sum of squares is correct
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
If you like mathematical puzzles or love algebra, try this! Otherwise, just trust that the computational formula for the sum of squares is correct. We have a sample of x values. The
| Σ(x - x)2 | = | Σ( 2 - 2xx + x2) | by binomial expansion | ||||||
| = | Σx2 - 2xΣ + Σx2 | by distributive property | |||||||
| = | Σx2 - 2xΣx + x2 | adding the same quantity, x, n times, is in fact multiplying it by n | |||||||
| = | Σx2 - 2x( x) + nx2 | by substitution, since (Σx)/n = x, hence Σx = nx | |||||||
| = | Σx2 - x2 + nx2 | by multiplication, and expansion | |||||||
| = | Σx2 - x2 | by addition, combination of alike terms | |||||||
| = | Σx2 - |
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by substitution, since (Σx)/n = x | ||||||
| = | Σx2 - |
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by distributive property | ||||||
| = | Σx2 - |
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by multiplication, cancellation |
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