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Educational Research: Data analysis and interpretation – 1 Descriptive statistics

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## Educational Research: Data analysis and interpretation – 1 Descriptive statistics

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**Educational Research: Data analysis and**interpretation – 1Descriptive statistics EDU 8603 Educational Research Richard M. Jacobs, OSA, Ph.D.**Statistics...**• A set of mathematical procedures for describing, synthesizing, analyzing, and interpreting quantitative data …the selection of an appropriate statistical technique is determined by the research design, hypothesis, and the data collected**Preparing data for analysis...**Data must be accurately scored and systematically organized to facilitate data analysis: scoring: assigning a total to each participant’s instrument tabulating: organizing the data in a systematic manner coding: assigning numerals (e.g., ID) to data**descriptive statistics...**…permit the researcher to describe many pieces of data with a few indices**statistics...**…indices calculated by the researcher for a sample drawn from a population**parameters...**…indices calculated by the researcher for an entire population**Types of descriptive statistics…**1. graphs 2. measures of central tendency 3. measures of variability**graphs...**…representations of data enabling the researcher to see what the distribution of scores look like**1. Graphs…**• frequency polygon • pie chart • boxplot • stem-and-leaf chart**measures of central tendency...**…indices enabling the researcher to determine the typical or average score of a group of scores**2. Measures of central tendency…**• mode • median • mean**mode...**…the score attained by more participants than any other score**median...**…the point in a distribution above and below which are 50% of the scores**mean...**…the arithmetic average of the scores**measures of variability...**…indices enabling the researcher to indicate how spread out a group of scores are**3. Measures of variability…**• range • quartile deviation • variance • standard deviation**range...**…the difference between the highest and lowest score in a distribution**quartile deviation...**…one half of the difference between the upper quartile (the 75%’ile) and the lower quartile (the 25%’ile) in a distribution**variance...**…a summary statistic indicating the degree of variability among participants for a given variable**standard deviation...**…the square root of variance providing an index of variability in the distribution of scores**Normal distributions of data(the normal curve)...**A bell-shaped distribution of scores having four identifiable properties… …50% of the scores fall above the mean and 50% of the scores fall below the mean …the mean, median, and mode are the same value**…most scores are near the mean and, the farther from the**mean a score is, the fewer the number of participants who attained that score …the same number, or percentage, of scores is between the mean and plus one standard deviation as is between the mean and minus one standard deviation**Non-normal distributions of data (skewed distributions)...**A non-bell-shaped distribution of scores where… …mean < median < mode (a “negatively skewed distribution”) …mean > median > mode (a “positively skewed distribution”)**measures of relative position...**…indices enabling the researcher to describe a participant’s performance compared to the performance of all other participants**4. Measures of relative position…**• percentile ranks • standard scores**percentile rank...**…indicates the percentage of scores that fall at or below a given score**standard score...**…a measure of relative position**Types of standard scores...**…z score …T score …stanines**z score...**…a statistic expressing how far a score is from the mean in terms of standard deviation units**T score...**…a transformed z score that voids negative numbers and decimals by multiplying the z score by 10 and adding 50**stanines...**…a standard score that divides a distribution into nine parts**measures of relationship...**…indices enabling the researcher to indicate the degree to which two sets of scores are related**5. Measures of relationship…**• Spearman Rho • Pearson r**correlations**…determines whether and to what degree a relationship exists between two or more quantifiable variables …the degree of the relationship is expressed as a coefficient of correlation**…the presence of a correlation does not indicate a**cause-effect relationship primarily because of the possibility of multiple confounding factors**Correlation coefficient…**-1.00 0.00 +1.00 strong positive strong negative no relationship**Spearman Rho...**…a measure of correlation used for rank and ordinal data**Pearson r...**…a measure of correlation used for data of interval or ratio scales …assumes that the relationship between the variables being correlated is linear**Mini-Quiz…**• True and false… …the analysis of the data is as important as any other component of the research process True**True and false…**…descriptive statistics are normally computed separately for each group in a research study True**True and false…**…every instrument administered must always be scored accurately and consistently, using the same procedures and criteria True**True and false…**…tentative scoring procedures must always be tried out beforehand by administering the instrument to the study participants False**True and false…**…a computer should not be used to perform an analysis that a researcher has never completed by hand or, at least, studied extensively True**True and false…**…the first step in data analysis is to describe, or summarize, the data using descriptive statistics True**True and false…**…the number resulting from the computation of a measure of central tendency represents the typical score attained by a group of participants True**True and false…**…the mean is the most precise, stable index of typical performance that is especially useful in situations in which there are extreme scores False**True and false…**…unless a correlation coefficient is used to compute the reliability of an instrument in a causal-comparative or experimental study, a correlation coefficient is only computed in a correlation study True**True and false…**…plus and/or minus two standard deviations includes more the 99% of the scores False**True and false…**…standard scores are rarely used in research studies True**True and false…**…to test a hypothesis adequately, more than descriptive statistics are normally needed True