**Pyrczak and Oh’s (2018) Making Sense of Statistics text, pages 132–133.**

**Chapter Objectives**

The reader will be able to:

n Know how the results of

t tests are reported in various widely used

forms such as a table or statement using various phrases and

wordings

n Know the distinction between statistically significant and

practical significance

In Chapters 21–24 the use of the t test to test the difference between

two sample means for significance was considered. Obviously, the

values of the means should be reported before the results of the statistical

test performed on them are reported. In addition, the values of the

standard deviations and the number of cases in each group should be

reported first. This may be done within the context of a sentence or in

a table. Table 25.1 shows a typical table.

The samples for Groups A and B were drawn at random. The null

hypothesis states that the 3.50-point difference (6.00 – 2.50 = 3.50)

between the means of 2.50 and 6.00 is the result of sampling errors (i.e.,

errors resulting from random sampling) and that the true difference in

the population is zero.

Table 25.1 Means and Standard Deviations

m s N

Group A 2.50 1.87 6

Group B 6.00 1.89 6

Pyrczak, Fred, and Deborah M. Oh. Making Sense of Statistics : A Conceptual Overview, Taylor & Francis Group, 2018. ProQuest Ebook Central,

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Part F: Means Comparison

144

This is one way to

report the result of a

significant

t test.

The phrase

significant

at the .01 level indi-

cates that

p was equal

to or less than .01.Rejecting the null

hypothesis is the same

as

declaring statistical

significance.

In Example 2, the researcher has used a slightly different wording

to indicate that significance was obtained at the .01 level. The phrase

significant at the .01 level indicates that p was equal to or less than .01,

which is the probability that the null hypothesis is correct. Thus, the

null hypothesis was rejected.

Example 3 below provides the same information as Examples 1

and 2 but with a different wording. The sentence indicates that the

difference is statistically significant because rejecting the null hypothesis

is the same as declaring statistical significance.

Example 1

The difference between the means is statistically significant

(t = 3.22, df = 10, p < .01).

Example 2

The difference between the means is significant at the .01 level

(t = 3.22, df = 10).

Example 3

The null hypothesis was rejected at the .01 level

(t = 3.22, df = 10).

Any of the forms of expression illustrated in the previous three

examples is acceptable. However, authors of journal articles seldom

explicitly mention the null hypothesis. Instead, they tend to use the forms

of expression in Examples 1 and 2. In theses and dissertations, in

contrast, explicit references to the null hypothesis are more common.

The result of a significant t test may be described in several ways.

Below are some examples for the results in Table 25.1. The statement

in Example 1 below implies that the null hypothesis has been rejected

because the term statistically significant is synonymous with rejecting

the null hypothesis.

Statistically significant

is synonymous with

rejecting the null

hypothesis.

Pyrczak, Fred, and Deborah M. Oh. Making Sense of Statistics : A Conceptual Overview, Taylor & Francis Group, 2018. ProQuest Ebook Central,

http://ebookcentral.proquest.com/lib/capella/detail.action?docID=5425416.

Created from capella on 2022-07-31 15:40:47.

Copyright © 2018. Taylor & Francis Group. All rights reserved.

When researchers use the word significant in reporting the results

of significance tests, they should modify it with the adjective statistically.

This is because a result may be statistically significant but not of any

practical significance. For instance, suppose a researcher found a statis-

tically significant difference of 2 points in favor of a computer-assisted

approach over a traditional lecture/textbook approach. While it is

statistically significant, it may not be of practical significance if the

school district has to invest sizeable amounts of money to buy new

hardware and software. In other words, the cost of the difference may

be too great in light of the absolute size of the benefit.1

Now, consider how researchers report the results of a t test when

the difference between means is not statistically significant. Table 25.2

presents descriptive statistics. Examples 4 through 6 show some ways

to express the results of the insignificant t test for the data in the table.

The fact that p is greater than (>) .05 in Example 4 below indicates

that the null hypothesis was not rejected.

Chapter 25: Reports of the Results of

t Tests

145

The abbreviation

n.s.

means

not significant.

It is best to indicate

the specific probability

level at which the null

hypothesis was not

rejected.

Example 4

The difference between the means is not statistically significant

(t = 1.80, df = 12, p > .05).

Example 5

For the difference between the means, t = 1.80 (df = 12, n.s.).

A result may be

statistically significant

but not of any

practical significance.

Table 25.2 Means and Standard Deviations

m S N

Group A 8.14 2.19 7

Group B 5.71 2.81 7

The author of Example 5 has used the abbreviation n.s. to indicate

that the difference is not significant. Because the example does not

indicate a specific probability level, most readers will assume that it was

not significant at the .05 level—the most liberal of the widely used levels.2

Example 4 is preferable to Example 5 because the former indicates the

specific probability level that was used to test the null hypothesis.

Pyrczak, Fred, and Deborah M. Oh. Making Sense of Statistics : A Conceptual Overview, Taylor & Francis Group, 2018. ProQuest Ebook Central,

http://ebookcentral.proquest.com/lib/capella/detail.action?docID=5425416.

Created from capella on 2022-07-31 15:40:47.

Copyright © 2018. Taylor & Francis Group. All rights reserved.

Example 6 shows how the results of the test might be expressed

with explicit reference to the null hypothesis.

While reading journal articles, theses, and dissertations, you will

find variations in the exact words used to describe the results of t tests.

The examples in this chapter illustrate some of the most widely used

forms of expression.

Part F: Means Comparison

146

Example 6

The null hypothesis for the difference between the means was not

rejected at the .05 level (t = 1.80, df = 12).

Exercise for Chapter 25

**Factual Questions**

1. Which statistics should be reported before the results of a t test are reported?

2. Suppose you read this statement: “The difference between the means is statistically

significant at the .05 level (t = 2.333, df = 11).” Should you conclude that the null

hypothesis has been rejected?

3. Suppose you read this statement: “The null hypothesis was rejected (t = 2.810, df = 40,

p < .01).” Should you conclude that the difference is statistically significant?

4. **Suppose you read this statement: “The null hypothesis was not rejected (t = –.926,****df = 24, p > .05).” Describe in words the meaning of the statistical term “p > .05.”**

5. For the statement in Question 4, should you conclude that the difference is statistically

significant?

6. Suppose you read this statement: “For the difference between the means, t = 2.111 (df = 5,

n.s.).” Should you conclude that the null hypothesis has been rejected?

7. Which type of author seldom explicitly mentions the null hypothesis?

A. Authors of dissertations

B. Authors of journal articles