Investigation
whose larger?
kiwi investigation
Problem
I wonder if the median weight of female kiwi are greater than the median weight of male kiwi found in the NZGrapher data base. I think that female kiwi are heavier than male kiwi because I discovered that they lay a very large egg (up to 20% of the birds body weight).
Plan
I will use the median weight (kg) to make an inference to see which gender of birds is larger/heavier in tha data set from NZGrapher.
I will use simple random sampling to select my samples from the NZGrapher database. There will be 100 samples taken, 50 from each.
Data
I wonder if the median weight of female kiwi are greater than the median weight of male kiwi found in the NZGrapher data base. I think that female kiwi are heavier than male kiwi because I discovered that they lay a very large egg (up to 20% of the birds body weight).
Plan
I will use the median weight (kg) to make an inference to see which gender of birds is larger/heavier in tha data set from NZGrapher.
I will use simple random sampling to select my samples from the NZGrapher database. There will be 100 samples taken, 50 from each.
Data
Analysis
Central Tendency
From the graph above I notice that the sample median for female kiwi is about 2.90 kg which is larger than the median weight for male kiwi at about 2.23 kg, a difference of 0.67 kg. This means that the female kiwi generally are heavier or larger than the male kiwi from the NZGrapher data base.
Central Tendency
From the graph above I notice that the sample median for female kiwi is about 2.90 kg which is larger than the median weight for male kiwi at about 2.23 kg, a difference of 0.67 kg. This means that the female kiwi generally are heavier or larger than the male kiwi from the NZGrapher data base.
Spread
I notice that the middle 50% of data (IQR) for females is 0.53kg,
(3.109 - 2.5565). This is larger than the middle 50 % of data (IQR) for males, 0.34 kg (2.393 - 2.049). This means there is more variation of weights within the sample of females.
I notice that the middle 50% of data (IQR) for females is 0.53kg,
(3.109 - 2.5565). This is larger than the middle 50 % of data (IQR) for males, 0.34 kg (2.393 - 2.049). This means there is more variation of weights within the sample of females.
Shape
Looking at the dot plot, I notice that the shape of the females data is skewed to the right and the shape of the males data is reasonably symmetrical.
Looking at the dot plot, I notice that the shape of the females data is skewed to the right and the shape of the males data is reasonably symmetrical.
Sampling Variation
If I did another sample my summary statistics would be different. This means the median and confidence intervals would also be different. However the population median would most likely still fall within the confidence intervals. Although if I took a larger sample the interval would have less variability and the confidence interval would be smaller.
Conclusion
From my samples gathered I am pretty sure that the population medians lie within my confidence intervals. The median weight for female kiwi lies between 2.78 kg and 3.01 kg. I am reasonably confident that from the NZGrapher database, the median weight for male kiwi lies between 2.16 kg and 2.31 kg. In conclusion from the results gathered the confidence intervals do not overlap therefore I can say that female kiwi are heavier than male kiwi from the NZGrapher database.
From my samples gathered I am pretty sure that the population medians lie within my confidence intervals. The median weight for female kiwi lies between 2.78 kg and 3.01 kg. I am reasonably confident that from the NZGrapher database, the median weight for male kiwi lies between 2.16 kg and 2.31 kg. In conclusion from the results gathered the confidence intervals do not overlap therefore I can say that female kiwi are heavier than male kiwi from the NZGrapher database.
MERIT EXCELLENCE
Problem
Within the species of kiwi I am already aware from my general knowledge that the female bird is heavier than that of the male bird, a phenomena described under the topic of 'dimorphism'. Dimorphism means that there is a difference in traits or characteristics within a given species. In shark species this usually refers to the difference in size between male and female. Dimorphic traits may differ so radically between sexes that they can be reliably used to differentiate males from females.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.
(https://web.stanford.edu/group/stanfordbirds/text/essays/Size_and_Sex.html).
So my question is:
I wonder if the median weights of female kiwi are greater than the median weights of male kiwi in the NZGrapher kiwi database. I will use the median weight as opposed to the mean weight as a measure of the average weight as this is less affected by large (or small) extreme values.
Plan
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 selected a sample of 100 birds, (50 from each gender) using simple random sampling from the NZGrapher database. Simple random sampling makes sure that each member of the Kiwi database which contains 700 samples, will have an equal chance of being selected. This means that the sample should be representative of the NZGrapher Kiwi database.
Using a large sample size of 100 means that the summary sample statistics produced are likely to be closer to the true median for the NZGrapher kiwi dataset than if a smaller sample size was taken.
Within the species of kiwi I am already aware from my general knowledge that the female bird is heavier than that of the male bird, a phenomena described under the topic of 'dimorphism'. Dimorphism means that there is a difference in traits or characteristics within a given species. In shark species this usually refers to the difference in size between male and female. Dimorphic traits may differ so radically between sexes that they can be reliably used to differentiate males from females.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.
(https://web.stanford.edu/group/stanfordbirds/text/essays/Size_and_Sex.html).
