Question

Introduction to T-tests Correlation looks for relationships between variables. T-tests compare means to look for differences between the means of two groups.

STATISTICAL GUIDE:  The t-test is used to see if the difference between two means is statistically significant. There are multiple kinds of t-tests.

In this exercise, we will focus on the t-test for independent groups (used to compare the mean scores of 2 different groups of participants in the same study)

This t-test is used if the two means you are comparing in your sample (did 2 different types of people score differently on the same question? ex: if have a sample with 2 gender identities reported: male and female; did the males and females answer the same way? or differently? (i.e. did they have different mean scores? and is that difference statistically significant?)

To use the t-test a number of assumptions need to be met. Two key assumptions are that (1) the data is normally distributed or nearly so, and (2) the data for the dependent variable is continuous, i.e., on an interval or ratio scale. If these two assumptions (as well as others) are not met, then different statistical tests should be used to compare the two group means.

The t-test yields a p-value, which indicates whether the mean differences are significant. As with most statistical tests, most researchers consider a difference to be statistically significant when p < .05.

So, in the t-test: the null hypotheses=there is no difference in group means

As with correlation, when researchers present t-test results in a table (like Table 1 below), they often note statistically significant results with an asterisk or some kind of superscript.

It is generally safe to assume that if a result has no superscript then the result is non-significant. Still, reading table notes is necessary, so you can make sure you know what certain symbols in the table mean (and in this table they use an asterisk and what to show significance?)

Review: in the table below:

n=number of participants (in this case in each group of participants)

M=mean

SD=standard deviation

t= independent samples t-test statistic

Below is the excerpt from a study:

This study had 2 groups (married and in a dating relationship)

The married sample comprised members of 100 heterosexual couples (54% were women and 46% were men) from a Midwestern university.

The dating sample also consisted of members of 100 heterosexual couples (59% were women and 41% were men) from the same Midwestern university.

All the married and dating couples were Euro-American. A researcher selected subjects in a haphazard fashion and asked them to complete a short survey. . . . The mean age of the sample was 26.7 years (SD = 2.6).

THE MEASURE IN THE STUDY:

The Affectionate Communication Index is a 19-item index that. . . assesses the amount of verbal and nonverbal affectionate communication and support on a 7-point. . . scale, with anchors of 1 = partners always engage in this type of affectionate activity to 7 = partners never engage in this type of activity.

Thus, lower scores indicate more affectionate communication. Table 1 shows the results for the nonverbal activities.]

Items		n	M	SD	t
Hold Hands	Dating Married	100 100	3.7 2.9	1.9 1.7	3.3t
Kiss on lips	Dating Married	100 100	2.9 2.0	1.5 1.1	4.9t
Kiss on the cheecks	Dating Married	100 100	3.6 2.7	1.6 1.3	4.5t
Give messages to each other	Datting Married	100 99	4.2 2.5	1.8 1.8	5.0t
Put arm around shoulder	Dating Married	100 92	3.6 2.5	1.8 1.5	4.6t
Hug each other	Dating Married	100 100	2.5 2.1	1.6 1.2	2.0*
Sit close to each other	Dating Married	96 100	2.9 2.0	1.6 1.6	3.9t
Look into each other’s eyes	Dating Married	100 100	3.3 3.0	1.6 1.8	1.0
Wink are each other	Dating Married	100 96	4.7 4.2	2.3 1.9	1.7

Table:
: Dating And Married Individuals Reports of Nonverbal Affectionate Communication:

Should the null hypothesis be rejected for hugging each other?

The differences are not statistically significant for which items?

Answer 1

Should the null hypothesis be rejected for hugging each other?

Hypothesis
Ho: The mean score of the two groups is equal
H1 :The mean score of the two groups is not equal.

From the data give we see that statistics with a star or cross are less than 0.05 and 0.01 respectively.
Incase of hugging it is less than 0.05, hence we reject the null hypothesis.

The differences are not statistically significant for which items?
Items which do not have any mark on the tstatistic are insignificant.

Based on this understanding
Looking into each other's eyes
Wink at each other

are not statistically signficant.