# Statistical Terminology

Of the thousands of statistical tests that exist, several are commonly used in dissertations. Some of them are explained here, as simply as possible and with applications to typical dissertation research.

# ANOVA (Analysis of Variance)

In a hurried conversation in the hall, your advisor told you to use ANOVA to analyze your dissertation data. She didn’t have time to answer any questions about what type of ANOVA to use.

### Definition

You use ANOVA to find out whether the means (averages) of three or more groups of people differ. Names you might hear are *one-way ANOVA* and *two-way ANOVA*. Special types of ANOVA include MANOVA (Multivariate Analysis of Variance), ANCOVA (Analysis of Covariance), and MANCOVA (Multivariate Analysis of Covariance).

### Example (One-Way ANOVA)

You want to compare how completely people fill out a survey, depending on how it is administered. One hundred fifty teachers all complete the same survey. The 150 teachers are divided into three groups: Fifty teachers fill it out online, fifty receive it via snail mail at home and mail it back, and fifty receive it in on paper in the teachers’ room at school and return it to the school office. Your hypothesis is that the teachers who fill out the survey online will skip the fewest questions.

*Note.* If the teachers are grouped by an additional factor, for example, gender (males and females), this becomes a two-way ANOVA having six groups of people.

### Analysis

We run the ANOVA for you in SPSS.

*Note.* Sometimes it is more efficient to perform ANOVA in SPSS using a regression procedure.

### Writeup

We write up the results formally in APA format, like this writeup for the above example.

The mean number of questions skipped online was 2.36 (*N* = 50; *SD* = 0.69), the mean number of questions skipped at home was 3.00 (*N* = 50; *SD* = 1.05), and the mean number of questions skipped in school was 3.34 (*N* = 50; *SD* = 1.00). A one-way ANOVA showed that there was at least one significant difference between groups (overall *F* = 14.36; *p* < .001). Post hoc tests using the Scheffe adjustment showed that significantly fewer questions were skipped by the teachers in the online group as compared to the at-home and in-school groups (*N* = 150; *F *= 24.97; *p *< .001). The effect size (f) was 0.40. Using Cohen’s (1988) conventions, this is a large effect.

Cohen, J. (1988). *Statistical power analysis for the behavioral sciences. *2nd ed. Hillsdale, NJ: Lawrence Erlbaum

To see your dissertation results written up just like this, contact us!

** **

### Table

We also produce tables, like the following:

* ANOVA of Number of Questions Skipped for the Three Survey Administration Methods*

Source | df |
Sum of squares | Mean square | F |

Between-groups | 2 | 24.76 | 12.38 | 14.36* |

Within-groups | 147 | 126.74 | 0.86 | |

Total | 149 | 151.50 |

**p* < .001, two-tailed.

For theoretical help with your ANOVA analysis, running it in SPSS, or deciding whether ANOVA is the appropriate technique for your data, please contact us!

# t-Test

Perhaps your dissertation advisor told you to run a *t*-test in SPSS to analyze your data. Or perhaps you are wondering if a *t*-test is appropriate for the data you collected for your dissertation.

**Definition**

Briefly and simply, you use a *t*-test to find out whether the means (averages) of two groups of people differ.

**Example**

The 50 children entering first grade in Sunny School are randomly assigned to one of two classes, 25 to each class. Both classes are taught by Ms. Moon. In one class, she teaches reading using the phonics method. In the other class, she teaches reading using the whole language method. After six months, all of the children are given the same reading test. Does one group read better than the other?

*Note. *If instead of two groups of people, the same people are used in both groups–for example, a class takes a test twice, once before a teaching intervention and once after–this can also be analyzed using a *t*-test. This is called a repeated-measures or a paired *t*-test.

**Writeup**

We do the *t*-test for you in SPSS, make sure you understand it, and can write up the results formally in APA format, like this writeup for the above example:

An independent samples *t*-test showed that the scores of the phonics class (*N* = 25; *M *= 85.04; *SD* = 5.49) and the whole language class (*N* = 25; *M* = 81.16; *SD* = 6.96) differed significantly (*t* = 2.19, *p* < .05), with the phonics class having better scores. The effect size (*d*) was 0.63. Using Cohen’s (1988) conventions, this is a medium-to-large effect.

Cohen, J. (1988). *Statistical power analysis for the behavioral sciences*. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum.

For another *t*-test example, or for help with your *t*-test, please contact us.

