inference kiwi
problem
(Achieved comments in bold)
The kiwi is the iconic bird that inspired Australian soldiers during the First World War to call their New Zealand comrades 'Kiwis'. The bird can't fly, has loose, hair-like feathers, strong legs and no tail. According to the Department of Conservation (https://www.doc.govt.nz/nature/native-animals/birds/birds-a-z/kiwi/) There are about 100,000 kiwi living in New Zealand. Having grown up with this national emblem for most of my life I am interested in how this vulnerable bird is being protected. The Department of Conservation and many community conservation groups are helping to build up kiwi numbers. They take eggs from the wild and release the chicks in predator-free zones such as an island or fenced sanctuary.
NZ Operation Nest Egg™ (BNZONE) involves collecting eggs from the wild, hatching the eggs in captivity, raising the chicks at crèche sites until they reach a weight of 1200 g or more (at this weight they are considered likely to be able to defend themselves against stoats), then returning the juvenile kiwi to the wild. A BNZONE bird has a 65% chance of surviving to adulthood compared with just 5% for wild-hatched and raised chicks.When they are big enough, they are returned to the wild. (Taxon plan for Northland brown kiwi 2010-2019 Craig, Gardner, Sporle & Renwick)
The little spotted kiwi female (not mentioned in the data sample) weighs on average only 1.3 kilograms and lays an egg weighing 300 grams!
NZ Operation Nest Egg™ (BNZONE) involves collecting eggs from the wild, hatching the eggs in captivity, raising the chicks at crèche sites until they reach a weight of 1200 g or more (at this weight they are considered likely to be able to defend themselves against stoats), then returning the juvenile kiwi to the wild. A BNZONE bird has a 65% chance of surviving to adulthood compared with just 5% for wild-hatched and raised chicks.When they are big enough, they are returned to the wild. (Taxon plan for Northland brown kiwi 2010-2019 Craig, Gardner, Sporle & Renwick)
The little spotted kiwi female (not mentioned in the data sample) weighs on average only 1.3 kilograms and lays an egg weighing 300 grams!
George A. Clark Jr, in his review on the body Weights of Birds states "I consider uses of weights as standards for body size, in assessing the physiological condition of individuals and in the analyses of ecological communities". (The Cooper Ornithological Society 1979).
Within the species of kiwi it is known that the female bird is heavier than that of the male bird, a phenomena described under 'dimorphism', which has modern day scientists scratching for answers. Female kiwi also lay a very large egg in proportion to their size (20%). Males usually are larger than their female counterparts in most species. However, in birds and some small rodents, those species where the male tends to exhibit 'motherly' characteristics and does most of the egg incubating may be smaller. This is disputed by some scientists. (https://web.stanford.edu/group/stanfordbirds/text/essays/Size_and_Sex.html). According to www.backyardkiwi.org , female kiwi are bigger than male kiwi, because she lays 2 large eggs in close succession (10 days apart). I cannot find any serious research that supports this argument but it is an idea that has some traction with non scientific websites I have found..
I want to see if female kiwi are larger than their male counterparts like a few other species I have read about discussed under dimorphism above.
The variable I will investigate are the weights of male and female Kiwi in kg. The population is the sample of 700 kiwi from the NZGrapher database. I would like to further investigate if the trend found in the NZ population is reflected in each of the species of North Island Brown, Southern Tokoeka and Great Spotted kiwi. The data for each species is also listed in sample from NZGrapher.
question
So my question is - I wonder what the difference is between the median weights of male and female kiwi in the sample of kiwi data from NZGrapher? 1
I will use the median (as opposed to the mean) as a measure of the average weights as this is less affected by large (or small) extreme values or outliers.
I will use the median (as opposed to the mean) as a measure of the average weights as this is less affected by large (or small) extreme values or outliers.
graphs and data 2
box and dot plot for the analysis
analysis 3
General observations: My initial impression of these two samples is that there is a considerable difference in the median weights between female and male kiwi from the NZGrapher sample representing the population of kiwi in New Zealand. The dot plot for female kiwi has a much wider spread than the dot plot for male kiwi. However, both female and male kiwi graphs follow a normal distribution curve (unimodal or symmetrical). There are some small gaps in the dot plots of both female and male graphs.
Central Tendency 3
Central Tendency:
The median weight for female kiwi is greater at 2.90 kg and the median weight for male kiwi is 2.25 kg, a difference of 0.65 kg. This indicates that the average female kiwi could be heavier than average male kiwi back in the population (data base sample of NZGrapher). This is supported by my research from www.puketi.org.nz that on average female kiwi are larger than male kiwi.
