Unit 1 Section 1 Exercise Answers

It is suspected that pond farming of sturgeon in Florida could become a large industry due to the rapid growth, value of processed sturgeon eggs (caviar) as well as the excellent quality of the fish meat. The composition of the fish diet is critical to all of the above factors. A researcher wishes to estimate the growth rate over six months of sturgeon maintained on two different commercial fish foods. Forty sturgeon fingerlings are selected from a large nursery pond and each is randomly assigned to one of the two diets, with twenty fish to each diet.

1. What is the population of interest here? [Sturgeon raised in ponds, although the statistical population will be weight of sturgeon measured over time.]
2. What characteristics of the population are of interest to the researcher? [Change in weight or size over time. Although, what we will be most interested in comparing are things like average growth rate or average final weight. From a production point of view, we might be interested in the uniformity (variability) of final weight as well.]
3. What kind of sample was selected? [Forty sturgeon fingerlings selected from the nursery pond. The report doesn't say how they were selected. If a net or poreous bag were used they we might assume selection was at random. Are there biases in the sample due to the selection method? A net has openings that the very small fingerlings might slip through. This might provide a more uniform set of fingerlings for the subsequent experiment. Randomness is used in the assignment of fish to the diet treatment, hence any potential biases of the selection process would be shared alike by the two treatment groups.]
4. Where do you expect to find variability in responses?[Each fish has a slightly different genetic makeup hence each will have its own growth trajectory. In addition, each fish will have lessor or greater success in getting food each day leading to variability in growth from day-to-day. Hence one would expect to find fish-to-fish variability as well as find differences between the two diet groups.]
5. A comparison is going to be made between the diets, what aspects of the effect of the diets on the population will be compared? [Two characteristics come to mind immediately. The first is average growth rate. The effect of diet may be to lower or raise the average growth rate for one group over the other. The second response is the average final weight. At the end of the study, we simply forget the time series nature of the data and concentrate on whether the two groups have the same means at final weighting.]

Sturgeon can grow to fairly large sizes, sizes typically larger than other freshwater fish (such as catfish or talipia) grown commercially in ponds. You have been asked to help a commercial sturgeon grower assess three commercial fish scaling devices for their use with sturgeon. Through each scaling machine you will pass 10 fish and at the end assess the completeness of scale removal.

1. What is the population of interest here?[The population of interest consist of pond grown sturgeon. From a statistical point of view, the population is the final completeness of scale removal for pond grown fish]
2. What characteristics of the population are of interest to the researcher? [Completeness of scale removal for pond grown sturgeon. Although, in reality what we will be concentrating on is the average proportion of scale removal for the three treatment groups. From a production point of view, we might also be interested in the uniformity (variability) in scale removal among the three treatments.]
3. What kind of sample was selected? [The description does not address this issue does it. The thirty fish needed from the study could have been selected at random for the same pond. The 30 fish could have been personally selected from a larger collection of fish for uniformity of size. ]
4. Where do you expect to find variability in responses? [ Variability in the responses can be found from fish-to-fish as well as between methods. That is, scaling method 1 might do a better job than scaling method 2 resulting in different average scores for the two methods. In addition, due to differences in body shape, each scaling device will do a better or poorer job of scaling than the average. ]
5. A comparison is going to be made between the scaling devices, what aspects of the effect of the processing will be compared? [ Clearly we might wish to compare the average proportion of scale removed. We might also choose to compare the median percent of scale removed. In fact, any of the measures of central tendency could be used as the basis for the comparison. We could also compare any of the measures of the variability if consistency of scaling were the interesting characteristic of the devices.]

Fish are at the top of the food chain and as such can be excellent bioaccumulators of contaminants. There is some concern that since sturgeon are bottom feeders, they may have higher exposure to contaminated bottom sediments and as such, eating commercially grown sturgeon might pose a health risk. The first step in a risk assessment is determining the level of contaminant in the fish meat. You select 3 fish from each of two ponds from each of 3 commercial growers (3 x 2 x 3 = 18 total fish). From each fish you select two samples of fish meat, one from the white (muscle) layer and one from the dark (fatty) layer. Each meat sample is then assessed for its level of contamination.

