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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

participants 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 75ile) and the lower quartile

(the 25ile) 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 lt median lt mode (a negatively skewed

distribution)

mean gt median gt mode (a positively skewed

distribution)

- measures of relative position...

indices enabling the researcher to describe a

participants 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

1.00

0.00

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

- 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 distribution

range

- 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 data

standard deviation

- Fill in the blank

the only appropriate measure of variability for

nominal data

range

- Fill in the blank

/- 1.00 standard deviations constitutes ____

of the sample

68

- 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...

descriptive statistics

...the statistical procedures for describing,

synthesizing, analyzing, and interpreting

quantitative data

The next module will focus on...

inferential statistics

...the statistical procedures for generalizing to

a population of individuals based on information

obtained from a limited number of research

participants

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