Statistical formulas documentation
mTAB Median Calculation from Income Brackets
| Approximate Annual HH Income | |
| Median | 71,180 |
| Unweighted Sample Total Count | 10,811 |
| Approximate Annual HH Income | Weighted Response (1) Accumulated Response |
||
| Less than 15,000||width="150"|11,714||11,714|−|15,000 - 24,999||46,054||57,768|−|25,000 - 34,999||83,965||141,733|−|35,000 - 44,999||102,093||243,826|−|45,000 - 59,999||155,721||‴399,546‴|−|60,000 - $74,999 || 161,435 || '''560,981''' <--''Median will fall here'' (3) |- | 75,000−99,999 || 193,540 || 754,521 |- | 100,000−124,999 || 134,706 || 889,227 |- | 125,000−149,999 || 59,748 || 948,975 |- | 150,000−199,999 || 41,971 || 990,946 |- | 200,000−249,999 || 16,391 || 1,007,337 |- | $250,000 or More | 32,409 | 1,039,746 | |
| Weighted Subset Total Count | 1,039,746 | ||
| Weighted Sample Total Count | 1,255,411 | ||
| (1) | Calculated Accumulated Weighted Response | |||||
| (2) | Divide total (1,039,746) by 2=519,873 | 519,873 | ||||
| (3) | Find first value in Accumulated Response column that is greater than step 2 value | |||||
| The median will fall between the 60,000−74,999 bracket | ||||||
| (4) | Step 2 amount (519,873) MINUS preceding break accumulated response 399,546 = | 120,327 | ||||
| (5) | Acc. Response where Median will fall 560,981 MINUS preceding break 399,546 = | 161,435 | ||||
| (6) | Step 4 Divided by Step 5 | 0.74536 | ||||
| (7) | Multiply Step 6 by the range 14,999 (60,000−75,999) | 11180 | ||||
| (8) | Add Step 7 to bottom of range $60,000 || '''71,180''' |} '''mTAB Mean/Weighted Average Calculation from Income Brackets {|width=275px |- |Approximate Annual HH Income |- | Mean/Weighted Average || 83,610 |- | Unweighted Sample Total Count || 10,811 |} {| |- | || (A) || || || (B) || (C) |- | width="225"|Approximate Annual HH Income || || STAT1 || STAT2 || Midpoint |- | Less than $15,000 | 11,714 | 1 | 14,999 | 7,500 | 87,857,249 |
| 15,000−24,999 | 46,054 | 15,000 | 24,999 | 20,000 | 921,059,004 | |
| 25,000−34,999 | 83,965 | 25,000 | 34,999 | 30,000 | 2,518,899,346 | |
| 35,000−44,999 | 102,093 | 35,000 | 44,999 | 40,000 | 4,083,654,266 | |
| 45,000−59,999 | 155,721 | 45,000 | 59,999 | 52,500 | 8,175,254,132 | |
| 60,000−74,999 | 161,435 | 60,000 | 74,999 | 67,500 | 10,896,752,251 | |
| 75,000−99,999 | 193,540 | 75,000 | 99,999 | 87,500 | 16,934,669,636 | |
| 100,000−124,999 | 134,706 | 100,000 | 124,999 | 112,500 | 15,154,345,342 | |
| 125,000−149,999 | 59,748 | 125,000 | 149,999 | 137,500 | 8,125,258,359 | |
| 150,000−199,999 | 41,971 | 150,000 | 199,999 | 175,000 | 7,344,910,850 | |
| 200,000−249,999 | 16,391 | 200,000 | 249,000 | 225,000 | 3,688,025,252 | |
| $250,000 or More | 32,409 | 250,000 | 300,000 | 275,000 | 8,912,452,979 | |
| Weighted Subset Total Count | 1,039,746 | 86,933,138,666 | ||||
| Weighted Sample Total Count | 1,255,411 |
- (1) Find Midpoint of data ranges - Column (B)
- (2) Multiply Weighted Counts (A) by Midpoints (B) to generate (C)
- (3) Divide the sum of column (C) by the total weighted response at the bottom of column (A)...
- 86,933,138,666 divided by 1,039,746 = 83,610
- You will notice the calculated average matches the mTAB produced average
Standard Deviation Calculation
For categorized questions, each response is assigned 1 or 2 stat weights. If a single weight is assigned, then this is the value used to calculate the standard deviation. If 2 weights are provided, the midpoint is used.
D = Question Mean - Stat Value as described above
SS = Sum of Squares, D*D*Weighted Response Count, for all table responses
Sample = Sum of all Weighted Response Counts for all table responses
Standard Deviation = SQRT(SS/Sample-1));
The calculation is the same for continuous variables except the actual data values are used instead of stat weight.
D = Question Mean - Response Value
SS = Sum of Squares, D*D*Respondent Weight Count for each response
Sample = Sum of all Respondent Weights for each response
Standard Deviation = SQRT(SS/Sample-1));
Comparison of two population means using T-Statistic
When the two populations have equal variances
t=m1−m2/sqrt/frac(n1−1)s21+(n2−1)s22n1+n2−2)(1n1+1n2)
√cfracn−12
Where
m1 = Mean of the 1st sample
s1 = Standard Deviation of the 1st sample
n1 = Un-weighted Sample of the 1st sample
m2 = Mean of the 2nd sample
s2 = Standard Deviation of the 2nd sample
n2 = Un-weighted Sample of the 2nd sample
Decision rules:
If |t|<1.65 then the two populations are NOT significantly different at 90%
If |t|≥1.65 then the two populations ARE significantly different at 90%
If |t|<1.95 then the two populations are NOT significantly different at 95%
If |t|≥1.95 then the two populations ARE significantly different at 95%
When the two populations have UNEQUAL variances
t=m1−m2/sqrt/fracs21n1+/fracs22n2
Where
m1 = Mean of the 1st sample
s1 = Standard Deviation of the 1st sample
n1 = Un-weighted Sample of the 1st sample
m2 = Mean of the 2nd sample
s2 = Standard Deviation of the 2nd sample
n2 = Un-weighted Sample of the 2nd sample
Decision rules:
If |t|<1.65 then the two populations are NOT significantly different at 90%
If |t|≥1.65 then the two populations ARE significantly different at 90%
If |t|<1.95 then the two populations are NOT significantly different at 95%
If |t|≥1.95 then the two populations ARE significantly different at 95%