# Regression

You may have studied regression in a statistics course years ago. Let’s refresh your memory, or teach you the basics so that you can properly use regression in your dissertation. We promise we will use only the most simple concepts.

**Definition**

In regression, you test your theory that something of interest (called the dependent variable or the outcome) is affected by one or more other entities of interest (called the independent variables or the predictors). Typically, a dissertation data set will have multiple independent variables.

*Note*. Regression can also be used to forecast the future based on trends. This specific type of regression is often used in economics and is called time-series regression.

**Examples**

*Simple Regression*

You can use simple regression to measure the effect of a single variable. An example would be seeing whether class size affects students’ test scores.

*Multiple Regression*

You can use multiple regression to measure the effect of more than one variable. An example would be seeing which of the following affect a teacher’s income: gender, years of education, years of teaching experience, or what grade the teacher teaches.

We present a writeup for the simple regression example.

**Writeup**

We run the regression for you in SPSS, make sure you understand it, and can write up the results formally in APA format, like this writeup for the above simple regression example:

Class size ranged between 10 and 37 students (*N* = 100; *M *= 24.27; *SD* = 5.08). Scores ranged between 10 and 84 (*N* = 100; *M* = 49.64; *SD* = 15.55). A simple regression analysis showed that class size significantly affects test scores. The smaller the class, the higher the test scores (*t* = -2.18; *p* < .05). The effect size (f^{2})was 0.05. Using Cohen’s (1988) conventions, this is a small effect.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum.

To see your dissertation results written up just like this, contact us!

**Table in APA Format**

Reporting regression requires more than one table, but this is one of them, in APA format of course:

For theoretical help with your regression analysis, running it in SPSS, or deciding whether regression is the appropriate technique for your data, please contact us.

# Sample Size

One of the worst things that can happen is that after you spend time, effort, and perhaps even money to run a survey or study, you find out that your sample size was inadequate! Sample size is important because when your sample size is too small, it is possible that even when your hypothesis really is true, your results show that it is false.

**Tips**

- If you are conducting a survey, you must distribute more questionnaires than your desired sample size to account for nonresponse.
- Many “sample size calculators” are available on the Internet, but you must make sure the one you are using is appropriate for your design and planned statistical analyses. A free trial of a versatile sample size calculator, called Power and Precision, is available at www.power-analysis.com. For more help with sample size calculation, contact us.

**How To Calculate Your Required Sample Size**

Various “rules of thumb” for determining sample size have been suggested (e.g., 30 subjects per independent variable for regression). A more precise way of determining the required sample size for your particular study is to take into account estimated effect size, alpha level* and power** based on previous similar studies in your field. Sample size, alpha level, effect size, and power are all interrelated; knowing the values of the three other parameters determines the necessary sample size.

*The probability of rejecting the null hypothesis when it is true. Also known as the *p*-value, the alpha level is typically set to .05.

**The probability of rejecting the null hypothesis when it is false (and thus should be rejected). In the social sciences, power is typically set to .80.

**Example: Sample Size Calculation for An Independent-Samples t-Test**

We calculated the sample size using the Power and Precision program. Specifying an effect size of .5, a power of .80, and a two-tailed alpha level of .05 yielded a required sample size of 128 (64 in each of the two groups).

For help with sample size calculation, contact us!

# Effect Size

“Statistically significant” results can be of trivial importance in the real world. Because of this, in recent years, many researchers and students have been required to report the effect size in addition to the significance level of their results.

**Definition**

Effect size is a measurement of how important an obtained effect is in reality, given that we have rejected the null hypothesis (i.e., obtained a significant result). Effect size can be thought of as the number of standard deviation units of difference. But if you don’t understand this, don’t worry about it, and please keep reading!

*Note*. Effect size is used in two ways. When planning your study, you use an estimate of the typical effect size in similar studies in your field to determine the required sample size for your study. The estimated effect size should represent the smallest effect that would be important for you to detect in your study. After you carry out the study, you calculate what its actual effect size was.

**Tip**

- A free trial of the versatile effect size calculator Power and Precision is available at http://www.power-analysis.com.

For help with effect size calculators, please contact us!

**Example: Effect Size for a Regression Analysis**

A simple regression analysis had an R^{2} of .20. For a simple regression, the effect size is f^{2} = R^{2} / (1 – R^{2}). Thus, the effect size is f^{2}= .25. Using Cohen’s (1988) conventions, this is a medium-to-large effect.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum.

For other effect size reports on this site, see Regression, t-Test and ANOVA.

For help with effect size calculation, contact us!