The sampling problem should have no impact on spend berthing costs, and insurance, “fixed” – which are represented by the y intercept in fig. 1 (£2,739 estimated this way - £2,991 when estimated directly from bids) but will impact on spend, in which servicing, chandlery, “variable” PPE, training and supplies have been included, which this graph then estimates as £41.44 per day. 2. On the confidence in the data As a consequence of the above issues, rather than simply calculate standard errors or confidence intervals, neither of which would give a robust indication of the likely spread of the estimates, the estimates generated from the sample have been treated in two ways: 1. For the optimistic estimate, it has been assumed that the sample is truly random and totals have simply scaled the average variable spend over the whole sample to total berth availability. This will tend to overestimate the spend, as it assumes that there is an equal probability of sampling any berth-holder whatever their attendance rate at the marina. This will tend to bias the estimates towards the spend rates of more frequent attendees. 2. For the pessimistic estimate, the scaled estimate of berth holders’ variable spend has been remodelled, using a weighting based on the probability of sampling a person with a given attendance rate on any given day. The model assumes that all days of the year are equivalent in terms of sampling probabilities. This will tend to bias the estimates towards the spend rates of less frequent attendees and hence underestimate overall variable spend. The true of variable spend should fall somewhere between the two as the actual sample of different frequency attendees will fall somewhere between the two, given that the sample days were all in the summer holidays and mainly on weekends and bank holidays. Sampling on these days should yield a much higher probability of actually sampling low rate attendees “favourable” than that used in the pessimistic estimate. It is difficult to see a justifiable way of modelling the sample probabilities for this intermediate situation that wouldn’t simply be a guess, so the between the optimistic and pessimistic methods has been taken as the best estimate available.
The sampling problem should have no impact on “fixed” spend – berthing costs, and insurance, which are represented by the y intercept in fig. 1 (£2,739 estimated this way - £2,991 when estimated directly from bids) but will impact on “variable” spend, in which servicing, chandlery, PPE, training and supplies have been included, which this graph then estimates as £41.44 per day. 2. On the confidence in the data As a consequence of the above issues, rather than simply calculate standard errors or confidence intervals, neither of which would give a robust indication of the likely spread of the estimates, the estimates generated from the sample have been treated in two ways: 1. For the optimistic estimate, it has been assumed that the sample is truly random and totals have simply scaled the average variable spend over the whole sample to total berth availability. This will tend to overestimate the spend, as it assumes that there is an equal probability of sampling any berth-holder whatever their attendance rate at the marina. This will tend to bias the estimates towards the spend rates of more frequent attendees. 2. For the pessimistic estimate, the scaled estimate of berth holders’ variable spend has been remodelled, using a weighting based on the probability of sampling a person with a given attendance rate on any given day. The model assumes that all days of the year are equivalent in terms of sampling probabilities. This will tend to bias the estimates towards the spend rates of less frequent attendees and hence underestimate overall variable spend. The true of variable spend should fall somewhere between the two as the actual sample of different frequency attendees will fall somewhere between the two, given that the sample days were all in the summer holidays and mainly on weekends and bank holidays. Sampling on these “favourable” days should yield a much higher probability of actually sampling low rate attendees than that used in the pessimistic estimate. It is difficult to see a justifiable way of modelling the sample probabilities for this intermediate situation that wouldn’t simply be a guess, so the between the optimistic and pessimistic methods has been taken as the best estimate available.