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RESEARCH & DATA ANALYSIS

Learn about collecting, analyzing, and interpreting statistical data for precise evaluation. Discover central tendency measures and standard deviation calculations for reliable research outcomes.

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RESEARCH & DATA ANALYSIS

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  1. RESEARCH & DATA ANALYSIS

  2. SCIENTISTS COLLECT STATISTICAL DATA FROM EXPERIMENTS • STATISTICAL OR NUMERICAL DATA ALLOWS FOR MORE ACCURATE ANALYSIS & EVALUATION OF THE RESULTS FROM EXPERIMENTS

  3. STATISTICSDEAL WITH COLLECTING, ANALYZING, AND INTERPRETING INFORMATION OR RESULTS

  4. TYPES OF DATA: • QUANTITATIVE DATA – AMOUNTS, MEASUREMENTS OR NUMERICAL DATA • QUALITATIVE DATA – NON-NUMERICAL IN NATURE (CHARACTERISTICS – COLOR, SHAPE, ETC.)

  5. TYPES OF DATA COLLECTED: • POPULATION: 100% OF DATA ARE COLLECTED (CAN BE EXACT) (GREEK LETTERS USED TO ABBREVIATE QUANTITIES) • SAMPLE: A SMALLER ESTIMATE OR REPRESENTATION IS COLLECTED (ENGLISH LETTERS STAND FOR QUANTITIES SURVEYED)

  6. EXPERIMENTS ARE CONDUCTED USING MULTIPLE REPLICATIONS • REPLICATION INSURES MORE RELIABLE / ACCURATE RESULTS

  7. DATA IS COLLECTED FROM MULTIPLE EXPERIMENTS AND AN AVERAGE IS DETERMINED FROM THOSE RESULTS • THE LARGER THE SAMPLE SIZE THE BETTER REPRESENTATION OF THE TRUE VALUE.

  8. MEASURES OF CENTRAL TENDENCY INCLUDE: • MEAN AVERAGE * • MEDIAN • MODE * USUALLY THE BEST CHOICE FOR GETTING CENTRAL TENDENCY

  9. THE AVERAGE FOR A SET OF DATA / NUMBERS IS ALSO CALLED THE MEAN EXAMPLE: 10 12 8 11 + 12 53 5 =10.6 MEAN (AVG)

  10. MEDIAN VALUE IS THE MIDDLE VALUE IN A SAMPLE OF VALUES • THERE MUST BE THE SAME NUMBER ABOVE AND BELOW THE MEDIAN SAMPLE: 6, 9, 10, 11, 12, 14, 18 MEDIAN VALUE = 11 MEAN / AVERAGE = 11.43

  11. MODEIS THE VALUE THAT OCCURS MOST OFTEN IN A SAMPLE • SAMPLE: 10, 8 11, 12, 14, 8, 11, 11 MODE = 11

  12. Which Example Below is a More Accurate Mean Average ? • MODE ? • MEAN ? • MEDIAN ? WHY IS IT MORE ACCURATE?

  13. MEASURES OF VARIATION • RANGE = HIGHEST SCORE – LOWEST SCORE in the set of numbers _ 2 STANDARD = Sq. Root ofE(x – x) • DEVIATION*n - 1 * BEST CHOICE - USES ALL NUMBERS IN THE LIST

  14. RANGE OF A SET OF DATA= HIGHEST VALUE – LOWEST VALUE EXAMPLE: 6, 7, 8, 11,12,14,14,15,15, 16, 19, 20 20 – 6 = 14 (RANGE) RANGE HAS LIMITED USE

  15. 10% RULE: Some researchers consider data to be valid and representative or significant within the10% range { EXAMPLE:10%RULE: 10 0.6 12 1.4 8 2.6 11 0.4 12 1.4 53 (10.6 MEAN) 10% of 10.6 (mean) is + / - 1.06 or a range of 9.54 – 11.66

  16. THE RANGE (9.54 – 11.66) REPRESENTS A VALID RANGE FOR ACCEPTING THE DATA EXAMPLE: 10 12 NOTE: USING THE 10% RULE 8 & THE RANGE(9.54 – 11.6) 11 WHICH VALUES WOULD BE 12CONSIDERED OUT OF RANGE? 53 8 & 12

  17. STANDARD DEVIATION (SD) IS A MEASUREMENT OF THE VARIATION FROM THE MEAN SD CONSIDERS THE # THAT ARE OUT OF RANGE AND HOW FAR OUT OF RANGE THEY ARE

  18. STANDARD DEVIATION REPRESENTS - HOW CLOSELY DATA ARE CLUSTERED AROUND THE MEAN

  19. STANDARD DEVIATION TERMS: _ X = MEAN X = INDIVIDUAL SCORES IN THE SET EX = SUM OF ALL SCORES / VALUES n = TOTAL NUMBER OF SCORES OR VALUES IN THE SET

  20. Calculating a Standard Deviation • Take a sample problem with the following values: • There are eight data points total, with a mean (or average) value of 5: • To calculate the standard deviation, compute the difference of each data point from the mean, • then square the result: • Next divide the sum of these values by the number of values, then take the square root to get the standard deviation: • The standard deviation of this example is 2.

