T-Test

T-Test

Questions to Analyze

T-Test History

How can we use a t-test for our questionnaire?

We can use an independent t-test and compare the mean of both groups (residents of MA and nonresidents of MA)

Why these questions?

#10- Where do you get the majority of your political information from?

#12- What news network do you prefer to turn to for political inform?

#15- How important do you think it is to be knowledgeable about current politics

#16- Although some of the candidates have dropped out, which 2016 presidential candidate do you prefer?

#17- Which attribute below do you most look for in a presidential candidate?

Hypothesis: Residents of MA will be more likely to prefer Bernie Sanders as a presidential candidate

• H(null) : A resident of MA would not be more likely to prefer Bernie Sanders
• H(alternative): A resident of MA would be more likely to prefer Bernie Sanders

• The t-test was created in 1908 by an Englishman named William Sealy Gosset (June 13, 1876- October 16, 1937) under the pseudonym "Student"
• Gosset obtained a degree in Mathematics in 1897 and a degree in Chemistry in 1899 from New College Oxford
• In 1905 he began working in Karl Pearson's lab
• At the time of the development of the t-test he worked for the Guiness brewing company in quality control as a chemist
• He developed the t-test to compare the qualities of beers
• He used the test to compare two small sets of data when samples were collected independently of one another

It is important to know where the participants get their political information from because there may be other factors that influence their preferences.

Depending on where they get their information, they may be biased towards a particular candidate.

Whether or not they find it important to be knowledgeable and how much they look for information may influence their preferences.

Once we collect the questionnaire and identify MA residents and non MA residents we can compare preferences of presidential candidates...

Objectives

3 Types of T-Tests

Example 1

Independent Samples T-Test (Between-Samples)

• Tests the means of two different groups

• Guenther et al. (2010) found in a study of alcohol use that women drank avg. 5.5 ounces of alcohol per day, in the 2003-2006 period.
• We believe that women’s alcohol use has changed since then, so we want to collect some data and see if that is true

Paired Samples T-Test (Within-Subjects)

• Tests the mean of one group twice

One Sample T-Test

• Tests the mean of 1 group against a set mean

• What is a t-test?
• Who created the t-test and why?
• When is a t-test is appropriate?
• Use of t-test in previous research
• Apply the t-test to our research surveys

Limitations of the T-Test

Step 1: state hypotheses

• H0: Alcohol consumption is on average 5.5 ounces a day in women

• H1: Alcohol consumption is on average ≠ 5.5 ounces a day in women

• This is a two tailed test

• We have not said that our M will be definitely larger than or definitely smaller than the population mew. So if our M ends up either smaller or larger than mew, we can reject null.

• Step 2: Find the critical rejection region—the cutoff value of T in the Table

• You can only generalize to a population that resembles your sample
• Your sample and population should be roughly normal in distribution
• You should have close to the same number of scores in each group

• Analyze each group after collecting the means of both groups.
• Determine if the calculated t-value is larger than the critical t-value
• If it is larger then reject the null hypothesis
• If it is smaller then fail to reject the null hypothesis

What is a T-Test?

We are testing the hypothesis that the population means are equal for the two samples. We assume that the variances for the two samples are equal.

H0: μ1 = μ2

Ha: μ1 ≠ μ2

Test statistic: T = -12.62059

Pooled standard deviation: sp = 6.34260

Degrees of freedom: ν = 326

Significance level: α = 0.05

Critical value (upper tail): t1-α/2,ν = 1.9673

Critical region: Reject H0 if |T| > 1.9673

Example 2

• A t-test is a statistic that verifies if two means are reliably different from each other.
• A statistically significant t-test indicates whether or not the two groups' averages reflect a real difference in the population from which the groups were sampled.
• Statistical significance is determined by the size of the difference between the group averages, sample size, and SD of the group.
• Each t-value has a corresponding p-value which tells us the probability that the pattern of data in the sample could be produced by random data.

The following two-sample t-test was generated for the AUTO83B.DAT data set. The data set contains miles per gallon for U.S. cars (sample 1) and for Japanese cars (sample 2); the summary statistics for each sample are shown below.

The absolute value of the test statistic for our example, 12.62059, is greater than the critical value of 1.9673, so we reject the null hypothesis and conclude that the two population means are different at the 0.05 significance level.

We choose an alpha of .05

• Our sample: 64 women, so n is 64, and df is 63

• In the table there IS no 63 df, so we use the smaller df that is there—60.

• The critical cutoff value of T for this test is 2.00

• Step 3: Collect data and calculate our sample T

• We sample 64 women on drinking habits

• The sample M is 6.3 ounces per day

• The standard deviation is 3.6 ounces.

• Remember our population mew was 5.5 ounces

• So: Tobt= = .9/.45= 2, Tobt=2

• Step 4: Make a decision

• Our T is equal to the critical T, so we reject the null and conclude that women’s average drinking habits have changed.

(Ch 8 PPT, Alice Frye, 2016)

SAMPLE 1:

NUMBER OF OBSERVATIONS = 249

MEAN = 20.14458

STANDARD DEVIATION = 6.41470

STANDARD ERROR OF THE MEAN = 0.40652

SAMPLE 2:

NUMBER OF OBSERVATIONS= 79

MEAN= 30.48101

STANDARD DEVIATION = 6.10771

STANDARD ERROR OF THE MEAN= 0.68717