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T Test for 2 Independent Variables, sample mean difference, df₁+ df₂ -…
T Test for 2 Independent Variables
Scenario 1:
2 sets of data from 2 separate group of participants. Group of students given laptops, group of students not given laptops.
Independent -measures research design or Between-subjects design
Assumptions: Observations within each sample must be independent.
The two populations must be normal
When populations are not normal, compensate with relatively large samples
The two populations must have equal variances (Homogeneity of variance)
If variance is different, the calculation and the averaging of variance is meaningless.
This is most important when there is a large descrepancy in sample sizes.
Hartleys F-Max Test
F-Max = s² Largest / s² Smallest
Large f Max value= large difference in sample variances
Compare value to critical value.
To locate critical value table you need to know:
3 more items...
Small value (near 1.0) indicates sample variances are similair and homogeneity assumption is reasonable.
Two tailed test: Step 1. Hypothesis Test, State alpha level
H𝘰: 𝛍₁ - 𝛍₂ = 0
No difference between pop means
H₁: 𝞵₁ - 𝞵₂ ≠ 0
There is a mean difference
𝞵₁ ≠ 𝞵₂
Step 2.
Locate critical region: df = (n₁-1) + (n₂-2)
Step 3. Obtain data and compute test statistic.
Find pooled variance
Estimate standard error
Compute t statistic
Step 4. Make a decision:
1 Tailed Test:
Step 1. State hypothesis and alpha level
Step 2: for 1 tailed test, check to see if data moves in direction predicted.
If iit does not, stop analysis₁
If it does, Determine if difference is large enough to be significant by finding one tailed vritical value in t distribution table.
Step 3. Collect data and calculate t statistic
Make a decision
Scenario 2
Two sets of data from the same group of participants: One set of scores before they begin therapy, a second set of data measuring same individuals after 6 weeks of therapy.
Repeated-measures research design or within-subjects design
T statistic- independent-measure t statistic
(M₁ - M₂) - (𝞵₁ - 𝞵₂)
t =
s(M₁ - M₂)
t =
estimated standard error
Standard Error for Sample Mean Difference s(M₁-M₂)
M₁-M₂ Measures:
Standard Distance between (M₁ - M₂) - (𝞵₁ - 𝞵₂)
When null hypothesis is true, it measures the standar or average size of (M₁ - M₂), meaning how much difference is reasonable to expect between the two sample means.
Standard Error:
M₁, sM =
√s₁²
√n₁
.
M₂, sM =
√s₂²
√n₂
Add errors together after dividing, then take square root
M₁, M₂ from sample
𝞵₁, 𝞵₂ from null hypothesis
Variability
Range for population 1 (X₁) (highest - lowest)
+
Range for population 2 (X₂) (highest - lowest)
Range for the differences: (X₁-X₂) by adding range pop X₁ + range pop X₂
Variability with different population sizes n₁ n₂
Pooled variance
Sp² =
SS₁ + SS₂
sample mean difference
df₁+ df₂
