Exam 4 - equations to remember

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Last updated 3:26 AM on 7/13/26
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24 Terms

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Z score

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Standard deviation

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Degrees of freedom

df = N - 1

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Upper and lower limit

Ta = Tc

<p>T<sub>a</sub> = T<sub>c </sub></p>
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Sx̄

Sx̄ = ŝ/√N

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effect size for 1 sample t-tests

we use N - ? for 1 sample t-tests

d = (x̄ - μ0)/ ŝ

N - 1

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Effect sizes

d < .20 = (meaningless)

d = .20 → .39 (small)

d = .40 → .79 (medium)

d = .80+ (large)

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test correlation for one sample t-tests

We use N - ? here

N - 2

<p>N - 2 </p>
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Pearson Correlation Coefficient (r - blanched)

use N - 1 during standard deviation

<p>use N - 1 during standard deviation </p>
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Pearson Correlation Coefficient (r - raw)

use N - 1 during standard deviation

<p>use N - 1 during standard deviation <br></p>
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What should we assume a (alpha) is if it is not given?

a = 0.05

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Paired samples

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<p>equation? </p>

equation?

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<p>equation?</p>

equation?

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two-sample t tests if they are independent samples

how to find degrees of freedom?

df = N1 + N2 - 2

<p>df = N1 + N2 - 2 </p>
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two-sample tests - independent samples with unequal Ns (N1 ≠ N2)

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two-sample tests - independent samples with equal Ns (N1 = N2)

Raw scores version

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two-sample tests - independent samples with equal Ns (N1 = N2)

But standard error is given

Use if they already tell you the standard errors.

They'll say something like:

  • Group 1: SX̄=2.1

  • Group 2: SX̄=1.7

No standard deviations. No raw scores.

(The standard error of each sample mean)

<p><strong>Use if they already tell you the standard errors.</strong> </p><p>They'll say something like:</p><p> </p><ul><li><p>Group 1: S<sub>X̄</sub>=2.1</p></li><li><p>Group 2: S<sub>X̄</sub>=1.7</p></li></ul><p> </p><p>No standard deviations. No raw scores.</p><p></p><p>(The <strong>standard error of each sample mean) </strong></p>
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two-sample tests - independent samples with equal Ns (N1 = N2)

But standard deviation is given

Use (b) if they tell you the standard deviations.

They'll give something like:

  • s1=8

  • s2=10

  • N1=25

  • N2=16

No raw data.

<p><strong>Use (b) if they tell you the standard deviations.</strong> </p><p>They'll give something like:</p><p> </p><ul><li><p>s<sub>1</sub>=8</p></li><li><p>s<sub>2</sub>=10</p></li><li><p>N<sub>1</sub>=25</p></li><li><p>N<sub>2</sub>=16</p></li></ul><p> </p><p>No raw data.</p>
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effect size for paired samples design =

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effect size for independent samples design =

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Ŝp equation?

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Confidence intervals for two sample t-tests (paired)

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Confidence intervals for two sample t-tests (independent)

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