The median weight for female kiwi is greater at 2.90 kg and the median weight for male kiwi is 2.25 kg, a difference of 0.65 kg. This indicates that the average female kiwi could be heavier than average male kiwi back in the population (data base sample of NZGrapher). This is supported by my research from www.puketi.org.nz that on average female kiwi are larger than male kiwi.
overlap-shift-spread-shape 3
Middle 50% (Interquartile range):
Overlap:
The middle 50% (IQR) for female kiwi weights are between 2.622 kg and 3.192 kg, whereas the middle 50% (IQR) for male kiwi weights are between 2.069 kg and 2.429 kg. There is no overlap of the middle 50% (IQR's) for female and male kiwi.
Shift:
The lower quartile for female kiwi weights (2.622 kg) is higher than the upper quartile for the male kiwi weights (2.429 kg)
Spread:
The IQR (middle 50%) for female kiwi weight is 0.57 kg whereas the IQR for male kiwi weight is 0.36 kg. This indicates that there is more variation in the weights of female kiwi. Overall visually the female kiwi seem to be more spread out than the male kiwi.
Shape:
The distribution of the weights of female and male kiwi are both relatively symmetrical with the with the LQ and UQ for female weights (2.622 kg and 3.192 kg, respectively) about 300 g from the median of 2.9 kg. Similarly, the LQ and UQ for male weights (2.069 kg and 2.429 kg respectively) about 180 g from the median of 2.246 kg.
I think the distributions of weights of female and male kiwi would also be symmetrical in the population of kiwi in New Zealand.
The distribution of the weights of female and male kiwi are both relatively symmetrical with the with the LQ and UQ for female weights (2.622 kg and 3.192 kg, respectively) about 300 g from the median of 2.9 kg. Similarly, the LQ and UQ for male weights (2.069 kg and 2.429 kg respectively) about 180 g from the median of 2.246 kg.
I think the distributions of weights of female and male kiwi would also be symmetrical in the population of kiwi in New Zealand.
special features 3
Special features:
Looking at the graphs I can see that the female kiwi have one sample that weighs more than all other kiwi. Referring to NZGrapher this particular bird is a great spotted kiwi weighing 4.143 kg. This bird could be an older one or carrying an egg which can account for up to 20% of a kiwi's body weight. https://www.kiwisforkiwi.org/about-kiwi/kiwi-facts-characteristics/enormous-egg/It could also have been kept in captivity and 'fattened up' before its release. This species of kiwi is generally larger than the other species like the North Island brown kiwi and the Southern Tokoeka. Age is another factor that might account for smaller birds of each gender as younger birds would be lighter than older birds, heavier.
[need to improve] According to Chris Wild www.stat.auckland.ac.nz/~wild/from the statistics dept Auckland University, the symmetrical nature of the distribution can be reflected in a sample eg the heights of YR 9 students. This is a natural phenomena that occurs in nature. For example, the heights of a sample of students at a school, the lengths of a sample of whales in the ocean. This means that the majority of the data are at a certain distance around the median, with some values being lower (shorter or lighter) at one end of the distribution and larger or longer at the other end of the distribution. This would easily account for the unimodal or normal distribution characteristics shown in the kiwi population from NZGrapher.
Looking at the graphs I can see that the female kiwi have one sample that weighs more than all other kiwi. Referring to NZGrapher this particular bird is a great spotted kiwi weighing 4.143 kg. This bird could be an older one or carrying an egg which can account for up to 20% of a kiwi's body weight. https://www.kiwisforkiwi.org/about-kiwi/kiwi-facts-characteristics/enormous-egg/It could also have been kept in captivity and 'fattened up' before its release. This species of kiwi is generally larger than the other species like the North Island brown kiwi and the Southern Tokoeka. Age is another factor that might account for smaller birds of each gender as younger birds would be lighter than older birds, heavier.
[need to improve] According to Chris Wild www.stat.auckland.ac.nz/~wild/from the statistics dept Auckland University, the symmetrical nature of the distribution can be reflected in a sample eg the heights of YR 9 students. This is a natural phenomena that occurs in nature. For example, the heights of a sample of students at a school, the lengths of a sample of whales in the ocean. This means that the majority of the data are at a certain distance around the median, with some values being lower (shorter or lighter) at one end of the distribution and larger or longer at the other end of the distribution. This would easily account for the unimodal or normal distribution characteristics shown in the kiwi population from NZGrapher.
looking at trends within the species (not for Achieved)
I would like to investigate the sample of data further by comparing the weights of female and male kiwi by species. There are three species represented in the data sample of 700 birds. These are:
Great Spotted Kiwi = 15000 birds (sample size in NZGrapher = 163)
North Island Brown Kiwi = 25000 birds (sample size in NZGrapher = 275)
Southern Tokoeka Kiwi = 26000 birds (sample size in NZGrapher = 262)
Missing from the sample are:
Rowi Kiwi with only 500 very protected birds in the wild. (www.kiwisforkiwi.org/about-kiwi/kiwi-species/rowi/)
Little Spotted Kiwi with 1500 birds in the wild. Because the number of birds in these populations are relatively small compared to the NZ population (2000/66000 = 3%) I don't think the data would be greatly affected by this fact. However, they are still not represented and an accurate analysis should account for this.
