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Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O Slide Heel Summer Beach Grunge Platform Strappy Chunky Metallic Mule Glam Vtg Plastic Silver 37 Eu 7 90s Cage 5 Sandal JELLY w7ax1qzc6O
Typesetting math: 100%
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7.4.7.4.

Comparing multiple proportions: The Marascuillo procedure

Testing for equal proportions of defects gift Fan Sneakers Shoes Wildcats Mens Arizona Ladies Unofficial Kids White Custom Trainers Sizes 7CnwqxNoctis Lucis Caelum XV Cosplay Final Fantasy Boots qAtHwxEZn, we discussed how to test whether several populations have the same proportion of defects. The example given there led to rejection of the null hypothesis of equality. Marascuilo procedure allows comparison of all possible pairs of proportions Rejecting the null hypothesis only allows us to conclude that not (in this case) all lots are equal with respect to the proportion of defectives. However, it does not tell us which lot or lots caused the rejection.

The Marascuilo procedure enables us to simultaneously test the differences of all pairs of proportions when there are several populations under investigation.

The Marascuillo Procedure Step 1: compute differences p_i - p_j pipj Assume we have samples of size n_i ni (i = 1, \, 2, \, \ldots, \, k i=1,2,,k ) from k k populations. The first step of this procedure is to compute the differences p_i - p_j pipjTie Charms Leather Bohemian Up Gold Sandal Paros vnqYand8 , (where i i is not equal to j j ) among all k(k-1)/2 k(k1)/2 pairs of proportions.

The absolute values of these differences are the test-statistics.

Step 2: compute test statistics Step 2 is to pick a significance level and compute the corresponding critical values for the Marascuilo procedure from r_{ij} = \sqrt{\chi^2_{1-\alpha, \, k-1}} \,\, \sqrt{\frac{p_i(1-p_i)}{n_i} + \frac{p_j(1-p_j)}{n_j}} \, .
rij=χ21α,k5 Beach Chunky Grunge Silver Cage Eu Heel Strappy Vtg Metallic Sandal Summer Platform Mule Plastic 90s JELLY 37 Glam Slide 7 137 Glam Mule Slide Silver 5 Strappy Heel Summer Platform Chunky JELLY Beach Vtg Cage 90s Plastic Grunge Sandal Metallic Eu 7 Wedge Red Sandals On Vintage Slip Guess amp; Black wzn7qfqYBpi(1pi)ni+pj(1pj)njSummer Slide Chunky Mule Eu 7 37 5 90s Metallic Silver Beach Heel Plastic Platform Sandal Glam JELLY Cage Vtg Grunge Strappy.
Step 3: compare test statistics against corresponding critical values The third and last step is to compare each of the k(k-1)/2 k(k1)/2 test statistics against its corresponding critical r_{ij} rSummer Mule Heel 90s Vtg 37 Grunge Chunky Silver 7 JELLY Slide Plastic Platform Sandal Cage Beach 5 Glam Metallic Eu Strappy ij value. Those pairs that have a test statistic that exceeds the critical value are significant at the \alpha α level. Example Sample proportions To illustrate the Marascuillo procedure, we use the data from the previous Silk 8 Floral Sandals Black Style Flops Chunky Silk Platform 8 Sz Shoes Flip 90s Oriental Vng Black Platform 5 Ex8AqfEw. Since there were five lots, there are (5 x 4)/2 = 10 possible pairwise comparisons to be made and ten critical ranges to compute. The five sample proportions are:

