1 / 22

# Chapter 10 The t Test for Two Independent Samples - PowerPoint PPT Presentation

The t Test for Two Independent Samples Compare means of two groups Experimental—treatment versus control Existing groups—males versus females Notation—subscripts indicate group M 1 , s 1 , n 1 M 2 , s 2 , n 2 Null and alternative hypotheses

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Chapter 10 The t Test for Two Independent Samples' - niveditha

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
The t Test for Two Independent Samples

• Compare means of two groups

• Experimental—treatment versus control

• Existing groups—males versus females

• Notation—subscripts indicate group

• M1, s1, n1 M2, s2, n2

• Null and alternative hypotheses

• translates into

• translates into

• Criteria for use

• Dependent variable is quantitative, interval/ratio

• Independent variable between-subjects

• Independent variable has two levels

• t-test

• Basic form

• One sample

• Difference between sample means M1 - M2

• Population parameter

• Sampling distribution of the difference

• Difference between M1 and M2 drawn from population

• Population variance known

• Sum of

• Estimate from samples

• Differences more variable than scores

• Randomly generated set of 1000 means

• Μ= 50, σM = 10

• Take difference between pairs

S2pooled Pooled Variance

• Homogeneity of variance

• Assume two samples come from populations with equal σ2’s

• Two estimates of σ2 — and

• Weighted average

df = df1 + df2 = (n1-1) + (n2-1) = n1 + n2 - 2

t-test

• Two-tailed

• H0: µ1 = µ2, µ1 - µ2 = 0

• H1: µ1 ≠ µ2, µ1 - µ2 ≠ 0

• One-tailed

• H0: µ1 ≥ µ2, µ1 - µ2 ≥ 0

• H1: µ1 < µ2, µ1 - µ2 < 0

• Determine α

• Critical value of t

• df = n1 + n2 - 2

• Random and independent samples

• Normality

• Homogeneity of variance

• SPSS—test for equality of variances, unequal variances t test

• t-test is robust

H0: µ1 = µ2, µ1 - µ2 = 0

H1: µ1 ≠ µ2, µ1 - µ2 ≠ 0

df = n1 + n2 - 2 =10 + 7 – 2 = 15

=.05

t(15) = 2.131

Example 1

• t(15) = –2.325, p < .05 (precise p = 0.0345)

df = n1 + n2 - 2 = 15 + 15 – 2 = 28

=.05, t(28) = 2.049

Example 2

• t(28)= –.947, p > .05

• Example 1

• -3.257 - (2.131*1.401) < µ1 - µ2 < -3.257 + (2.131*1.401) = -6.243 < µ1 - µ2 < -0.272

• Example 2

• -0.867 - (1.701*5.221) < µ1 - µ2 < -0.867 + (1.701*5.221) = -9.748 < µ1 - µ2 < 8.014

• Includes 0 retain H0

• Analyze

• Compare Means

• Independent-Samples T Test

• Dependent variable(s)—Test Variable(s)

• Independent variable—Grouping Variable

• Define Groups

• Cut point value

• Output

• Levene’s Test for Equality of Variances

• t Tests

• Equal variances assumed

• Equal variances not assumed

• Cohen’s d =

• Example 1 Cohen’s d

• Example 2 Cohen’s d

• r2 or η2

• G = grand mean

Factors Influencing t–test and Effect Size

• Mean difference M1 – M2

• Larger difference, larger t

• Larger difference, larger r2 and Cohen’s d

• Magnitude of sample variances group

• As sample variances increase:

• t decreases

• Cohen’s d and r2 decreases

• SSExplainedunchanged, SSErrorand SSTotal increases, S2pooled increases

• Sample size group

• Larger sample smaller t affects

• No effect on Cohen’s d, minimal effect on r2

• First example increase n1from 10 to 30 and n2 from 7 to 21