Statistics Reports Example

Introduction

In this paper I will show how the basic concepts of statistical analysis and probability theory can be applied to a real world problem. In this paper we will consider the data of prices of electricity per 500 kwhs (Source: Bureau of Labor Statistics). Our goal is to describe and use such techniques as descriptive statistics and hypothesis testing in the research. All calculations are provided in SPSS 22 statistical software.

Data Description

We are given with a data set of prices of electricity in the United States for 17 years. The price is given by month, from 1979 to 1995. The first step of our analysis is to display descriptive statistics. I use average indicator for each year to show the descritptives.
The average value of price per 500 kwhs of electricity during the considered period is $40.4355 with a standard deviation of $6.36221. The data is negatively skewed (skeweness is -0.831). The distribution is close to normal. According to the box plot, there is an outlier in the data – the price of electricity in 1979 seems to be significantly lower than in other years. That’s why I decide to remove this observation from the data set. The further analysis is performed only based on 16 years.

Hypotheses

In this paper I would like to show how two sample Student’s t-test and One-way ANOVA work.
For this purpose I would like to check two hypotheses:
Hypothesis 1: There is a significant difference in prices of electricity in summer and in winter.
Hypothesis 2: The average seasonal prices are significantly different from each other.
Analysis and Results
H0: μ1=μ2Ha: μ1≠μ2

Set level of significance alpha at 0.05

Perform testing:
In this output 1 represents January prices and 2 represents July prices.
According to the output, the significance of the test is higher than 0.05 (p-value = 0.22). That’s why I failed to reject the null hypothesis. There is no evidence to say that the prices of electricity are different in summer and winter (at 5% level of significance).
Now I want to check hypothesis 2. For each season compute average prices. There will be 4 groups.
H0: μ1=μ2=μ3=μ4Ha: not all means are equal

Set level of significance alpha at 0.05

Perform testing:
The results of ANOVA are the following: F=0.389, p=0.761.
Since p-value of the test is lesser than 0.05, we failed to reject the null hypothesis. There is no significant difference in prices between the seasons of the year (at 5% level of significance).