you want to investigate on. It must not be longer than 15 words) v RATIONALE (The rationale is the justification why you intend to conduct a study on your proposed title) v STATEMENT OF THE PROBLEM (The SOPs are the research questions you intend to answer in the course of your study.) v BRIEF REVIEW OF RELATED LITERATURE & STUDIES (minimum of 10 references within 10-year recency; A summary of previous researches that have been done on your proposed research, and use these to identify the weaknesses or gaps that still need to be addressed ) v METHODOLOGY Research Design (The specific quantitative research design that you will use in the study ) Sample and Sampling Technique (Specify the people from whom you will gather research information to answer your Statement of the Problem, and the appropriate sampling method to be used. ) Data to be collected (This refers to the information to be gathered from the respondents) Methods of data collection (e.g. survey questionnaire, interview, observation, etc.) Research Instrument/s (Discuss the development of the instrument to be used) Data Analysis (EXPLAIN WHAT DESCRIPTIVE & INFERENTIAL STATISTICAL TOOLS WILL BE APPLIED) Ethical Consideration v REFERENCES (with in-text citation) - List all the sources cited in the research proposal based on 7th edition APA format. v APPENDIX (Attach the draft of the proposed research instrument to be used for data collection)  RESEARCH PROPOSAL REQUIREMENT FOR THE DOCUMENT FILE COPY: THE RESEARCH PROPOSAL WILL BE TYPE-WRITTEN IN LETTER SIZE PAPER (15 TO 20 PAGES). USE OF APA 7TH EDITION STANDARDS MUST BE OBSERVED IN IN-TEXT CITATION AND LISTING REFERENCES. *DOCUMENT SPECIFICATIONS: MARGIN: 1” ALL SIDES SPACING: DOUBLE SPACE FONT STYLE: TIMES NEW ROMAN/ARIAL FONT SIZE: 12 FOR THE POWERPOINT/VIDEO PRESENTATION MECHANICS: THE GROUP MUST PRESENT THE PREPARED POWERPOINT SLIDES IN A RECORDED VIDEO. THE 5 TO 10-MINUTE RESEARCH PRESENTATION MUST COVER ALL THE REQUIRED CONTENT ABOVE. AT LEAST 50% OF THE GROUP MEMBERS MUST PARTICIPATE IN THIS VIDEO. THE MEMBERS MUST PROPERLY INTRODUCE THEMSELVES (NAME AND SECTION) AT THE START OF THE PRESENTATION AND INDICATE THEIR INDIVIDUAL CONTRIBUTION IN THE COMPLETION OF THE TASK.  RESEARCH PROPOSAL REQUIREMENT SUBMISSION DETAILS A.) UPLOAD THE DOCUMENT FILE COPY OF YOUR PROPOSAL SAVED IN PDF FORMAT ON THE CANVAS ASSESSMENT BOARD. B.) UPLOAD YOUR VIDEO-RECORDED RESEARCH PRESENTATION ON YOUTUBE (UNLISTED) AND POST THE LINK (WEBSITE URL) ON THE COMMENT SECTION/BOX FOR THIS ASSESSMENT. C.) FILE NAME FORMAT: MATHMWORLD_RESEARCH PROPOSAL_ SEM/SY__ GROUP NO._ SECTION *REFER TO THE PROVIDED RUBRIC FOR YOUR GUIDANCE AND REFERENCE IN ACCOMPLISHING THIS TASK.  