STATISTICS VERSUS PARAMETERS
• A parameter is a characteristic of a population. It is a numerical or graphic way to
summarize data obtained from the population.
• A statistic, on the other hand, is a characteristic of a sample. It is a numerical or
graphic way to summarize data obtained from a sample.
TYPES OF NUMERICAL DATA
• There are two fundamental types of numerical data a researcher can collect. Quantitative
data are obtained by determining placement on a scale that indicates amount or
degree. Categorical data are obtained by determining the frequency of occurrences in
each of several categories.
TYPES OF SCORES
• A raw score is the initial score obtained when using an instrument; a derived score
is a raw score that has been translated into a more useful score on some type of standardized
basis to aid in interpretation.
• Age/grade equivalents are derived scores that indicate the typical age or grade associated
with an individual raw score.
• A percentile rank is the percentage of a specific group scoring at or below a given
raw score.
• A standard score is a mathematically derived score having comparable meaning on
different instruments.
TECHNIQUES FOR SUMMARIZING QUANTITATIVE DATA
• A frequency distribution is a two-column listing, from high to low, of all the scores
along with their frequencies. In a grouped frequency distribution, the scores have
been grouped into equal intervals.
• A frequency polygon is a graphic display of a frequency distribution. It is a graphic
way to summarize quantitative data for one variable.
• A graphic distribution of scores in which only a few individuals receive high scores is
called a positively skewed polygon; one in which only a few individuals receive low
scores is called a negatively skewed polygon.
• A histogram is a bar graph used to display quantitative data at the interval or ratio
level of measurement.
• A stem-leaf plot is similar to a histogram, except it lists specific values instead of
bars.
• The normal distribution is a theoretical distribution that is symmetrical and in which
a large proportion of the scores are concentrated in the middle.
• A distribution curve is a smoothed-out frequency polygon.
• The distribution curve of a normal distribution is called a normal curve. It is bell
shaped, and its mean, median, and mode are identical.
• There are several measures of central tendency (averages) that are used to summarize
quantitative data. The two most common are the mean and the median.
• The mean of a distribution is determined by adding up all of the scores and dividing
this sum by the total number of scores.
The median of a distribution marks the point above and below which half of the
scores in the distribution lie.
• The mode is the most frequent score in a distribution.
• The term variability, as used in research, refers to the extent to which the scores on a
quantitative variable in a distribution are spread out.
• The most common measure of variability used in educational research is the standard
deviation.
• The range, another measure of variability, represents the difference between the
highest and lowest scores in a distribution.
• A five-number summary of a distribution reports the lowest score, the first quartile,
the median, the third quartile, and the highest score.
• Five-number summaries of distributions are often portrayed graphically by the use
of boxplots.
STANDARD SCORES AND THE NORMAL CURVE
• Standard scores use a common scale to indicate how an individual compares to other
individuals in a group. The simplest form of standard score is a z score. A z score
expresses how far a raw score is from the mean in standard deviation units.
• The major advantage of standard scores is that they provide a better basis for comparing
performance on different measures than do raw scores.
• The term probability, as used in research, refers to a prediction of how often a particular
event will occur. Probabilities are usually expressed in decimal form
.
CORRELATION
• A correlation coefficient is a numerical index expressing the degree of relationship
between two quantitative variables. The one most commonly used in educational
research is the Pearson r .
• A scatterplot is a graphic way to describe a relationship between two quantitative
variables.
TECHNIQUES FOR SUMMARIZING CATEGORICAL DATA
• Researchers use various graphic techniques to summarize categorical data, including
frequency tables, bar graphs, and pie charts.
• A crossbreak table is a graphic way to report a relationship between two or more
categorical variables
• A parameter is a characteristic of a population. It is a numerical or graphic way to
summarize data obtained from the population.
• A statistic, on the other hand, is a characteristic of a sample. It is a numerical or
graphic way to summarize data obtained from a sample.
TYPES OF NUMERICAL DATA
• There are two fundamental types of numerical data a researcher can collect. Quantitative
data are obtained by determining placement on a scale that indicates amount or
degree. Categorical data are obtained by determining the frequency of occurrences in
each of several categories.
TYPES OF SCORES
• A raw score is the initial score obtained when using an instrument; a derived score
is a raw score that has been translated into a more useful score on some type of standardized
basis to aid in interpretation.
• Age/grade equivalents are derived scores that indicate the typical age or grade associated
with an individual raw score.
• A percentile rank is the percentage of a specific group scoring at or below a given
raw score.
• A standard score is a mathematically derived score having comparable meaning on
different instruments.
TECHNIQUES FOR SUMMARIZING QUANTITATIVE DATA
• A frequency distribution is a two-column listing, from high to low, of all the scores
along with their frequencies. In a grouped frequency distribution, the scores have
been grouped into equal intervals.
• A frequency polygon is a graphic display of a frequency distribution. It is a graphic
way to summarize quantitative data for one variable.
• A graphic distribution of scores in which only a few individuals receive high scores is
called a positively skewed polygon; one in which only a few individuals receive low
scores is called a negatively skewed polygon.
• A histogram is a bar graph used to display quantitative data at the interval or ratio
level of measurement.
• A stem-leaf plot is similar to a histogram, except it lists specific values instead of
bars.
• The normal distribution is a theoretical distribution that is symmetrical and in which
a large proportion of the scores are concentrated in the middle.
• A distribution curve is a smoothed-out frequency polygon.
• The distribution curve of a normal distribution is called a normal curve. It is bell
shaped, and its mean, median, and mode are identical.
• There are several measures of central tendency (averages) that are used to summarize
quantitative data. The two most common are the mean and the median.
• The mean of a distribution is determined by adding up all of the scores and dividing
this sum by the total number of scores.
The median of a distribution marks the point above and below which half of the
scores in the distribution lie.
• The mode is the most frequent score in a distribution.
• The term variability, as used in research, refers to the extent to which the scores on a
quantitative variable in a distribution are spread out.
• The most common measure of variability used in educational research is the standard
deviation.
• The range, another measure of variability, represents the difference between the
highest and lowest scores in a distribution.
• A five-number summary of a distribution reports the lowest score, the first quartile,
the median, the third quartile, and the highest score.
• Five-number summaries of distributions are often portrayed graphically by the use
of boxplots.
STANDARD SCORES AND THE NORMAL CURVE
• Standard scores use a common scale to indicate how an individual compares to other
individuals in a group. The simplest form of standard score is a z score. A z score
expresses how far a raw score is from the mean in standard deviation units.
• The major advantage of standard scores is that they provide a better basis for comparing
performance on different measures than do raw scores.
• The term probability, as used in research, refers to a prediction of how often a particular
event will occur. Probabilities are usually expressed in decimal form
.
CORRELATION
• A correlation coefficient is a numerical index expressing the degree of relationship
between two quantitative variables. The one most commonly used in educational
research is the Pearson r .
• A scatterplot is a graphic way to describe a relationship between two quantitative
variables.
TECHNIQUES FOR SUMMARIZING CATEGORICAL DATA
• Researchers use various graphic techniques to summarize categorical data, including
frequency tables, bar graphs, and pie charts.
• A crossbreak table is a graphic way to report a relationship between two or more
categorical variables
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