WHAT ARE INFERENTIAL STATISTICS?
Main Points
• Inferential statistics refer to certain procedures that allow researchers to make inferences
about a population based on data obtained from a sample.
• The term probability, as used in research, refers to the predicted relative frequency
with which a given event will occur.
SAMPLING ERROR
• The term sampling error refers to the variations in sample statistics that occur as a
result of repeated sampling from the same population.
THE DISTRIBUTION OF SAMPLE MEANS
• A sampling distribution of means is a frequency distribution resulting from plotting
the means of a very large number of samples from the same population.
• The standard error of the mean is the standard deviation of a sampling distribution of
means. The standard error of the difference between means is the standard deviation
of a sampling distribution of differences between sample means.
CONFIDENCE INTERVALS
• A confidence interval is a region extending both above and below a sample statistic
(such as a sample mean) within which a population parameter (such as the population
mean) may be said to fall with a specified probability of being wrong.
HYPOTHESIS TESTING
• Statistical hypothesis testing is a way of determining the probability that an obtained
sample statistic will occur, given a hypothetical population parameter.
• A research hypothesis specifices the nature of the relationship the researcher thinks
exists in the population.
• The null hypothesis typically specifies that there is no relationship in the population.
SIGNIFICANCE LEVELS
• The term significance level (or level of significance ), as used in research, refers to the
probability of a sample statistic occurring as a result of sampling error.
• The significance levels most commonly used in educational research are the .05 and
.01 levels.
• Statistical significance and practical significance are not necessarily the same. Even if a
result is statistically significant, it may not be practically (i.e., educationally) significant.
TESTS OF STATISTICAL SIGNIFICANCE
• A one-tailed test of significance involves the use of probabilities based on one-half of
a sampling distribution because the research hypothesis is a directional hypothesis.
• A two-tailed test, on the other hand, involves the use of probabilities based on both sides
of a sampling distribution because the research hypothesis is a nondirectional hypothesis.
PARAMETRIC TESTS FOR QUANTITATIVE DATA
• A parametric statistical test requires various kinds of assumptions about the nature
of the population from which the samples involved in the research study were taken.
• Some of the commonly used parametric techniques for analyzing quantitative data
include the t -test for means, ANOVA, ANCOVA, MANOVA, MANCOVA, and the
t -test for r .
PARAMETRIC TESTS FOR CATEGORICAL DATA
• The most common parametric technique for analyzing categorical data is the t -test
for differences in proportions.
NONPARAMETRIC TESTS FOR QUANTITATIVE DATA
• A nonparametric statistical technique makes few, if any, assumptions about the nature
of the population from which the samples in the study were taken.
• Some of the commonly used nonparametric techniques for analyzing quantitative
data are the Mann-Whitney U test, the Kruskal-Wallis one-way analysis of variance,
the sign test, and the Friedman two-way analysis of variance.
NONPARAMETRIC TESTS FOR CATEGORICAL DATA
• The chi-square test is the nonparametric technique most commonly used to analyze
categorical data.
• The contingency coefficient is a descriptive statistic indicating the degree of relationship
between two categoriPOWER OF A STATISTICAL TEST
• The power of a statistical test for a particular set of data is the likelihood of identifying
a difference, when in fact it exists, between population parameters.
• Parametric tests are generally, but not always, more powerful than nonparametric testscal variables
Main Points
• Inferential statistics refer to certain procedures that allow researchers to make inferences
about a population based on data obtained from a sample.
• The term probability, as used in research, refers to the predicted relative frequency
with which a given event will occur.
SAMPLING ERROR
• The term sampling error refers to the variations in sample statistics that occur as a
result of repeated sampling from the same population.
THE DISTRIBUTION OF SAMPLE MEANS
• A sampling distribution of means is a frequency distribution resulting from plotting
the means of a very large number of samples from the same population.
• The standard error of the mean is the standard deviation of a sampling distribution of
means. The standard error of the difference between means is the standard deviation
of a sampling distribution of differences between sample means.
CONFIDENCE INTERVALS
• A confidence interval is a region extending both above and below a sample statistic
(such as a sample mean) within which a population parameter (such as the population
mean) may be said to fall with a specified probability of being wrong.
HYPOTHESIS TESTING
• Statistical hypothesis testing is a way of determining the probability that an obtained
sample statistic will occur, given a hypothetical population parameter.
• A research hypothesis specifices the nature of the relationship the researcher thinks
exists in the population.
• The null hypothesis typically specifies that there is no relationship in the population.
SIGNIFICANCE LEVELS
• The term significance level (or level of significance ), as used in research, refers to the
probability of a sample statistic occurring as a result of sampling error.
• The significance levels most commonly used in educational research are the .05 and
.01 levels.
• Statistical significance and practical significance are not necessarily the same. Even if a
result is statistically significant, it may not be practically (i.e., educationally) significant.
TESTS OF STATISTICAL SIGNIFICANCE
• A one-tailed test of significance involves the use of probabilities based on one-half of
a sampling distribution because the research hypothesis is a directional hypothesis.
• A two-tailed test, on the other hand, involves the use of probabilities based on both sides
of a sampling distribution because the research hypothesis is a nondirectional hypothesis.
PARAMETRIC TESTS FOR QUANTITATIVE DATA
• A parametric statistical test requires various kinds of assumptions about the nature
of the population from which the samples involved in the research study were taken.
• Some of the commonly used parametric techniques for analyzing quantitative data
include the t -test for means, ANOVA, ANCOVA, MANOVA, MANCOVA, and the
t -test for r .
PARAMETRIC TESTS FOR CATEGORICAL DATA
• The most common parametric technique for analyzing categorical data is the t -test
for differences in proportions.
NONPARAMETRIC TESTS FOR QUANTITATIVE DATA
• A nonparametric statistical technique makes few, if any, assumptions about the nature
of the population from which the samples in the study were taken.
• Some of the commonly used nonparametric techniques for analyzing quantitative
data are the Mann-Whitney U test, the Kruskal-Wallis one-way analysis of variance,
the sign test, and the Friedman two-way analysis of variance.
NONPARAMETRIC TESTS FOR CATEGORICAL DATA
• The chi-square test is the nonparametric technique most commonly used to analyze
categorical data.
• The contingency coefficient is a descriptive statistic indicating the degree of relationship
between two categoriPOWER OF A STATISTICAL TEST
• The power of a statistical test for a particular set of data is the likelihood of identifying
a difference, when in fact it exists, between population parameters.
• Parametric tests are generally, but not always, more powerful than nonparametric testscal variables
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