RESEARCH PROPOSAL REQUIREMENT RUBRIC (CRITERIA FOR SCORING) PAPER FOCUS: PURPOSE/ POSITION STATEMENT (5 POINTS) RESEARCH QUESTIONS/HYPOTHESIS (10 POINTS) RESEARCH METHODOLOGY (10 POINTS) PROPOSED STATISTICAL/DATA ANALYSIS (10 POINTS) APPENDIX: PROPOSED RESEARCH INSTRUMENT (5 POINTS) APPROPRIATE CITATION OF SOURCES/REFERENCES USING THE APA STYLE (5 POINTS) STYLE/DELIVERY (5 POINTS) CONTENT, ORGANIZATION AND SMOOTHNESS OF THE PRESENTATION (5 POINTS) TEAM COLLABORATION (5 POINTS) TOTAL: 60 POINTS STATISTICS IS A BRANCH OF MATHEMATICS THAT DEALS WITH THE SCIENTIFIC COLLECTION, ORGANIZATION, PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA IN ORDER TO OBTAIN USEFUL AND MEANINGFUL INFORMATION. TWO AREAS OF STATISTICS 1.DESCRIPTIVE STATISTICS 2.INFERENTIAL STATISTICS AREAS OF STATISTICS DESCRIPTIVE STATISTICS INFERENTIAL STATISTICS METHODS CONCERNED W/ METHODS CONCERNED WITH COLLECTING, DESCRIBING DRAWING CONCLUSIONS, MAKING (ORGANIZING, PRESENTING, PREDICTIONS, FORECAST OR ABOUT SUMMARIZING), AND ANALYZING A THE ENTIRE SET OF DATA SET OF DATA WITHOUT DRAWING CONCLUSIONS (OR INFERENCES) ABOUT A LARGE GROUP  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 GENDER  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. EXERCISE: TELL WHETHER EACH OF THE FOLLOWING WILL MAKE USE OF DESCRIPTIVE STATISTICS OR INFERENTIAL STATISTICS. 1. A TEACHER COMPUTES THE AVERAGE GRADE OF HIS STUDENTS AND THEN DETERMINES THE TOP 10 STUDENTS. Descriptive Statistics 2. A MANAGER OF A BUSINESS FIRM PREDICTS FUTURE SALES OF THE COMPANY BASED ON THE PRESENT SALES. Inferential Statistics 3. A PSYCHOLOGIST INVESTIGATES IF THERE IS A SIGNIFICANT RELATIONSHIP BETWEEN THE MENTAL AGE AND CHRONOLOGICAL AGE. Inferential Statistics 4. A RESEARCHER STUDIES THE EFFECTIVENESS OF A NEW FERTILIZER IN INCREASING FOOD PRODUCTION. Inferential Statistics 5. A JANITOR COUNTS THE NUMBER OF VARIOUS FURNITURE INSIDE THE SCHOOL. Descriptive Statistics SOME STATISTICAL TERMINOLOGIES DATA – ANY PIECES OF INFORMATION USEFUL TO THE RESEARCHER; THE MEASUREMENTS OBTAINED IN A RESEARCH STUDY VARIABLE – IS A CHARACTERISTIC OR PROPERTY OF AN INDIVIDUAL TO BE MEASURED OR OBSERVED. QUANTITATIVE VARIABLE – HAS A VALUE OR NUMERICAL MEASUREMENT FOR WHICH OPERATIONS SUCH AS ADDITION OR AVERAGING MAKE SENSE. a. DISCRETE VARIABLE – IS A VARIABLE THAT CAN BE OBTAINED BY COUNTING. b. CONTINUOUS VARIABLE – IS A VARIABLE THAT CAN BE OBTAINED BY MEASURING. QUALITATIVE VARIABLE – DESCRIBES AN INDIVIDUAL BY PLACING THE INDIVIDUAL INTO A CATEGORY OR GROUP SUCH AS MALE OR FEMALE. SOMETIMES, THEY ARE REFERRED TO AS CATEGORICAL VARIABLE. INDIVIDUALS – ARE THE PEOPLE, PLACES, EVENTS OR OBJECTS INCLUDED IN THE STUDY.  TYPES OF VARIABLES QUALITATIVE (ATTRIBUTE, OR CATEGORICAL VARIABLE) -A VARIABLE THAT CATEGORIZES OR DESCRIBES AN ELEMENT OF A POPULATION. EX. GENDER, HAIR COLOR, ETHNIC, CIVIL STATUS, ETC. QUANTITATIVE (NUMERICAL VARIABLE) -A VARIABLE THAT QUANTIFIES AN ELEMENT OF A POPULATION. EX. DISTANCE TRAVELED TO SCHOOL, NUMBER OF CHILDREN IN A FAMILY, MONTHLY ELECTRIC BILL, ETC.  EXERCISE : IDENTIFY EACH OF THE FOLLOWING AS QUALITATIVE OR QUANTITATIVE VARIABLES. IF QUANTITATIVE, DETERMINE IF IT’S DISCRETE OR CONTINUOUS. 