In this project we will look at historical temperature records for several cities and use statistical methods to determine whether the data shows any significant patterns or trends in temperature over time.
The SPSS data file for the project, TempRecs.sav is posted on Piazza along with Excel version. The file contains theAnnual Average Temperature records for two cities: New York, USA and Sydney, Australia. For each year, theAnnual Average Temperature value is calculated by averaging high temperature readings from every day of that year, observed in a specific location, Central Park for New York and Observatory Hill for Sydney.
In the project data file, three variables are recorded for each data point: the year (“year”), the Annual Average Temperature for NYC (“NYCtemp”) and theAnnual Average Temperature for Sydney (Sydtemp”.) The data are sorted by year in ascending order. For your convenience, Sydney temperatures have been converted to Fahrenheit.
Original data sources:
(for NYC)http://www.bom.gov.au/jsp/ncc/cdio/weatherData/av?p_nccObsCode=36&p_display_type=dataFile&p_startYear=&p_c=&p_stn_num=066062(for Sydney)
a)Use SPSS to produce a scatter plot of the temperatures for New York City using the “year” as x-axis.
b)Provide a paragraph describing whether you see any trends or patterns in the data from your graph.
c)Produce a similar plot for Sydney.
d)In a paragraph, describe what you see for that city e) Describe any similarities and/or differences you observe between Sydney and New York City.
Online, find the temperature records for the city of your choice, the records have to go back at least 120 years. In one sentence, explain why you chose this specific city. Repeat Exercise 1 for your city.
a)Use SPSS to find summary measurements for the annual average temperatures in New York City over the entire recorded period (1869-2013): min, max, mean, median and standard deviation.
Identify the hottest year and the coldest year.
b)Use SPSS to make a Box Plot of the data set.
c)Repeat this exercise for the historical temperature values in Sydney.
d)Write a paragraph describing how the two cities differ in temperature. Hint: Base you answer on any notable differences you observe in the two Box Plots.
Extra Credit: Repeat exercise 2 for the city of your choice.
a)Use SPSS to obtain a frequency distribution histogram of the annual average temperatures in New York City. Describe the “shape” of distribution.
b)Repeat the process for Sydney, using the same class limits you had for New York City.
c)In a paragraph, describe any similarities and differences you observe between the shapes of the two distributions and interpret the meaning of these differences.
Extra Credit: Repeat exercise 3 for the city of your choice.
Exercise 4ALimit your attention to the most “recent” temperature data, (which we define as years 1990-2013), for New York City. Answer the following questions:
- For how many years during the recent period, did the annual temperature rise above the historical mean calculated for the entire period? Does this represent a reasonable, relatively large or relatively small percentage of the recent years?
- Of the 25 warmest years in recorded history, what percentage occurs during the recent period? Do you think the recent period has more or less than its fair share of warmer years? (Hint: It may help to re-sort the data according to temperature).
- Is the mean temperature for the recent period higher or lower than that of the entire period? Calculate the z-score for the recent mean based on the mean and standard deviation for the entire period. What does the value of the z-score tell you about the difference between the two means?
- Draw a Box Plot for the recent years and place it next to the Box Plot obtained from the data corresponding to the years prior to 1990. Are there any noteworthy differences between the two?
- Write a paragraph to summarize your findings: are NYC annual temperatures notably different in recent times from what they were in the earlier part of the observation period. In what way?
Repeat the process for Sydney
Extra Credit: Repeat exercise 4 for the city of your choice.
a) Use a statistical package to find the value of the linear correlation coefficient between “year” and “NYCtemp”b) Is the correlation significant? Explain the reason for your answerc) If the correlation is significant, what does it imply about the trend in temperatures?d) Find the equation for the least squares regression (LSR) linee) Interpret the meaning of the slope of the LSR line.f) Based on the equation of LSR line, what is the “best predicted” value for the NYC Annual Average Temperature for 2013? How accurate is the prediction?g) Can we use this LSR line equation to predict the Annual Average Temperatures for the future? Explain.h) Write a paragraph to summarize your findings: Is there statistically significant evidence of any pattern or trend in temperature over the observation period in NYC?
Exercise 5B Repeat the process for Sydney.
Extra Credit: Repeat exercise 5 for the city of your choice.
- Does your analysis of the historical temperature data for several cities, provide evidence for the existence of the temperature increasing trendaround the world? Why or why not?
Include one graph or chart to support your claim.
- Can you conclude, based on your analyzes, whether the Global Warming is occurring? Why or why not?