Updated: Nov 11th, 2024

Daily Low Temperatures Across the Three Cities Report

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Introduction

Evaluation and comparison of weather across various states are significant. It aids in making important decisions such as choosing where to live and selecting a city to locate a business among others. The paper seeks to carry out an analysis to ascertain if there is a difference in weather patterns across three cities in the United States of America. The cities selected are New York City, Los Angeles, and Chicago. The three dependent variables that will be compared are low temperature, high temperature, and precipitation levels. Data will be collected over the same period across the cities. The analysis will focus on establishing whether the differences in values of the three variables across the cities are statistically significant. The tests that will be used are ANOVA and t-test. Also, the descriptive statistics of the variables will be compared.

Hypothesis and Research Questions

The paper seeks to carry out tests to ascertain if the weather patterns differ across the three states. The research questions and the hypotheses for the tests are presented below.

First

Research Question

Are there any differences in the daily low temperatures across the three cities?

Hypothesis

Null hypothesis: There is no difference in the daily low temperatures across the three cities.

H₀: µ_ltNY = µ_ltLA = µ_ltCH

Alternative hypothesis: There is a difference in the daily low temperatures across the three cities.

H₁: µ_ltNY ≠ µ_ltLA ≠ µ_ltCH

Second

Research Question

Are there any differences in the daily high temperatures across the three cities?

Hypothesis

Null hypothesis: There is no difference in the daily high temperatures across the three cities.

H₀: µ_htNY = µ_htLA = µ_htCH

Alternative hypothesis: There is a difference in the daily high temperatures across the three cities.

H₁: µ_htNY ≠ µ_htLA ≠ µ_htCH

Third

Research Question

Are there any differences in the daily precipitation across the three cities?

Hypothesis

Null hypothesis: There is no difference in the daily precipitation across the three cities

H₀: µ_pNY = µ_pLA = µ_pCH

Alternative hypothesis: There is a difference in the daily precipitation across the three cities.

H₁: µ_pNY ≠ µ_pLA ≠ µ_pCH

Fourth

Research Question

Are there any differences in low temperature, high temperature, and precipitation levels across the three cities?

Hypothesis

Null hypothesis: There is no difference in mean low temperature, high temperature, and precipitation levels across the three cities.

Alternative hypothesis: There is a difference in mean low temperature, high temperature, and precipitation levels across the three cities.

Data Collection

The data that will be used in the analysis is collected from the AccuWeather.com website (“United States Weather” par. 1). It is a website that contains historical data of various variables such as temperature, snow, and precipitation of various cities in the United States. The data that will be collected from the website is the daily low temperature for January (measured in Fahrenheit), daily high temperature for July (measured in Fahrenheit), and daily precipitation for July (measured in inches). Further, the data for the three variables were collected for the three cities (Baltagi 108). Besides, the data covered the same period across the three cities. The data collected for the analysis are presented in Table 1 below.

Table 1: Data

	New York City (1)			Los Angeles (2)			Chicago (3)
	Jan	July	July	Jan	July	July	Jan	July	July
Date	Low temperature	High temperature	Precipitation	Low temperature	High temperature	Precipitation	Low temperature	High temperature	Precipitation
	Fahrenheit	Fahrenheit	Inches	Fahrenheit	Fahrenheit	Inches	Fahrenheit	Fahrenheit	Inches
1	28	83	0.39	47	82	0	19	84	0
2	28	83	0	47	82	0	19	84	0
3	28	83	0	47	82	0	19	84	0
4	27	84	0	47	82	0	19	84	0
5	27	84	0	48	82	0	19	84	0
6	27	84	0	48	82	0	18	84	0.56
7	27	84	0.12	48	82	0	18	84	0.25
8	27	84	0	48	83	0	18	84	0
9	27	84	0.3	48	83	0	18	85	0.04
10	27	84	0	48	83	0	18	85	0
11	27	84	0	48	83	0	18	85	0.03
12	27	84	0	48	83	0	18	85	0.06
13	27	84	0	48	83	0	18	85	0.66
14	27	84	0.42	48	83	0	18	85	0
15	27	84	0.12	48	83	0	18	85	0
16	27	84	0	48	83	0	18	84	0.52
17	27	84	0	48	83	0	18	84	0.03
18	26	84	0.32	48	84	0.36	18	84	0.03
19	27	84	0	48	84	0.02	18	84	0
20	27	84	0	48	84	0	18	84	0
21	27	84	0	48	84	0	18	84	0
22	27	84	0	48	84	0	18	84	0
23	27	84	0	48	84	0	18	84	0
24	27	84	0	48	84	0	18	84	0
25	27	84	0	48	84	0	18	84	0
26	27	84	0	48	84	0	18	84	0
27	27	84	0.36	48	84	0	18	84	0
28	27	84	0	48	84	0	18	84	0
29	27	84	0	48	84	0	18	84	0.07
30	27	84	1.95	48	84	0	18	84	0
31	27	84	0	48	84	0	18	83	0

