Intro to StatsIndependent t-tests

Use when:

You are examining differences between groups

Each participant is tested once Comparing two groups only

Independent t-tests

Mean Group 1 - Mean Group 2___________________________________ Spread of the groups' data points

t is larger (more likely significant) when: ◦ Two groups’ means are very different◦ When spread (variance) is very small

What does it mean?

Observations are independent Samples are normally distributed Samples should have equal variance

◦ There is a “fix” for violations of this assumption that will be discussed in lab

Assumptions

t = X1 – X2

(n1-1) s12 + (n2 – 1)s2

2 n1+n2

n1 + n2 - 2 n1n2

X1 = mean for group 1

X2 = mean for group 2

n1 = number of participants in group 1

n2 = number of participants in group 2

s12 = variance for group 1

s22 = variance for group 2

Calculating

Study: ◦ Effects of GRE prep classes on test scores◦ One group given prep classes

(1400, 1450, 1200, 1350, 1300)◦ One group given no classes

(1400, 1200, 1050, 1100, 1200)

Example 1

1. State hypotheses◦ Null hypothesis: there is no difference between

test scores in the groups with or without prep classes μprep = μnoprep

◦ Research hypothesis: there is a difference in test scores between the groups with and without prep classes Xprep ≠ Xnoprep

Example 1

t = X1 – X2

(n1-1) s12 + (n2 – 1)s2

2 n1+n2

n1 + n2 - 2 n1n2

X1 = mean for group 1

X2 = mean for group 2

n1 = number of participants in group 1

n2 = number of participants in group 2

s12 = variance for group 1

s22 = variance for group 2

Example 1

X1 – X2

Prep group: 1400, 1450, 1200, 1350, 1300

Noprep group: 1400,1200, 1050, 1100, 1200

The Numerator

Degrees of freedom ( df ): Describes number of scores in sample that are free to vary (without changing value of descriptive statistic).

Needed to identify the critical value

df = (n1 - 1) + (n2 – 1) (for t-test only)

Degrees of Freedom

**if dfs are bigger than biggest value in chart, use infinity row

**if precise dfs are not listed, use the next smallest to be conservative

Example 1

6. Determine whether the statistic exceeds the critical value◦ 2.03 < 2.31◦ So it does not exceed the critical value

◦ THE NULL IS REJECTED IF OUR STATISTIC IS BIGGER THAN THE CRITICAL VALUE – THAT MEANS THE DIFFERENCE IS SIGNIFICANT AT p < .05!!

7. If not over the critical value, fail to reject the null

& conclude that there was no effect of GRE training on test scores

Example 1

In results◦ There was no significant difference in test scores

between participants given the GRE prep course (M = 1340, SD = 96.18) and those given no GRE prep course (M = 1190, SD = 134.16), t(8) = 2.03, n.s.

If it had been significant:◦ Participants given the GRE prep course had

significantly higher test scores (M = 1340, SD = 96.18) than those given no GRE prep course (M = 1190, SD = 134.16), t(8) = 2.80, p < .05.

Example 1

Whether the effect/difference was significant or not

The outcome in the study The different groups or categories being

compared in the study The mean and SD for each group or

category The t statistic and p-value, as shown in

examples

An interpretation should include:

Remember: Just because means are different, it does not mean they are meaningfully different

Need to examine significance◦ i.e., likelihood that the differences are due to

chance

Significance

A measure of the magnitude of the difference between groups

ES = X1 – X2

SD

Effect Sizes