  21. FINDING STANDARD DEVIATION CAN BE CONFUSING & DIFFICULT IN SOME SITUATIONS • PROCEDURES VARY DEPENDING ON THE PURPOSE & TYPE OF DATA RECORDED • COMPUTER PROGRAMS & SCIENTIFIC CALCULATORS WILL MAKE THE TASK EASIER

  22. Use of Standard Deviation: One standard deviation away from the mean in either direction represents around 68 % of the population in this group. Two standard deviations away from the mean account for roughly 95 % of the population. And three standard deviations account for about 99 % of the population. If the curve were flatter and more spread out, the standard deviation would be larger in order to account for 68 % of the population. So standard deviation can tell you how spread out the examples in a set are from the mean. This is useful if you are comparing results for different things (drugs, equipment, etc.). Standard deviation will tell you how diverse the test scores are for each specific thing being measured.

  23. NORMAL DISTRIBUTION OR A BELL CURVE Each colored band has a width of one standard deviation. MEAN

  24. GAUSSIAN CURVE • SCORES ARE PLOTTED ON A GRAPH • ALSO KNOWN AS: NORMAL DISTRIBUTION CURVE

  25. NORMAL DISTRIBUTION OR Gaussian Curve Shows Normal Frequency: • 68.26% of the values are within 1 standard deviations from the mean. • 95.44% of the values are within 2 standard deviations from the mean. Common Choice • 99.73% of the values are within 3 standard deviations from the mean.

  26. STANDARD DEVIATION: EXAMPLE: 2 SD: 10 12 10 12 13 9 } SD FROM 11 MEAN 14 53 5 = 10.6 MEAN • MOST RESEARCHERS CONSIDER +/- 2SD DATAVALID / ACCEPTABLE DATA

  27. ACCURACYIS HOW CLOSE A RESULT IS TO THE TRUE VALUEWHERE ASPRECISION REFERS TO THE REPRODUCIBILITY OF RESULTS,OR HOW CLOSE THE RESULTS ARE TO EACH OTHER

  28. LABORATORY INSTRUMENTS MUST BE PRECISE AS WELL AS ACCURATE • CLOSE • TRUE

  29. Coefficient of Variation • Precision of a new instrument will be compared to the precision of old instrument • CV = STANDARD DEVIATION X 100% MEAN AVERAGE OR % DIFFERENCE = LOW # - HIGH # X 100% HIGH

  30. COEFFICIENT OF VARIATION -(CV) IS THE STANDARD DEVIATION RELATIVE TO THE MEAN OF THAT SAMPLE • MAYBE EXPRESSED AS A % OF THE MEAN CV = s x 100 x

  31. PURPOSE OF DETERMINING COEFFICIENT OF VARIATION IS TO COMPARE VARIATION OF TWO DIFFERENT SAMPLES OR PRECISION OF TWO DIFFERENT INSTRUMENTS OR METHODS

  32. Chi Square Analysis • A STATISTICAL MEASURING INSTRUMENT THAT DETERMINES HOW WELL A SET OF DATA SUPPORT THE HYPOTHESIS OR EXPECTED VALUES • [MAJOR USE IS IN GENETICS] • [EMPLOYS THE PUNNETT SQUARE] • PREDICTIONS ARE BASED ON PROBABILITY

  33. Chi Square Analysis • TESTS WHETHER ITEMS IN VARIOUS CATEGORIES DEVIATE OR ARE THE SAME • NULL HYPOTHESIS MEANS IT MEETS EXPECTATIONS OR LITTLE DIFFERENCE • A PROBABILITY OF 0.05 OR LESS SHOWS AN EXTREME DIFFERENCE FROM EXPECTATED OBSERVATION / HYPOTHESIS • THE SMALLER THE # THE GREATER THE LIKELYHOOD IT SUPPORTS THE HYPOTHESIS

  34. IN SUMMARY: • THERE ARE A VARIETY OF DATA ANALYSIS INSTRUMENTS • EACH INSTRUMENT IS BEST SUITED TO MEASURE CERTAIN PARAMETERS OF DATA • SCIENTISTS AND RESEACHERS USE THE INSTRUMENTS TO INTERPRET TEST RESULTS

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