educational research: data analysis and interpretation 1 descriptive statistics edu 8603...

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

EDU 8603

Educational Research

Richard M. Jacobs, OSA, Ph.D.

Medicine needs data to advanceMedicine needs data to advance

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 tendency3. 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 confounding factorsfactors

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

Fill in the blank……the values calculated for a sample

drawn form a population

statistics

Fill in the blank……the values calculated for an entire

population

parameters

Fill in the blank……a convenient way to describe a set of

data with a single number

measures of central tendency

Fill in the blank……the index of central tendency

appropriate for nominal data

mode

Fill in the blank……the index of central tendency

appropriate for ordinal data

median

Fill in the blank……the index of central tendency

appropriate for interval or ratio data

mean

Fill in the blank……the score attained by more

participants than any other score

mode

Fill in the blank……the point in a distribution above and

below which are 50% of the scores

median

Fill in the blank……the arithmetic average of the scores

mean

Fill in the blank……the difference between the highest

and lowest score in a distributionrange

Fill in the blank……the measure of variability identifying

one half of the difference between the 75th percentile and the 25th percentile

quartile deviation

Fill in the blank……the measure of variability used for

interval and ratio datastandard deviation

Fill in the blank……the only appropriate measure of

variability for nominal datarange

Fill in the blank……+/- 1.00 standard deviations

constitutes ____ % of the sample68%

Fill in the blank……extreme scores at the lower end of

the distribution indicates a ______ skewed distribution

positively

Fill in the blank……indices describing where a score is

in relation to all other scores

measures of relative position

Fill in the blank……indicates the percentage of scores

that fall at or below a given score

percentile ranks

Fill in the blank……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

Fill in the blank……a set of standard scores that divide a

distribution into nine parts

stanines

Fill in the blank……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