1. THE TEMPERATURE IN ANGELES CITY AT 12:00 PM ON ANY GIVEN DAY Quantitative, Continuous 2. THE NUMBER OF PARTICIPANTS IN A WEBINAR Quantitative, Discrete 3. WHETHER OR NOT A 6 VOLT LANTERN BATTERY IS DEFECTIVE Qualitative 4. THE WEIGHT OF A LEAD PENCIL Quantitative, Continuous 5. THE LENGTH OF TIME BILLED FOR A LONG DISTANCE TELEPHONE CALL Quantitative, Continuous 6. THE BRAND OF CEREAL CHILDREN EAT FOR BREAKFAST Qualitative 7. THE NUMBER OF FULLY-VACCINATED STUDENTS WHO ATTENDED THE FORUM Quantitative, Discrete SOME STATISTICAL TERMINOLOGIES POPULATION – REFERS TO THE TOTALITY OF ALL THE INDIVIDUALS WHICH ONE HAS AN INTEREST AT A PARTICULAR TIME. SAMPLE – IS A PART OF A POPULATION DETERMINED BY SAMPLING PROCEDURES. PARAMETER – IS A VALUE THAT DESCRIBES AN ASPECT OF A POPULATION. STATISTIC – IS A VALUE THAT DESCRIBES AN ASPECT OF A SAMPLE. SAMPLING METHODS SAMPLING METHODS CAN BE: § RANDOM (PROBABILITY SAMPLING): EACH MEMBER OF THE POPULATION HAS AN EQUAL CHANCE OF BEING SELECTED § NONRANDOM (NON-PROBABILITY SAMPLING) EX. PURPOSEFUL/PURPOSIVE SAMPLING – BASED ON THE CRITERIA LAID DOWN BY THE RESEARCHER; QUOTA SAMPLING; CONVENIENCE SAMPLING; SNOWBALL METHOD THE ACTUAL PROCESS OF SAMPLING CAUSES SAMPLING ERRORS. FOR EXAMPLE, THE SAMPLE MAY NOT BE LARGE ENOUGH OR REPRESENTATIVE OF THE POPULATION. FACTORS NOT RELATED TO THE SAMPLING PROCESS CAUSE NON- SAMPLING ERRORS. A DEFECTIVE COUNTING DEVICE CAN CAUSE A NON- SAMPLING ERROR. RANDOM SAMPLING METHODS q SIMPLE RANDOM SAMPLING: EACH SAMPLE OF THE SAME SIZE HAS AN EQUAL CHANCE OF BEING SELECTED. q STRATIFIED SAMPLING: DIVIDE THE POPULATION INTO GROUPS CALLED STRATA AND THEN TAKE A SAMPLE FROM EACH STRATUM. q CLUSTER SAMPLING (AREA SAMPLING): RESEARCHERS DIVIDE A POPULATION INTO SMALLER GROUPS KNOWN AS CLUSTERS. THEY THEN RANDOMLY SELECT AMONG THESE CLUSTERS TO FORM A SAMPLE. CLUSTER SAMPLING IS A METHOD OF PROBABILITY SAMPLING THAT IS OFTEN USED TO STUDY LARGE POPULATIONS, PARTICULARLY THOSE THAT ARE WIDELY GEOGRAPHICALLY DISPERSED. q SYSTEMATIC SAMPLING: RANDOMLY SELECT A STARTING POINT AND TAKE EVERY K-TH PIECE OF DATA FROM A LISTING OF THE POPULATION. DETERMINING THE SAMPLE SIZE SAMPLE SIZE CAN BE DETERMINED USING VARIOUS SOFTWARE PROGRAMS AND WEBSITES THAT OFFER A FREE ON-LINE SAMPLE SIZE CALCULATOR. EXAMPLES OF SUCH A SITE ARE G-POWER (HTTP://DOWNLOAD.CNET.COM/G-POWER/3000- 2054_4-10647044.HTML), EPI INFOTM , (HTTPS://WWW.CDC.GOV/EPIINFO/INDEX.HTML), AND THE SURVEY SYSTEM HTTPS://WWW.SURVEYMONKEY.COM/MP/SAMPLE-SIZE-CALCULATOR/. SUCH ON-LINE APPLICATIONS USUALLY REQUIRE TO ENTER THE TARGET POPULATION SIZE, CONFIDENCE LEVEL AND MARGIN OF ERROR. e = DESIRED MARGIN OF ERROR (PERCENT ALLOWANCE FOR NON-PRECISION BECAUSE OF THE USE OF THE SAMPLE INSTEAD OF THE POPULATION (e.g., e = 0.01, 0.05, 0.10) LEVEL OR SCALES OF MEASUREMENT 1. NOMINAL LEVEL OF MEASUREMENT 2. ORDINAL LEVEL OF MEASUREMENT 3. INTERVAL LEVEL OF MEASUREMENT 4. RATIO LEVEL OF MEASUREMENT NOMINAL LEVEL OF MEASUREMENT IT APPLIES TO DATA THAT CONSIST OF NAMES, LABELS, OR CATEGORIES. THERE ARE NO IMPLIED CRITERIA BY WHICH THE DATA CAN BE ORDERED FROM SMALLEST TO HIGHEST. EXAMPLES: GENDER, SPORTS, BLOOD TYPE, CIVIL STATUS, BRAND OF VACCINE INJECTED, ETC. ORDINAL LEVEL OF MEASUREMENT IT APPLIES TO DATA THAT CAN BE ARRANGED IN ORDER/RANK. DIFFERENCES BETWEEN THE DATA VALUES EITHER CANNOT BE DETERMINED OR ARE MEANINGLESS. EXAMPLE: RANKING OF STUDENTS, MILITARY RANKS, SIZES OF SHIRT, ETC. INTERVAL LEVEL OF MEASUREMENT IT APPLIES TO DATA THAT CAN BE ARRANGED IN ORDER. DIFFERENCES BETWEEN DATA VALUES