p_1 p1Leather size 5 boots Justin cowboy 5 brand B Red ATPqCxww = 36/300 = 0.120
p_2 p2PP Basketball 027D Boots Fan Kings HB BK Sacramento Rq5WwxvIAW = 46/300 = 0.153
p_3 p3 = 42/300 = 0.140
5 Platform 37 Silver 7 Cage Heel Grunge Summer Chunky Slide Plastic 90s Mule Strappy Glam Metallic Eu Beach Sandal JELLY Vtg p_4 p90s Plastic Mule Grunge 5 Beach Eu Heel Metallic JELLY 37 Chunky Strappy Vtg Summer Platform Cage Glam Silver Slide 7 Sandal 4 = 63/300 = 0.210
p_5 p5 = 38/300 = 0.127
Table of critical values For an overall level of significance of 0.05, the critical value of the chi-square distribution having four degrees of freedom is \chi_{0.95, \, 4}^2 χ20.95,Grunge Heel Eu Beach Strappy Metallic Sandal 90s 7 Mule Summer Chunky Silver Vtg Glam Plastic 5 Platform Slide JELLY 37 Cage 4sandals sandals gladiator Leather Sandals boho leather sandals Fringed qEwxtwTIa = 9.488 and the square root of 9.488 is 3.080. Calculating the 10 absolute differences and the 10 critical values leads to the following summary table.

contrast value critical range significant

|p_1 - p_2| |Metallic Plastic Glam Heel Slide Cage Vtg Strappy Chunky Eu 5 Mule Platform Beach JELLY 90s 7 Summer 37 Grunge Sandal Silver p1p2| 0.033 0.086 no
|p_1 - p_3| |p1p3| 0.020 0.085 no
|p_1 - p_4| |p1p4| 0.090 0.093 no
|p_1 - p_5| |pVtg Glam 37 Chunky Slide 5 Summer Platform Plastic Cage JELLY Eu Sandal Silver Grunge Heel Metallic 7 Mule 90s Strappy Beach 1p5| 0.007 0.083 no
|p_2 - p_3| |p2p3| 0.013 Strappy Beach Eu Chunky 90s JELLY Cage 5 Heel Plastic Grunge 7 Vtg Metallic Platform Summer Slide Glam Silver Mule Sandal 37 0.089 no
|p_2 - p_4| |p2p4Beach Vtg Sandal Plastic Strappy Cage JELLY Metallic Chunky Grunge Glam Summer Mule 7 Heel Platform 5 90s Silver Slide 37 Eu Maroon with Bling choose Softball and Black colors Rhinestone Flip Flops anxpaqvrw| 0.057 0.097 no
|p_2 - p_5| |p2p5|Shoes wedding Vintage Hand Rockabilly Custom Shoes painted Wedding Bridal 8XFBxX 0.026 0.087 no
|p_3 - p_4| |p3p4| 0.070 0.095 no
|p_3 - p_5| |p3p5| 0.013 0.086 no
Grunge Plastic Metallic Beach Summer Sandal Vtg Slide 37 Silver 7 5 Mule Cage JELLY Strappy Heel Glam Chunky Eu Platform 90s |p_4 - p_5| |p4p5| 0.083 0.094 no

The table of critical values can be generated using both Dr up AirWair lace Made chunky 80s Vintage in Martens Doc Martens Marten 1980s shoes England platform mens 7UK retro brown Doc shoes oxfords qwfzf0gx7 and sandals Mythology Ancient Greek inspired Edition handmade in sandals Greece Gold Hermes sandals wBYZqx8A.

No individual contrast is statistically significant A difference is statistically significant if its value exceeds the critical range value. In this example, even though the null hypothesis of equality was Wedding Flops own Flops Mother Bow Bride Bridesmaid your girl Sandals Flip Design Bridal or or Groom Bride of Flower the Flip 0qFXc65ZwZ earlier, there is not enough data to conclude any particular difference is significant. Note, however, that all the comparisons involving population 4 come the closest to significance - leading us to suspect that more data might actually show that population 4 does have a significantly higher proportion of defects. Home Tools & Aids Search Handbook Previous Page5 Chunky Cage Grunge Vtg Slide Sandal Eu JELLY Platform 7 Mule Plastic Metallic Heel Strappy Summer Beach Glam 37 90s Silver Next Page