20150920230913descriptive Statistics

Educational Research Method in Special Educational Research Method in Special Education 2: Education 2: Data analysis and interpretation – 1Data analysis and interpretation – 1Descriptive statisticsDescriptive statistics

KBR 3023

GRACE ANNAMMAL

Statistics...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...Preparing data for analysis...

Data must be accurately scored and systematically organized to facilitate data analysis:

tabulatingtabulating: organizing the data in a systematic manner

codingcoding: assigning numerals (e.g., ID) to data

scoringscoring: assigning a total to each participant’s instrument

descriptive statistics...descriptive statistics...…permit the researcher to describe

many pieces of data with a few indices

statistics...statistics...…indices calculated by the researcher

for a sample drawn from a population

parameters...parameters...…indices calculated by the researcher

for an entire population

Types of descriptive statistics…Types of descriptive statistics…

1. graphs2. measures of central tendency

3. measures of variability

graphs...graphs...…representations of data enabling the

researcher to see what the distribution of scores look like

1. Graphs…1. Graphs…

frequency polygon pie chart boxplot stem-and-leaf chart

measures of central tendency...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…2. Measures of central tendency…

mode median mean

mode...mode...…the score attained by more

participants than any other score

median...median...…the point in a distribution above and

below which are 50% of the scores

mean...mean...…the arithmetic average of the scores

measures of variability...measures of variability...…indices enabling the researcher to

indicate how spread out a group of scores are

3. Measures of variability…3. Measures of variability…

range quartile deviation variance standard deviation

range...range...…the difference between the highest

and lowest score in a distribution

quartile deviation...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...variance...…a summary statistic indicating the

degree of variability among participants for a given variable

standard deviation...standard deviation...…the square root of variance providing

an index of variability in the distribution of scores

Normal distributions of dataNormal distributions of data(the normal curve)...(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 Non-normal distributions of data (skewed distributions)...(skewed distributions)...

A non-bell-shaped distribution of scores where…

…mean < median < mode (a “negatively skewed distributionnegatively skewed distribution”)

…mean > median > mode (a “positively skewed distributionpositively skewed distribution”)

measures of relative position...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…4. Measures of relative position…

percentile ranks standard scores

percentile rank...percentile rank...…indicates the percentage of scores

that fall at or below a given score

standard score...standard score...…a measure of relative position

Types of standard scores...Types of standard scores...…z score…T score…stanines

z score...z score...…a statistic expressing how far a score

is from the mean in terms of standard deviation units

T score...T score...…a transformed z score that voids

negative numbers and decimals by multiplying the z score by 10 and adding 50

stanines...stanines...…a standard score that divides a

distribution into nine parts

measures of relationship...measures of relationship...…indices enabling the researcher to

indicate the degree to which two sets of scores are related

5. Measures of relationship…5. Measures of relationship…

Spearman Rho Pearson r

correlationscorrelations…determines whether and to what

degree a relationship exists between two or more quantifiable variablesvariables

…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 factorsconfounding factors

Correlation coefficient…Correlation coefficient…

-1.00 +1.00

strong negative strong positive

0.00

no relationship

Spearman Spearman RhoRho......…a measure of correlation used for

rank and ordinal data

Pearson Pearson rr......…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…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

True and false…

…if the extreme scores are at the upper, or higher, end of the distribution, it is said to be positively skewed

True

True and false…

…the median of a set of scores corresponds to the 50% percentile

True

True and false…

…a standard score is a measure of relative position that is appropriate when the data represent a nominal scale

False

True and false…

…a z score expresses how far a score is from the mean in terms of standard deviation units

True

True and false…

…the Spearman Rho is the appropriate measure of correlation when the variables are expressed as ranks instead of scores

True

True and false…

…the assumption associated with the application of Pearson r is that the relationship between the variables being correlated is linear

True

Fill in the blank…

…statistics which permit the researcher to describe many scores with a small number of indices

descriptive statistics


…the values calculated for a sample drawn form a population

statistics


…the values calculated for an entire population

parameters


…a convenient way to describe a set of data with a single number

measures of central tendency


…the index of central tendency appropriate for nominal data

mode


…the index of central tendency appropriate for ordinal data

median


…the index of central tendency appropriate for interval or ratio data

mean


…the score attained by more participants than any other score

mode


…the point in a distribution above and below which are 50% of the scores

median


…the arithmetic average of the scores

mean


…the difference between the highest and lowest score in a distribution

range


…the measure of variability identifying one half of the difference between the 75th percentile and the 25th percentile

quartile deviation


…the measure of variability used for interval and ratio data

standard deviation


…the only appropriate measure of variability for nominal data

range


…+/- 1.00 standard deviations constitutes ____ % of the sample

68%


…extreme scores at the lower end of the distribution indicates a ______ skewed distribution

positively


…indices describing where a score is in relation to all other scores

measures of relative position


…indicates the percentage of scores that fall at or below a given score

percentile ranks


…if a set of scores is transformed into a set of z scores, the new distribution has a mean of ____ and a standard deviation of ____

zero; one


…a set of standard scores that divide a distribution into nine parts

stanines


…the most appropriate measure of correlation when the sets of data to be correlated represent either interval or ratio scales

Pearson r

This module has focused on...This module has focused on...

descriptive statistics

...the statistical procedures for describing, synthesizing, analyzing, and interpreting quantitative data

The next module will focus on...The next module will focus on...

...the statistical procedures for generalizing to a population of individuals based on information obtained from a limited number of research participants

inferential statistics

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20150920230913descriptive Statistics