accuracy of digitized maps and statistical testing of these 
results. This study aims to introduce a method of determining 
the number of sample map sheets required to evaluate the 
accuracy of digital maps considering consumer and producer 
constraints. 
2. STATISTICAL EVALUATION OF DIGITIZED 
MAPS 
2.1 Producer risk and consumer risk 
The accuracy of all the maps can be assumed as one hypothesis. 
The testing of the hypothesis involves determining whether the 
digital map is accurate or not but because the position of the 
producer and consumer is different, different results are 
obtained depending on whose position is considered when 
establishing the hypothesis. 
The hypothesis from the position of the producer 
H, : The accuracy of the digitized maps are as accurate or more 
accurate than the requirement. 
Hi; : The accuracy of the digitized maps are less accurate than 
the requirement 
If Qo is the required accuracy, the following equations can be 
made. 
Ho: Q2 Qo 
Hi: Q«Qo 
If the test is made with 5% test level , 1.e. 9596 confidence 
level, this means that 1f the result is not included in the left 
0.05 part of the of Fig. 2.1, the test 1s accepted. But from the 
position of the consumer the following equations can be made. 
Ho:Q «Qo 
Hi: .Q&Qo 
And the test is accepted if the result is not included in the right 
0.05 part of the Fig. 2.1. 
  
  
  
  
Fig 2.1 Test of the left end and right end 
Even though the required accuracy 1s the same the result can be 
different depending on the position when the hypothesis is 
established. If the minimum required accuracy is Qi, the 
hypothesis is established from the position of the consumer and 
this hypothesis 1s of error type 1, i.e. the probability that the Ho 
is not rejected despite the map 1s less accurate is 0.05 and this 
is the risk of the consumer. From the producer position, it is 
advantageous that the probability of Qu which is higher than 
Qr being rejected be minimized. This is error of type 2, this 
means minimizing the probability of rejecting H; despite being 
accurate (producer risk) and this can be achieved by increasing 
the consumer risk or by increasing the number of samples. 
Illustrating this with figures, Qi is fixed to the minimum 
required map accuracy and the hypothesis Ho is accepted as 
long as the probability that accuracy 1s lower than Qi, is not 
less than 5%. The critical level Qr 1s computed with the 
assumption that map accuracy has the accuracy of Qi and as 
the probability that Qr has more that 596 of the samples. If the 
ratio of accurate samples is larger than or is equal to Qr, Ho 
is rejected and the map accuracy is accepted as being more 
accurate or is equal to. than Qi. 
The producer risk is the probability that the maps are not 
selected, i.e the probability of not being selected despite Qu 
> Qu and this is shown as the region smaller than Qr. This 
can be seen from the first graph of Fig. 2.2, when the number 
of samples is small, the risk of the producer is more than 50%, 
and this means that it 1s difficult for the map to be evaluated as 
being accurate. This risk can be reduced by increasing the 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996 
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