1. What is the population of interest here? [ The population of interest is the contaminant level of sturgeon fishes in commercially grown ponds. The population here relates to a broader population than simply the two ponds we sample from since we would like, in the future to extrapolate the study findings to all sturgeon grown in all commercial ponds, at least all those grown in the geographical region of the study. Note that many times in risk assessments we are only interested in one pond that is suspected of being contaminated. In this case, the population of interest would be just those sturgeon grown in that pond, but this could include all past and future sturgeon grown in the pond.]
2. What characteristics of the population are of interest to the researcher? [ We might be interested in average contaminant concentrations. From a risk perspective we might be more interested in some upper percentile of the distribution, say the 90th, 95th or 99th percentiles (something EPA has been debating recently). We might also be interested in something like the standard deviation, worring that while the mean were low there could be a lot of variability from fish-to-fish which would present a different risk perspective than if overall the average level were high but the variability low.]
3. What kind of sample was selected? [The scenario description doesn't say does it. This is fairly common. We can only assume that fish were selected at random. An associated question might be, were the fish of similar size and/or age. If not, where fish from one pond/grower different in size from fish of another pond/grower?]
4. Where do you expect to find variability in responses? [ Certainly we expect to find variability from fish-to-fish within a pond. We might also expect to find variability in average concentrations among ponds under a growers management and we might also expect to find variability in average concentrations in fish between growers. ]
5. A comparison is going to be made between the fish meat layers, what aspects will be compared? [In this study there are two "Factors" being considered. One comparison is in average concentrations among growers. Are there differences among growers in the average concentrations of fish meat. The second comparison might be between the white and dark meat components. Is average concentration of white meat different from average concentrations of dark meat. A secondary comparison is whether the white/dark meat comparison is the same for all growers. This if dark meat has higher concentrations than white meat, is this pattern consistent for all growers?]

Over one-hundred years ago, sturgeon meat could be found in most fish markets along the US Eastern seaboard. Overfishing reduced stocks to commercially unsustainable levels and sturgeon were no longer available at the market. Since Florida is thinking of investing in sturgeon fish production, it has been determined that a marketing survey is needed to assess potential consumer acceptance. Three eastern US cities of comparable size are chosen for the initial survey. In each city, five supermarkets are selected as test sites. On a prespecified day, shoppers at each selected supermarket are offered processed sturgeon meat to taste and asked to complete a short questionnaire about aspects of the meat.

1. What is the population of interest here? [ The population of interest is the preference scores for processed sturgeon meat in urban dwellers along the US Eastern seaboard. Note that the population is not the people but the response we hope to elicit from the people. ]
2. What characteristics of the population are of interest to the researcher? [The characteristic of interest could be any number of things. It could be the average taste preference score for cities and supermarkets in cities. If preference scores were discrete (e.g. "Low", "Med", "High", "Don't Care" or a 1 to 10 scale with only integer values) then we might be interested in the relative frequences in each of the response categories. We might also be interested in the median preference score, the min or max, actually any of the basic statistics might be of interest here.]
3. What kind of sample was selected? [The protocol does not come out and say directly what kind of sample this is. Clearly on any one day, the individuals selected represent a "convience sample", that is, this is a sample of just those individuals who happened to be there at the same time the surveyer was working. How representative would this sample be of the overall populations to which we plan to draw inferences. Hopefully the survey is replicated on a number of days and different times of the day in order to get good representation of shoppers at the store. Could a random sample be drawn here? Probably not. Could more randomness be included in the sampling protocol? Certainly it can. How do you think this could be done? ]
4. Where do you expect to find variability in responses? [We will get variation in individual-to-individual preference scores within a store on a given day. We may also have variation between days within a store as well as time of the day when the survey was taken. We will also have variation between stores in distribution of responses or in distribution statistics such as measures of central tendency (i.e. in means, medians, midrange) or in variability (standard deviation, range). As you can see there are a number of factors that might need considering if we were to design such a survey.]
5. A comparison is going to be made between the cities, what aspects will be compared? [ This is a good question. Do we compare average scores, variance in scores, median scores, etc. ? Of course all these descriptive statistics are possible. Another choice might be to compare the proportion of responses in a given category (i.e. compare fractions of responses that recored "High".) A further choice might be to simultaneously compare the relative frequences in all response categories between the cities. ]