Analysis

Statistical Tests

The first three hypotheses will be tested using ANOVA. This can be attributed to the fact that ANOVA is the most suitable technique for the testing hypothesis that entails comparing the mean of more than one group. One-way ANOVA will be used because there is only one independent variable under each research question. The fourth hypothesis will be tested using an independent t-test. This can be attributed to the fact that the independent t-test is suitable for comparing the means between unrelated groups on the same variable. All the tests are carried out at the 95% confidence level (Verbeek 237). The results of all the tests are presented in the Tables below.

Table 2. Descriptive
		N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
		N	Mean	Std. Deviation	Std. Error	Lower Bound	Upper Bound	Minimum	Maximum
Lowtemp	1	31	27.06	.359	.065	26.93	27.20	26	28
	2	31	47.87	.341	.061	47.75	48.00	47	48
	3	31	18.16	.374	.067	18.02	18.30	18	19
	Total	93	31.03	12.522	1.298	28.45	33.61	18	48
Hightemp	1	31	83.90	.301	.054	83.79	84.01	83	84
	2	31	83.23	.805	.145	82.93	83.52	82	84
	3	31	84.19	.477	.086	84.02	84.37	83	85
	Total	93	83.77	.694	.072	83.63	83.92	82	85
prep	1	31	.1284	.36381	.06534	-.0051	.2618	.00	1.95
	2	31	.0123	.06464	.01161	-.0115	.0360	.00	.36
	3	31	.0726	.17622	.03165	.0079	.1372	.00	.66
	Total	93	.0711	.23858	.02474	.0219	.1202	.00	1.95

Table 3. ANOVA
		Sum of Squares	df	Mean Square	F	Sig.
Lowtemp	Between Groups	14413.355	2	7206.677	5.616E4	.000
	Within Groups	11.548	90	.128
	Total	14424.903	92
Hightemp	Between Groups	15.290	2	7.645	23.753	.000
	Within Groups	28.968	90	.322
	Total	44.258	92
prep	Between Groups	.209	2	.105	1.872	.160
	Within Groups	5.028	90	.056
	Total	5.237	92

Table 4. Multiple Comparisons
Tukey HSD
Dependent Variable	(I) State	(J) State	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
Dependent Variable	(I) State	(J) State	Mean Difference (I-J)	Std. Error	Sig.	Lower Bound	Upper Bound
Lowtemp	1	2	-20.806^*	.091	.000	-21.02	-20.59
	1	3	8.903^*	.091	.000	8.69	9.12
	2	1	20.806^*	.091	.000	20.59	21.02
	2	3	29.710^*	.091	.000	29.49	29.93
	3	1	-8.903^*	.091	.000	-9.12	-8.69
	3	2	-29.710^*	.091	.000	-29.93	-29.49
Hightemp	1	2	.677^*	.144	.000	.33	1.02
	1	3	-.290	.144	.115	-.63	.05
	2	1	-.677^*	.144	.000	-1.02	-.33
	2	3	-.968^*	.144	.000	-1.31	-.62
	3	1	.290	.144	.115	-.05	.63
	3	2	.968^*	.144	.000	.62	1.31
prep	1	2	.11613	.06003	.135	-.0269	.2592
	1	3	.05581	.06003	.623	-.0873	.1989
	2	1	-.11613	.06003	.135	-.2592	.0269
	2	3	-.06032	.06003	.576	-.2034	.0827
	3	1	-.05581	.06003	.623	-.1989	.0873
	3	2	.06032	.06003	.576	-.0827	.2034
*. The mean difference is significant at the 0.05 level.