ARE MEANINGFUL. DATA AT THIS LEVEL HAVE NO TRUE, OR NO MEANINGFUL ZERO. EXAMPLES: TEMPERATURE IN DEGREE CELSIUS, TEST RESULTS, GRADES, IQ, ETC. RATIO LEVEL OF MEASUREMENT IT APPLIES TO DATA THAT CAN BE ARRANGED IN ORDER. IN ADDITION, BOTH DIFFERENCES BETWEEN DATA VALUES, AND RATIO OF DATA VALUES ARE MEANINGFUL. DATA AT THE RATIO LEVEL HAVE A TRUE OR MEANINGFUL ZERO. EXAMPLE: AREA OF A CIRCLE, DISTANCE TRAVELLED, VOLUME OF WATER, ETC. EXERCISE: WHAT TYPE OF DATA ARE THE FOLLOWING: 1. PREFERRED HOBBIES Nominal 2. BIRTH ORDER Ordinal 3. SPEED OF A CAR Ratio 4. BODY BUILT (S, M, L, XL ) Ordinal 5. TELEPHONE/CELPHONE NUMBERS Nominal 6. BOARD EXAM SCORE Interval 7. SPEED OF A CAR Ratio 8. BRANDS OF SOAP PURCHASED Nominal 9. TEMPERATURE IN KELVIN Ratio 10.COLLEGE ENTRANCE TEST RESULT Interval  SUMMARY: Quantitative Qualitative *Data – values assigned to a variable) Numerical Categorical (Discrete or Continuous) Interval Ratio Can order, know the Can order, know the difference, no true difference, can be in ratio, has zero true zero (e.g. time, temp in (e.g. height, speed, volume) Celsius)  DESCRIPTIVE STATISTICS COLLECT DATA E.G., SURVEY PRESENT DATA E.G., TABLES AND GRAPHS SUMMARIZE DATA E.G., SAMPLE MEAN = å X i n COLLECTION OF DATA CLASSIFICATIONS OF DATA 1.PRIMARY DATA 2.SECONDARY DATA  SOURCES OF INFORMATION Primary Source Secondary Source Data are collected by Data are collected, researcher himself compiled or written by other Data are gathered researchers (e.g. books, through questionnaire, journals, newspapers) interviews, Any references must observations etc. be acknowledged METHODS OF COLLECTING DATA 1. INTERVIEW METHOD 2.QUESTIONNAIRE METHOD 3.REGISTRATION METHOD/CENSUS 4.OBSERVATION METHOD 5.EXPERIMENTATION METHODS OF PRESENTING DATA TTEXTUAL TTABULAR TGRAPHICAL  SUMMARY STATISTICS DESCRIBE DATA IN JUST 2 NUMBERS Measures of central tendency Measures of variability typical average score typical average variation 1. MEAN: arithmetic average 1. RANGE: distance from the lowest to 2. MEDIAN: middlemost value the highest (use 2 data points) 3. MODE: most frequently 2. VARIANCE: (use all data points) occurring value 3. STANDARD DEVIATION  MEASURES OF CENTRAL TENDENCY QUANTITATIVE DATA: MODE – THE MOST FREQUENTLY OCCURRING OBSERVATION MEDIAN – THE MIDDLE VALUE IN THE DATA MEAN – ARITHMETIC AVERAGE (MOST APPROPRIATE FOR RATIO/INTERVAL SCALE) QUALITATIVE DATA: MODE – ALWAYS APPROPRIATE MEAN – NEVER APPROPRIATE MEAN THE MOST COMMON AND MOST Notation USEFUL AVERAGE MEAN = SUM OF ALL OBSERVATIONS Sample vs population NUMBER OF ALL OBSERVATIONS Sample mean = X OBSERVATIONS CAN BE ADDED IN ANY ORDER. Population mean =µ Sample å size = n Population size = N Measures of Variability/Dispersion Variance: (use all data points): average of the distance that each score is from the mean (Squared deviation from the mean) Notation for variance s2 Standard Deviation = s = 𝑠 ! Example: (Sample) Data: 10 12 14 15 17 18 18 24 n=8 𝟏𝟎#𝟏𝟐#𝟏𝟒#𝟏𝟓#𝟏𝟕#𝟏𝟖#𝟏𝟖#𝟐𝟒 𝟏𝟐𝟖 Mean: 𝒙 >= = =16 𝟖 𝟖 𝟏𝟓#𝟏𝟕 𝟑𝟐 Median: 𝒙 A = = =16 𝟐 𝟐 Mode: 𝒙 B = 𝟏𝟖 (10 - 16)2 + (12 - 16)2 + (14 - 16)2 + (15 - 16)2 + (17 - 16)2 + (18 - 16)2 + (24 - 16)2 s= 7 = 4.309