**Academic Success Center (ASC). (2020).***Statistics resources*. National University.**This LibGuide includes all of the statistics resources curated by NU's Academic Success Center. Use the headings on the left side of this ASC page to navigate to your particular area of need.****Analysis of variance.****Boone, E. L. (2018). Analysis of variance. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 87-89). SAGE.**

When comparing differences between three groups or more, one of the most common analyses is the analysis of variance (ANOVA). This resource provides a thorough explanation of this parametric technique.**Effect size.****Fritz, C. O., & Morris, P. E. (2018). Effect size. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 577-578). SAGE.**

This section describes the different measures of effect size used in statistics. These effects are important in terms of the size and the possibility of being observed in further studies where the sample is obtained from the same population.**Eta squared****Fritz, C. O., & Morris, P. E. (2018). Eta squared. In B. B. Frey (Ed.),***The SAGE encyclopedia of educational research, measurement, and evaluation*(pp. 607). SAGE.

Eta squared is a measure of effect size estimate. It is very often used in the analysis of variance (ANOVA).**Interaction****Fritz, C. O., & Morris, P. E. (2018). Interaction. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 849-853). SAGE.**

This section explains how to interpret the effect of two or more independent variables in a dependent variable. Interaction is occurring when the effect of one variable changes depending on the value of another variable.**Type I error****Hannon, B. (2018). Type I error. In B. B. Frey (Ed.),***The SAGE encyclopedia of educational research, measurement, and evaluation*(pp. 1741-1743). SAGE.

Type I error in hypothesis testing occurs when the null hypothesis is equivocally rejected. In other words, assuming that significant differences exist, when in fact they don’t exist.*t*- tests.**Korosteleva, O., & Song, B. (2018).***t*- tests. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 1652-1654). SAGE.

The*t*- test is used with the*t*distribution to examine differences between two groups when the variances are not known. This section describes the three different*t*- tests and when each of them are used.**Type II error****Liu, X. S. (2018). Type II error. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 1743-1745). SAGE. v**

Type II error in hypothesis testing occurs when the null hypothesis is equivocally not rejected—in other words, assuming that significant differences do not exist, when they do in fact exist.*F*distribution.**Raunig, D. (2018).***F*distribution. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 659-662). SAGE. 10.4135/9781506326139

The*F*distribution is very important because it is related to the ANOVA. The*F*distribution is the most powerful analysis to compare two variances.**Inferential Analysis (ANOVAS)****Kulas, J., Roji, R. & Smith, A. Inferential Analysis (ANOVAS). In***IBM SPSS Essentials: Managing and analyzing social sciences data.*John Wiley & Sons.**Inferential statistics.****Seaman, M. (2018). Inferential statistics. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 819-820). SAGE. <.br> This source discusses the importance of inferential statistics and how they are applied to the analysis of observed data from a sample. Furthermore, how the results of the observed data can be applied to make inferences to the general population.****Post hoc analysis.****Tipton, R., & Morgan, G. (2018). Post hoc analysis. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 1271-1273). SAGE.**

These analyses are conducted after the rejection of the null hypothesis. They are used to examine mean differences. This section provides an overview of these tests used in the ANOVA.**Results section****Zheng, C. (2018). Results section. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 1432). SAGE.**

This resource describes the research paper section that includes the results of the statistical analysis. The results section is very important in the research paper because provides the answer to the research questions.

**Supplemental Resources**

**Hypothesis testing.**Coleman, J. S. (2018). Hypothesis testing. In B. B. Frey (Ed.),*The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 803-804). SAGE.*

**This resource was introduced in a previous week. Hypotheses are formed in inferential statistics and used to make decisions about the population using a sample. This source provides discussion regarding the decisions that are made based on hypothesis testing.****Significance**Harlow, L. (2018). Significance. In B. B. Frey (Ed.),*The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 1514-1516). SAGE.*

**The author of these pages presents the concept of significance in statistics. Significance indicates the probability of an event (e.g., the difference between two groups) happening by chance—or that true differences exist.****Alpha level.**Kim, H. W. (2018). Alpha level. In B. B. Frey (Ed.),*The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 65-66). SAGE.*

**The alpha level is chosen a priori as a level (typically .05) used to reject or not reject the null hypothesis, and this value is compared to p - value obtained from the statistical analysis. This chapter defines and discusses the concepts related to the alpha level.***p*value**Kim, H. W. (2018).***p*Value. In B. B. Frey (Ed.), The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 1195-1198). SAGE.

As you learned from this resource in a previous week, the*p*- value is the probability value that is used in conjunction with the concept of significance. This chapter discusses the different uses of the*p*- value.**Levene’s homogeneity of variance test.**Chen, Y. H., Wang, Y., & Kromrey, J. (2018). Levene’s homogeneity of variance test. In B. B. Frey (Ed.),*The SAGE encyclopedia of educational research, measurement, and evaluation (pp. 970-972). SAGE.*

**The Levene’s test is a test to examine the assumption of homogeneity of variance. This assumption is used in the independent t - test analysis and the analysis of variance.****Academic Success Center (ASC). (2020).***Statistics resources*. National University.**This LibGuide includes all of the statistics resources curated by NU's Academic Success Center. Use the headings on the left side of this ASC page to navigate to your particular area of need.****Presenting Statistics in Text****This page from the ASC offers support on how to use appropriately the different elements of statistics within text that you write.**

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