If you can answer these 2 questions, data analysis will be easy
1) is the variable to be analyzed by itself or in relationship with other variables?
2) What level of measurement was used?
•Analysis involving individual
variables is univariate analysis
•Analysis involving multiple
variables is multivariate analysis
•Is the variable to be analyzed by
itself or in relationship with other variables?
•Nominal and ordinal measures are
referred to as categorical measures
•Interval and ratio measures are
referred to as continuous measures
•What level of measurement was
used?
A count of the number of cases that fall into each of the response categories
Uses:
•Communicate the results of a
study via univariate categorical analysis
•Determine the degree of item
nonresponse
•Identify blunders
•Identify outliers
•Determine the empirical
distribution of a variable
•Frequency Analysis
________ are a projection of the range
within which a population parameter will lie at a given level of confidence
based on a statistic obtained from a probabilistic sample
Interval estimates
•Interval estimates are a projection of the range
within which a population parameter will lie at a given level of confidence
based on a statistic obtained from a probabilistic sample
•This probability is normally
referred to as the confidence level
•Drawing a probability sample
allows for the appropriate calculation of confidence intervals
Confidence Intervals for
Proportions
p - sampling error ≤ π ≤ p +
sampling error
•Confidence intervals are p -
sampling error ≤ π ≤ p + sampling error
•p = the relevant proportion
obtained from the sample
•sampling error considers the
desired degree of confidence (z) and the number of valid cases overall for the
proportion (n) in addition to p
•π = population proportion
•Statistics that describe the
distribution of responses on a variable
•The most commonly used are the mean and standard deviation
•The
mean (pronounced x bar) is a measure of central tendency
•The
standard deviation (s) is measure of dispersion
•Descriptive Statistics
•A projection of the range within
which a population mean will lie at a given level of confidence
Confidence Intervals for Means
•A statement about the value of a population parameter developed for the purpose of
testing
Hypothesis
•The hypothesis that a proposed
result is not true for the population
•Researchers typically attempt to
reject the null hypothesis in favor of some alternative hypothesis
Null Hypothesis (H0)
•The hypothesis that a proposed
result is true for the population
•Often, we are interested in the
alternative hypothesis
Alternative Hypothesis (HA):
Steps in Hypothesis Testing (6 steps)
Step 1 - Specify Null and Alternative Hypotheses
Step 2 - Choose the Appropriate Test Statistic
Step 3 - Specify the Significance Level
Step 4 Collect the Data and Compute the Appropriate Test Statistic
Step 5 Determine the Probability under the Null
Step 6 Compare the Obtained Probability with the Specified Significance Level to Assess the
Null
•A decision
rule is needed to decide whether to
reject or fail to reject the null hypothesis.
They are stated in terms of their _________________.
•The acceptable level of Type I
error selected by the researcher, usually set at 0.05
•Type I error is the probability
of rejecting the null hypothesis when it is actually true for the population
Significance Level (α)
•The probability of obtaining a
given result if in fact the null hypothesis were true in the population
•A result is regarded as
statistically significant if this value is less than the chosen significance
level of the test
p-value
•A statistical test to determine
whether some observed pattern of frequencies corresponds to an expected pattern
•Chi-Square Goodness-of-Fit Test
for Frequencies
for Comparing Sample Mean Against
a Standard
t-test
for Comparing Sample Proportion
Against a Standard