So my question is:
I wonder if the median weights of female kiwi are greater than the median weights of male kiwi in the NZGrapher kiwi database. I will use the median weight as opposed to the mean weight as a measure of the average weight as this is less affected by large (or small) extreme values.
Plan
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 selected a sample of 100 birds, (50 from each gender) using simple random sampling from the NZGrapher database. Simple random sampling makes sure that each member of the Kiwi database which contains 700 samples, will have an equal chance of being selected. This means that the sample should be representative of the NZGrapher Kiwi database.
Using a large sample size of 100 means that the summary sample statistics produced are likely to be closer to the true median for the NZGrapher kiwi dataset than if a smaller sample size was taken.
Central Tendency
Female kiwi have a median weight of 2.90 kg compared with the male median weight of 2.23 kg. From my sample, this suggests that female kiwi are heavier than males in the NZGrapher database.This is supported by my research from www.puketi.org.nz that on average female kiwi are larger than male kiwi.
Spread
I notice that the middle 50% of data (IQR) for females is 0.53kg. This is a larger spread than the middle 50 % of data (IQR) for males, 0.34 kg . This means there is more variation of weights within the sample of females. I would expect this trend to be present in length data in the NZGrapher database.
Shape
The female kiwi box plot shows some left skewing as the median is to the right of the box centre. However, the dot plot shows right skewing caused by the number of heavy females creating a data tail trailing to the right. The male data distribution is fairly symmetrical. I would expect that this distribution feature will likely be present back in the NZGrapher.
Female kiwi have a median weight of 2.90 kg compared with the male median weight of 2.23 kg. From my sample, this suggests that female kiwi are heavier than males in the NZGrapher database.This is supported by my research from www.puketi.org.nz that on average female kiwi are larger than male kiwi.
Spread
I notice that the middle 50% of data (IQR) for females is 0.53kg. This is a larger spread than the middle 50 % of data (IQR) for males, 0.34 kg . This means there is more variation of weights within the sample of females. I would expect this trend to be present in length data in the NZGrapher database.
Shape
The female kiwi box plot shows some left skewing as the median is to the right of the box centre. However, the dot plot shows right skewing caused by the number of heavy females creating a data tail trailing to the right. The male data distribution is fairly symmetrical. I would expect that this distribution feature will likely be present back in the NZGrapher.
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 and older birds, heavier.
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 and older birds, heavier.
Sample size
The larger the sample size, the closer the estimate will be to the true median. This is because larger sample sizes reduce variation. This means the confidence intervals will also be smaller. So in this example, the gap between the confidence intervals representing the two genders will be wider showing more separation of kiwi in the NZGrapher database.
I am fairly confident that if I took another sample, even though the sample might be similar but different, including the graphs and summary statistics and confidence intervals, I would still make the same call that female kiwi weigh more than male kiwi in the NZGrapher database. The true median values will still fall between the confidence intervals generated.
The larger the sample size, the closer the estimate will be to the true median. This is because larger sample sizes reduce variation. This means the confidence intervals will also be smaller. So in this example, the gap between the confidence intervals representing the two genders will be wider showing more separation of kiwi in the NZGrapher database.
I am fairly confident that if I took another sample, even though the sample might be similar but different, including the graphs and summary statistics and confidence intervals, I would still make the same call that female kiwi weigh more than male kiwi in the NZGrapher database. The true median values will still fall between the confidence intervals generated.
Conclusion
Based on looking at my graph and data I am pretty sure that the true median weights will fall within the confidence intervals shown. The median weight for female kiwi lies between 2.78 kg and 3.01 kg. The median weight for male kiwi lies between 2.16 kg and 2.31 kg. Because the confidence intervals do not overlap I can confidently say that female kiwi are heavier than male kiwi from the NZGrapher database.
Based on looking at my graph and data I am pretty sure that the true median weights will fall within the confidence intervals shown. The median weight for female kiwi lies between 2.78 kg and 3.01 kg. The median weight for male kiwi lies between 2.16 kg and 2.31 kg. Because the confidence intervals do not overlap I can confidently say that female kiwi are heavier than male kiwi from the NZGrapher database.
Further Investigation
The key assumption with this method is that my original sample was representative of the NZGrapher database. However, I notice that the 700 Kiwi in the data set are also a sample of the 50 thousand or so kiwi that exist in the wild. My inference is based on a database of 700 birds and not the whole population of kiwi in New Zealand. I could further investigate to see if the trend is affected by different species or even location of kiwi of which there are about 5 species spread throughout New Zealand. I could 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.
No other information is known about those species not listed in this investigation. However, based on this investigation, I feel confident to apply the same conclusion to those populations.
The key assumption with this method is that my original sample was representative of the NZGrapher database. However, I notice that the 700 Kiwi in the data set are also a sample of the 50 thousand or so kiwi that exist in the wild. My inference is based on a database of 700 birds and not the whole population of kiwi in New Zealand. I could further investigate to see if the trend is affected by different species or even location of kiwi of which there are about 5 species spread throughout New Zealand. I could 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.
No other information is known about those species not listed in this investigation. However, based on this investigation, I feel confident to apply the same conclusion to those populations.