Table 5. Independent Samples Test
		Levene’s Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	Lower	Upper
Lowtemp	Equal variances assumed	.372	.544	-233.966	60	.000	-20.806	.089	-20.984	-20.629
Lowtemp	Equal variances not assumed			-233.966	59.834	.000	-20.806	.089	-20.984	-20.629
Hightemp	Equal variances assumed	42.469	.000	4.392	60	.000	.677	.154	.369	.986
Hightemp	Equal variances not assumed			4.392	38.212	.000	.677	.154	.365	.990
prep	Equal variances assumed	8.992	.004	1.750	60	.085	.11613	.06637	-.01662	.24888
prep	Equal variances not assumed			1.750	31.892	.090	.11613	.06637	-.01907	.25133

Variables

The variables that will be tested are daily low temperature, high temperature, and precipitation. These are the dependent variables. It is worth mentioning that the data for the three variables will be collected over the period across the three cities. The three cities represent the groups that will be used when carrying out the test. The test will ascertain if there is a difference in three variables across the three cities.

Results

Descriptive statistics

Despite being in the United States of America, the three cities had different levels of temperature and precipitation. From the results of descriptive statistics, it can be observed that Los Angeles (47.87°) had the highest value of average low temperature while Chicago (18.16°) had the lowest mean value of low temperature. Further, it can be observed that Chicago (0.374) had the highest variation in low temperature while Los Angeles (0.341) had the least variation in temperature. For the second variable, high temperature, it can be observed that Los Angeles (83.23°) had the lowest mean value of high temperature while Chicago (84.19°) had the highest mean value of high temperature (Mankiw 341).

In the case of standard deviation, New York (0.301) had the lowest value while Los Angeles (0.805) had the highest value. Further analysis shows that there was a slight difference between the mean high temperatures across the three cities. Under precipitation, it can be noted that New York (0.1284in) had the highest mean value while Los Angeles (0.0123in) had the lowest value of mean precipitation. A similar trend was observed in the case of standard deviation. The descriptive statistics show that the values of the three variables were different across the three cities. The results do not give much information on whether the differences are statistically significant (Baltagi 108). The significance of these differences will be evaluated in the subsequent section.

ANOVA

As mentioned above, ANOVA will be used to test the significance of the differences that are observed in the three dependent variables across the cities. For the first hypothesis, the results show that the value of F-calculated is 5.616E4. Further, the p-value (0.000) is less than the value of alpha (0.05). Thus, the null hypothesis for the first test will be rejected at the 95% confidence level. It can be concluded that the difference in the value of daily low temperatures across New York, Los Angeles, and Chicago is statistically significant. The results of the second hypothesis show that the value of F-calculated is 23.753. Further, the p-value (0.000) is less than the value of alpha (0.05). Thus, the null hypothesis of the second test will be rejected at the 95% confidence level (Bade and Parkin 246).

It can be concluded that the difference in the value of daily high temperatures across the three cities is statistically significant. For the third hypothesis, the value of F-calculated is 1.872. Also, the p-value (0.160) is greater than the value of alpha (0.50). The null hypothesis will not be rejected at the 95% confidence level. This indicates that the difference in precipitation levels across the three cities is not statistically significant. The results of ANOVA show that the difference in temperature across the three states is statistically significant while the difference in precipitation level is not statistically significant (Bade and Parkin 208).

T-test

The results for the fourth test focus on the equality of means. The value of t-calculated for low temperature is -233.966, 4.392 for high temperature, and 1.750 for precipitation. The value of t-critical is 1.96. Further, the results show that the p-values are 0.000 for low temperature, 0.000 for high temperature, and 0.085 for precipitation. The null hypothesis will be rejected for the low and high temperatures at the 95% confidence level. This shows that the temperature differences are significant across the cities. Further, the null hypothesis will not be rejected for the level of precipitation at the 95% level of confidence. This indicates that the difference in precipitation level is not statistically significant. Further, the test of equality of variances shows that the difference in the variance of low temperature is not statistically significant (Greene 98). Also, the differences in variance for high temperature and precipitation were statistically significant across the three groups.

Discussion

Since the three cities are in one nation, it is expected that the differences that are observed in weather patterns are not statistically significant. However, the results above show that the difference in temperature across the three cities is statistically significant. However, the difference observed in the mean level of precipitation is not statistically significant. Therefore, evaluation of the significance of variables and differences of values across various groups is important because it aids in making sound decisions.

References

Bade, Robin, and Michael Parkin. Essential Foundations of Economics, USA: Pearson Education, 2013. Print.

Baltagi, Badi. Econometrics, New York: Springer Publishers, 2011. Print.

Greene, William. Econometric Analysis, Harlow: Prentice–Hall, 2003. Print.

Mankiw, Gregory. Principles of economics, USA: South-Western Cengage Learning, 2011. Print.

United States Weather 2015. Web.

Verbeek, Marno. A Guide to Modern Econometrics, England: John Wiley & Sons, 2008. Print.

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