Interestingly, kiwi female and kiwi males of this species share the same amount of time on the nest during incubation, as well as assistance from young "single" kiwi. This behaviour trait makes them unique in NZ. - www.kiwisforkiwi.org/about-kiwi/kiwi-species/rowi/)
Great Spotted Kiwi = 15000 birds (sample size in NZGrapher = 163)
North Island Brown Kiwi = 25000 birds (sample size in NZGrapher = 275)
Southern Tokoeka Kiwi = 26000 birds (sample size in NZGrapher = 262)
Missing from the sample are:
Rowi Kiwi with only 500 very protected birds in the wild. (www.kiwisforkiwi.org/about-kiwi/kiwi-species/rowi/)
Little Spotted Kiwi with 1500 birds in the wild. Because the number of birds in these populations are relatively small compared to the NZ population (2000/66000 = 3%) I don't think the data would be greatly affected by this fact. However, they are still not represented and an accurate analysis should account for this.
Interestingly, kiwi female and kiwi males of this species share the same amount of time on the nest during incubation, as well as assistance from young "single" kiwi. This behaviour trait makes them unique in NZ. - www.kiwisforkiwi.org/about-kiwi/kiwi-species/rowi/)
The graph below shows the comparison of weights between the three species of kiwi being studied. The North Island Brown and the Southern Tokoeka kiwi are very similar in terms of the median weight and distribution.
The smallest kiwi is a male Southern Tokoeka located in Fiordland weighing 1.57 kg. This could be a small or juvenile bird. Although the two species here look very similar, a bootstrap comparison shows that the NIbr kiwi are slightly larger on average and we can be confident this is by 62.5 to 117 grams.
This is also a reflection of the trend in the wider population sample data base on NZGrapher.
This is also a reflection of the trend in the wider population sample data base on NZGrapher.
making a formal inference
bootstrapping for the confidence interval 5
From the bootstrapping confidence interval we can see that the median weights of female kiwi is somewhere between be 0.596 and 0.718 kg more than the median weight of male kiwi.
conclusion
Based on looking at my sample I am reasonably confident that back in the population of all kiwi in New Zealand that the median weight of female kiwi will be more than the median weight of male kiwi. I can make this call as the bootstapping confidence interval tells us that the female median weight is likely to be between 0.596 kg and 0.718 kg more than the median weight of male kiwi. 6
I am also able to make a clear-cut call whether or not there is a substantial difference in the weights of female and male kiwi from the sample population of kiwi in New Zealand as there is a considerable gap between the middle 50% of both data sets, with the lower quartile of the middle 50% for the female kiwi at 2.622 kg is a higher than the upper quartile of the middle 50% for the male kiwi weight at 2.429 kg, a difference of 0.193 kg. My bootstrap confidence interval for the difference between the median female kiwi weights and median male kiwi weights indicates that a clear call can be made. That is, female kiwi are heavier on average than male kiwi.
I am also able to make a clear-cut call whether or not there is a substantial difference in the weights of female and male kiwi from the sample population of kiwi in New Zealand as there is a considerable gap between the middle 50% of both data sets, with the lower quartile of the middle 50% for the female kiwi at 2.622 kg is a higher than the upper quartile of the middle 50% for the male kiwi weight at 2.429 kg, a difference of 0.193 kg. My bootstrap confidence interval for the difference between the median female kiwi weights and median male kiwi weights indicates that a clear call can be made. That is, female kiwi are heavier on average than male kiwi.
I am basing this conclusion on the bootstrap confidence interval I calculated, which involves re-sampling from my original sample of 700 kiwi whose weight were recorded. The key assumption with this method is that my original sample was representative of the population of all NZ kiwi. As the trend of female kiwi weighing more than male kiwi was also observed within the three species of kiwi I think it reasonable to believe that my original sample is representative of the population.
I could further investigate to see if the trend is affected by location. For example compare a sample of kiwi from the North Island to a sample of kiwi from the South Island using the same weight variable. An extension to other organisms such as animals and fish could also be used to examine this trend.
For a more definite conclusion, the sample size would need to be increased to decrease the variation in the data. I would also include the other two species of kiwi which have not been represented in the sample. However I still believe that it would be found that there is a difference between the median weights of female and male kiwi.
I could further investigate to see if the trend is affected by location. For example compare a sample of kiwi from the North Island to a sample of kiwi from the South Island using the same weight variable. An extension to other organisms such as animals and fish could also be used to examine this trend.
For a more definite conclusion, the sample size would need to be increased to decrease the variation in the data. I would also include the other two species of kiwi which have not been represented in the sample. However I still believe that it would be found that there is a difference between the median weights of female and male kiwi.
I am assuming my original sample is representative of the population of all kiwi in New Zealand. I am fairly confident that, if I took another sample, even though the sample might be different including the graphs and summary statistics, I would still make the same call that female kiwi are weigh more than male kiwi back in the kiwi population. 4