Table of critical values

Many of you didn't copy the appendix containing the table of critical values in Bartz's book. I have scanned the tables containing critical values of Pearson r, Spearman r and t. Here they are. Just click on the pictures below to have larger view.

Pearson r

Spearman r

t value

Difference between means

A teacher teaches pronunciation using several techniques such as drills and songs. She may wonder which technique is more effective, drills or songs. To find out which one is more effective, she needs to conduct experimental research. In this research she asks the following research question:

Is there a difference in pronunciation
between students who are taught using songs
and those who are not?

She has two pronunciation classes and assigns them into two groups:

Experimental group --> taught using songs
Control group --> taught without using songs

At the beginning of the semester, she gives both groups a pronunciation test as a pretest. Then she teaches them pronunciation for one semester. At the end of the semester, she gives them the same pronunciation test as a posttest. The results of the posttest are compared. If the mean of the experimental group is higher than the mean of the control group, she can conclude that using songs is a more effective technique than drills only.

The following table summarises the design of the research.


The teacher can find out whether the difference is significant or not by computing the t value using t-test formula. If her t value is higher than the t value in the table, the difference is significant. However, if her t value is lower than the t value in the table, the difference is not significant.

Correlation

Correlation indicates the relationship between two variables. If you ask such questions as:

• Is there a relationship between writing ability and grammar competence?
• Is there a relationship between reading ability and vocabulary size?

...actually you want to know whether the two variables (writing ability & grammar competence, reading ability & vocabulary size) are correlated. You could get the answers to these questions by drawing a scattergram or computing the correlation coefficient.

Scattergram

A scattergram is a graph which shows the relationship between two variables. If you have two sets of data in the form of scores and plot them in the graph, it will look like the following:


The dots form an oval which leans to the right. It means there's a positive, high relationship between the two variables. If, however, the dots form an oval which leans to the left, there's a negative, high relationship between the variables.


The problem with scattergram is the ambiguity in interpreting the strength of the correlation. How high is high? And how low is low? To get a precise results, it is better to use statistical formulas.

Formulas

There are two formulas that you can use to compute the correlation coefficient.

1. Pearson Product Moment. Use this formula if you have two sets of data which are interval or ratio.
2. Spearman Rank. Use this formula if you have two sets of data which are different types, eg. interval and nominal. Convert both sets of data into ordinal by changing the interval/ratio/nominal numbers into ranks.