Read the directions twice and solve the examples before working other problems.
PEr. Move the slide until the given r on the r sole is opposite the given N on the N scale. The line 1PE, at the extreme left, points to PEr, on the B scale. E.g., if r = .60 and N = 50, PEr = .061. (See next two paragraphs.)
σr Move the slide until the given r on the r scale is opposite thell7en N on the N scale.
The line lσ, points to σ, on the B scale. E.g., if r = .80 and N = 240, σr = .023.
When N is large or r is high, the lines 1PE or 1σ may not point to any number on the B scale.
If this happens, find the value of 10 PEr or 10 σr near the right end of the B scale and divide by ten, i.e. simply insert a zero after the decimal point. E.g., if r = .92 and N = 175, PEr = .0078 and σr = .0116. Or, if r = .866 and N = 1950, PEr = .0038 and σr = .0057.
Note:
All integral multiples of PEr and σr up to 10 are given. E.g., the values of 4 PEr and 3 σr may be read directly.
Thus, if r = .20 and N = 360, 4 PEr = .134, 3 σr = .151, etc.
The longest lines, labeled c, are chances; the medium lines, labeled σ, give multiples of σr; and the shortest lines give multiples of PEr.
Probability That An Obtained Difference Is Due To Chance.
The r expected by hypothesis is .60.
If N = 44 and the obtained r is .76, how significant is the difference of .16?
Move the slide until the expected r (.60) is opposite 44 on the N scale. Find the difference (.16) on the B scale.
Then read the number below this on the chance scale.
This number, 20, means that the probability is about one in 20 of a deviation of such size occurring in this direction by chance.
σ1.2 Move the slide until the given r12 on the σ1.2 scale at the left opposite the given σ1 on the σ scale.
The arrow, σ1.2, at the extreme left points to the value of σ1.2 on the σ scale.
E.g., if σ1 = 5.5 and r12 = .80, σ1.2 = 3.3.
Standard Error of Measurement, σ(M).
Move the slide until the given r11 on the σ(M) scale is opposite the given σ1 on the σ scale.
The arrow, σ(M), points to the value of σ(M) on the σ scale.
E.g., if σ1 = 115 and r1I = .86, σ(M) = 43.
Multiplication, Division, Percentaces, etc.
Use the C and D scales as an ordinary slide rule, locating the decimal point by inspection.
Thus, to multiply 35 by 20, move the slide no that 10 on the C scale is directly above 35 on the D scale.
Directly below 20 (on the C scale) will be found the product (on the D scale) which is read as 700.
To multiply .123 by 4.56, move the slide so that 10 on the C scale is directly above 12.3 on the D scale.
Directly below 45.6 (on the C scale) will be found the product which is read as .56.
When the multiplier on the C scale extends beyond the right end of the D scale, move the slide to the left so that the number 100 on the C scale is directly above the multiplicand on the D scale and proceed as above.
To divide 876 by 543, move the slide until 543 on the C scale is directly above 876 on the D scale.
Directly below 10 (on the C scale) will be found the quotient which is read as 1.6.
If no number appears on the D scale below the 10 on the C scale read the number below 100 on the C scale as the quotient.
To divide several numbers by 256, move the slide until 256 on the C scale is directly above 10 on the D scale.
Directly below each numerator (on the C scale) will be found the corresponding quotient (on the D scale). Thus, 32/156 = .125; 56/156 = .219.
When the numerator extends beyond the D scale, place the denominator above 100 on the D scale and proceed as before.
Thus, 18/256 = .07.
Spearman-Brown Formula.
The line graph r1/2 I/II to r1I is in the center of the slide.
Remove the slide and find r1/2 1/II on one side of the scale and on the opposite side read r1I. E.g., if r1/2 1/II = .17,r1I = .29. Or, if r1I = .925, r1/2 1/II = .86.
Line Graphs on Back of Rule.
Find the given value on the appropriate scale and read the value of the corresponding function from the other side of the scale.
E.g., if N = 144, σz = .084.
Or, if σz is reported as .041; N must have been about 600.
E.g., if r = .986, z = 2.48.
Or, if z = 1.10, r = .80.
E.g., if r = ±.33, k = .944.
Or, if k = .880, r = ±.475
Or, if r = ±.992, k = .126.
E.g., if x/σ = 2.46, the area between the mean and 2.46σ is .493 or 49.3%.
For values of x/σ greater than 4.0, use the chance scale on the front of the slide rule.
E.g., if A = 2.4,, √A = 1.55.
But if A = 24.0,, √A = 4.9.
Inversely, if A = 5.7, find 5.7 on the √A side of the scale and read A² from the A side as 32.5.
Or, if A = .036, A² = .0013.
Standard Error of the Mean, σM.
Remove the slide and insert it upside down so that the given value of σ on the C scale is directly below 100 on the N scale.
Find the given N on the N scale and directly below this, read σM, locating the decimal point by inspection.
E.g., if σ = 18 and N = 190, σM = 1.3.
Or, if σ = .77 and N = 580, σM = .032.
Other Uses Spearman's formula for correction for attenuation may be solved by dividing r12 by √r1I (Just as σ is divided by √N in obtaining σM and then dividing this result by √r2 II.
The formula σ1 √1 − r1 = σs √1 − rs, which shows the relation between standard deviations and reliability coefficients in two ranges, may be solved by setting σ1 and r1 (or σs and rs, which-ever are known) opposite each other on the σ and σ(M) scales, and reading rs opposite σs.
By inverting the slide as was done in solving for σ(M), equations of the types A = B/√C; C = B²/A² = (B/A)²; B/√C = B'/√C'; etc. may be solved.
Note. In every one of the above examples it has been assumed that a particular function is desired as the answer.
If, however, this function is known and one of the other values is unknown, the unknown value may be solved for on this slide rule.