This week you will locate three quantitative studies addressing a topic in your area of specialization. At minimum, two different statistical tests should be represented.

For example, you might search the literature for studies in transformational leadership and you may find two that used regression analysis and a third that used a t-test. For each study:

State the null and alternative hypotheses (Hint. The authors will note the alternative hypotheses, but you will have to infer the null as those aren’t typically stated in published research)

Identify the statistical test used to determine statistical significance (e.g., t-test, analysis of variance, multiple regression, etc.).

Identify the test statistic, note it, and explain what it means (e.g., t=3.47).

Identify the significance level used in each study

Identify whether or not the authors found support for their hypotheses. Consider sample size and Type I and Type II error.

Explain the implications of each finding.

Identify whether or not the authors found support for their hypotheses. Consider sample size and Type I and Type II error.

Explain the implications of each finding.

Length: 6 pages

References: Include a minimum of 3 scholarly resources.

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Instructions

Hypothesis Testing: An Introduction to Various Parametric Applications

A variety of statistical tools can be used to investigate a hypothesis. These tools allow us to compare an average score against a standard (e.g., the z-test).

Other tools allow us to compare the means of two groups. One is the independent samples t-test that is used to explore mutually exclusive groups (e.g., treatment and control, men and women, etc.) across one dependent variable. You will have the opportunity to conduct a t-test for the signature assignment.

A paired samples t-test (also called a t-test for related samples) compares two related samples, or the same samples (subjects) observed at two different time points. A example of the latter is a comparison of pre-test to post-test scores following an intervention.

Another set of statistics used for hypothesis testing includes analysis of variance (also known as ANOVA). We use ANOVA to test the statistical significance of differences among means of three or more groups across one dependent variable. For example, we may wish to compare work engagement across three different age groups. For example, we may hypothesize that people under 30 years of age (group 1) are less engaged in their jobs than those from 31 to 50 years of age (group 2), while those over 50 years of age (group 3) are the most engaged. ANOVA can be used to examine mean job engagement scores across these age groups. You will have the opportunity to conduct an ANOVA test for the signature assignment.

A repeated measures ANOVA is used to examine the evolution of a variable over several time periods (i.e., longitudinal analysis) or more than two groups and how they differ on a variable of interest.

Other tests that may be used to examine differences across three or more groups are:

Analysis of Covariance (ANCOVA). This test extends the ANOVA to provide a method to control for variables extraneous to the test that may influence variance in the dependent variable. These variables are referred to as covariates.

Multivariate Analysis of Variance (MANOVA). This test extends the ANOVA to provide a method to include multiple dependent variables that are related.

Multivariate Analysis of Covariance (MANCOVA). This test extends the ANCOVA to examine multiple dependent variables while controlling for one or more covariates.

Each of these are omnibus tests. That is, they provide an overall test to determine statistically significant difference among three or more groups however, they do not specify what kind of differences exist among which groups. Post hoc comparisons are performed to test the statistically significance of differences between group means computed post (after) having performed the omnibus test. In SPSS, the researcher needs to request post-hoc testing. Multiple post hoc tests are offered based on the assumption of (substantially) equal variances (homogeneity of variance).

Last, we will discuss how we can use a tool called linear regression to make predictions about how one variable may influence another. In Week 6, we will focus solely on the correlation, which is an element of the regression analysis.

Be sure to review this week’s resources carefully. You are expected to apply the information from these resources when you prepare your assignments.

Reference:

Weiers, R. M. (2011). Introduction to business statistics (7th ed.). Boston, MA: Cengage Learning. https://platform.virdocs.com/r/s/0/doc/530457/sp/179092989/mi/571019625

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