Evaluating data for Evaluating data for statistical treatment statistical treatment

ESSENTIALITIES ESSENTIALITIES AND COMPLEXITIES AND COMPLEXITIES IN THESIS WRITINGIN THESIS WRITING

Sequence of Sequence of PresentationPresentation

1. How important statistics is in research2. Dangers of (mis)using statistics3. Why data should be statistically treated 4. Purposes of Statistics (in Research Writing)5. The Data Analysis Process6. What to measure and how7. Levels of Measurement8. Matrix for Statistical Treatment of Data9. Common Statistical Operations10. Statistical Tests

How important How important statistics is in statistics is in

researchresearchIn theory they are very important. Without statistics it is almost impossible to come to an informed conclusion in any piece of research. The use of statistics is wide ranging in the field of research and without the use of statistics it is virtually impossible to interpret a true meaning of what the research shows. Not to exaggerate, statistics is the BACKBONE OF A RESEARCH.

Dangers of (mis)using Dangers of (mis)using statisticsstatistics

1. Statistics, no matter how carefully collected, can always be flawed e.g. without a sample of thousands of people (ensuring they are representative of the whole population), you cannot be certain that the results can be wholly generalized.

2. Statistical information can be easily manipulated to show very different results.

Why data should be Why data should be statistically treated statistically treated

1. Data come in different volume and form.

2. Data are subject to different interpretations.

3. “Words (data) differently arranged have different meanings; meanings differently arranged have different impacts.”11 att. to Charles Babbage, Father of

Modern Computer

Purposes of Statistics Purposes of Statistics (in Research Writing)(in Research Writing)Essentially, statistics 1.helps organize the data. (Tables and graphs are the essential non-letter cues for interpretation) 2.makes inferring guided, which yields to more meaningful interpretations. It makes use of descriptive statistics for collection of data and inferential statistics for drawing inferences from this set of data.3.provides platform for research

What to Measure and What to Measure and HowHowIdentify the observable characteristics of the

concepts being investigated record and order observations of those behavioral characteristics.

1.Quantitative measurements employ meaningful numerical indicators to ascertain the relative amount of something.2.Qualitative measurement employ symbols to indicate the meaning people have of something.

Levels of MeasurementLevels of Measurement1.1. ((NN))ominal variables are differentiated on the basis of ominal variables are differentiated on the basis of

type or category.type or category.

2.2. ((OO)rdinal measurement scales not only classify a )rdinal measurement scales not only classify a variable into nominal categories but also rank order variable into nominal categories but also rank order those categories along some dimension. (The number those categories along some dimension. (The number does not express the size of the difference.)does not express the size of the difference.)

3.3. ((II)nterval measurement scales not only categorize a )nterval measurement scales not only categorize a variable and rank order it along some dimension but variable and rank order it along some dimension but also establish equal distances between each of the also establish equal distances between each of the adjacent points along the measurement scale.adjacent points along the measurement scale.

4.4. ((RR)atio measurement scales not only categorize and )atio measurement scales not only categorize and rank order a variable along a scale with equal intervals rank order a variable along a scale with equal intervals between adjacent points but also establish an absolute, between adjacent points but also establish an absolute, or true, zero point where the variable being measured or true, zero point where the variable being measured ceases to exist.ceases to exist.

Matrix for Matrix for Statistical Treatment of DataStatistical Treatment of Data

Matrix for Statistical Matrix for Statistical Treatment of Regularly Treatment of Regularly

Gathered DataGathered DataVariablesVariables TreatmentsTreatmentsGenderGender f, %f, %

Age, Height, Age, Height, Weight, Weight,

Mo. IncomeMo. Income

f, %, mean, sdf, %, mean, sd

Educl. AttainmentEducl. Attainment f, %f, %PerceptionsPerceptions WM, Ave. WM, Grand WMWM, Ave. WM, Grand WM

ChoiceChoice f, %, rank f, %, rank CorrelationsCorrelations Pearson, SpearmanPearson, Spearman

Test of SignificanceTest of Significance t-test (z-test)t-test (z-test)Chi-squareChi-square

RankRank Kendall’s Tau and Coefficient of Kendall’s Tau and Coefficient of ConcordanceConcordance

Test Test standardizationstandardization

Item AnalysisItem Analysis

Common Statistical Common Statistical OperationsOperations

1.1. Measures of Central Tendency indicate what is Measures of Central Tendency indicate what is typical of the average subject. E.g. Mean, typical of the average subject. E.g. Mean, Median, ModeMedian, Mode

2.2. Measures of Variance indicate the distribution of Measures of Variance indicate the distribution of the data around the center. E.g. standard the data around the center. E.g. standard deviation and variancedeviation and variance

3.3. Correlation and regression analysis deals with Correlation and regression analysis deals with the degree (extent) to which two variables move the degree (extent) to which two variables move in sync with one another. E.g. pearson product-in sync with one another. E.g. pearson product-moment of correlation and spearman rank.moment of correlation and spearman rank.

4.4. Test of significant difference/Test of significant difference/ relationships.relationships.

Statistical Tests – Statistical Tests – Two-sided vs. one-sided testTwo-sided vs. one-sided test

These tests for comparison, for instance between methods These tests for comparison, for instance between methods AA and and B,B, are based on the assumption that there is no are based on the assumption that there is no significant difference (the "null hypothesis").significant difference (the "null hypothesis").

In other words, when the difference is so small that a In other words, when the difference is so small that a tabulated tabulated critical valuecritical value of of FF or or tt is not exceeded, we can be is not exceeded, we can be confident (usually at 95% level) that confident (usually at 95% level) that AA and and BB are not different. are not different.

Two fundamentally different questions can be asked Two fundamentally different questions can be asked concerning both the comparison of the standard deviations concerning both the comparison of the standard deviations ss11 and and ss22 with the with the FF-test, and of the means¯x-test, and of the means¯x11, and ¯x, and ¯x22, with the , with the tt-test: -test:

1. are 1. are AA and and BB different? different? (two-sided(two-sided test) test)2. is 2. is AA higher (or lower) than higher (or lower) than B? (one-sidedB? (one-sided test). test).

Statistical Tests – Statistical Tests – F-test (Fisher’s Test)F-test (Fisher’s Test)

The The FF-test (or -test (or Fisher's testFisher's test) is a comparison of the ) is a comparison of the spread of two sets of data to test if the sets belong to spread of two sets of data to test if the sets belong to the same population, in other words if the precisions the same population, in other words if the precisions are similar or dissimilar. are similar or dissimilar.

The test makes use of the ratio of the two variances: The test makes use of the ratio of the two variances:

If If FFcalcal ≤ ≤ FFtabtab one can conclude with 95% confidence one can conclude with 95% confidence that there is no significant difference in precision (the that there is no significant difference in precision (the "null hypothesis" that "null hypothesis" that s1,s1, = = s,s, is accepted). Thus, is accepted). Thus, there is still a 5% chance that we draw the wrong there is still a 5% chance that we draw the wrong conclusion. In certain cases more confidence may be conclusion. In certain cases more confidence may be needed, then a 99% confidence table can be used.needed, then a 99% confidence table can be used.

References References

Retrieved from 4 Aug to 10 Aug 2012

1.http://www.blurtit.com/q799907.html2.http://wiki.answers.com/Q/What_is_the_importance_of_statistics_in_research3.http://www.bcps.org/offices/lis/researchcourse/data_process.html4.http://ion.chem.usu.edu/~sbialkow/Classes/3600/Overheads/Stat%20Narrative/statistical.html5. http://www.fao.org/docrep/W7295E/w7295e0a.htm#TopOfPage