Statistics Report On Investor Data Analysis

Prepare basic advice for people for new employees at the XYZ company based on the previous findings, if this is too difficult give a general discussion about the issues with using samples.

Summary of the Actual Dataset

In the present world, business statistics is the tool and science behind the critical decision making (often limited to uncertainty) for a number of different business disciplines such as for marketing research, production and service optimization, econometrics, financial analysis, etc. In our research field, the use of various descriptive and inferential statistical techniques on the bulk of information (primary or secondary data) of customers can immensely help a financial advisor or a financial institution to identify and understand the investment preferences of their customers (potential investors), so as to provide appropriate financial advices to a customer specific to his/her requirements.

The main aim of this statistical report is to identify similar customers’ preferences and any other significant relationships between different data variables for the investor data test of XYZ Investment Advisors. In line with this, a randomly sampled dataset containing the recorded observations for 100 investors was used for our research analysis. It is assumed that the sample dataset is unbiased and is also the true representation of the actual investor population.

Fundamentally, there are several techniques of collecting data for a research study, that is, through observational or experimental studies, interviews, paid market surveys, etc. The XYZ investor data is obtained through an observational study and records observations for 40,000 investors on a number of numerical and categorical variables, including their demographic characteristics, personal information and other investment related data (discussed in the summary table on the following page).

The sampled data on 100 investors will be used to present a simple bivariate analysis that identifies significant relationship, if any, between the categorical variable ‘Gender’ and the numerical variable ‘Invested Amount’. Further, the variable ‘return per $1000 investment’ is analysed by computing a 90% confidence interval estimate for the mean return and also performing a hypothesis test to check the validity of the claim that this mean annual return (per $1000) is above $30.

The following table defines the name, type and measure of different variables in the XYZ investor dataset:

Variable	Type	Measures/Records
Income	Numerical	Annual income of the investor (in $).
Amount invested	Numerical	Amount invested by the investor (in $).
Return (per $1000)	Numerical	Return on per $1000 investment (in $).
Investment type	Categorical	‘High risk’ or ‘Low risk’ investment.
Fees paid	Numerical	Fees paid to the XYZ company (in $).
Fees too high	Categorical	Investor believes fees paid is ‘Too high’ or ‘Not too high’.
Gender	Categorical	Gender of the investor: ‘Male’ or ‘Female’. This variable is critical to the study as to identify and understand the investment differences and choices of male and female investors.
Age	Numerical	Age of the investor (in years).
Age group	Categorical	Age category: ‘aged above 50’ or ‘aged 50 or below’. Critical to the study as it helps to identify and understand the investment differences and choices of adult and young investors.
Married	Categorical	Investor is ‘Married’ or ‘Unmarried’.
Number of children	Numerical	Number of children investor has.
Have children	Categorical	Investor ‘has children’ or ‘no children’. Critical to the study as it helps to identify and understand the investment differences and choices of investors having children and not having children.
Country	Categorical	Investor belongs to ‘country1’ or ‘country2’. Critical to the study as it helps to identify and understand the investment differences and choices of investors from different countries.

According to Hitchings (2017), females are not making equal level of investments as males are, and are therefore, held back from future returns and other competent opportunities. The articles also explains that why it is likely that  women invest lesser to a man reasoning to their financial risk-taking abilities.

In line with this, the later section of this report will perform a hypothesis test on our sample dataset to determine if the mean amount invested by male and female investors is actually (or rather significantly) different from each other.

Based on the sampled XYZ investor data for 100 investors, this section of the report presents and discusses the results of a simple bivariate analysis performed to identify a relationship, if any, between the categorical variable ‘Gender’ and the numerical variable ‘Amount Invested (in $)’. 

Summary Outputs (computations were done in MS-Excel)

• Following table summarises the mean and standard deviation of the amount invested by the male and female investors:

Gender	Count	Total amount invested (in $)	Average amount invested (in $)	StdDev of amount invested (in $)
Female	47	6539068	139129.11	66930.63
Male	53	9912248	187023.55	87109.50
Grand Total	100	16451316	164513.16	81512.62

Comments

• The average amount invested by a male investor is $187023.55 while that by a female investor is $139129.11, suggesting that on average, male invest higher than females.
• Notably, the amounts invested by male investors are expected to differ about its mean value by $87109.5. For female investors, the amounts are expected to differ by $66930.63 from the respective mean value. Comparing the two, the variation in the amounts invested by male investors is higher.
• Frequency Distribution Table and Combined Histogram for the amount invested (in $) by male and female investors:

Amount Invested (in $)	Females_Frequency	Males_Frequency
20000 to less than 70000	10	3
70000-<120000	6	8
120000-<170000	10	16
170000-<220000	18	10
220000-<270000	3	6
270000-<320000	0	6
320000-<370000	0	1
370000 and over	0	3

Comments

• No female investors were recorded to make an investment above $270000, while about 9 male investors were recorded to have an investment above $270000.
• The number of female investors having an investment amount below $70000 (and above $20000) was higher than the number of male investors within this range.
• As can be observed from the combined histogram plot above, females are more likely to go for a lower investment when compared to males. The observations are in line with the statement made in Section 2 of this report.
• Following table represents the output summary of a two-sample independent -test conducted to determine if the mean amounts (in $) invested by male and female investors are significantly different (at a significance level of 0.05) from each other or not.

t-Test: Two-Sample Assuming Equal Variances
	Female_amount invested	Male_amount invested
Mean	139129.11	187023.55
Variance	4479709499	7588064324
Observations	47	53
Pooled Variance	6129040630
Hypothesized Mean Difference	0
df	98
t Stat	-3.0533
P(T<=t) one-tail	0.0015
t Critical one-tail	1.6606
P(T<=t) two-tail	0.0029
t Critical two-tail	1.9845

The hypotheses are stated as:

Null hypothesis

Alternative hypothesis

Here,  are the hypothesized population means of amount invested by male and female investors, respectively. The null hypothesis is rejected if the populations means of two groups are significantly different from each other (at a significance level of ). To test the hypothesis, a two-tailed (non-directional) two-sample independent -test is used (assuming equal variances for both the groups).

Review of an academic website related to investors

Comments

• As read from the Excel output, the two-tailed -value is computed to be 0.0029
• Since the -value is less than the significance level of 0.05, the null hypothesis is rejected, thus concluding that the mean amounts invested by male and female investors are significantly different from each other.
• It can further be concluded (using one-tailed -value) that the mean amount invested by male investors is significantly higher than the mean amount invested by female investors. Again, the conclusion is in line with the statement made in Section 2 of this report.

Section 4: Investigating and Analysing the variable ‘return per $1000’

Note: The following computations are performed manually (in the report) and using appropriate Excel functions (in the Excel file).

The table below represents the summary statistics obtained for the variable “Return per $1000” data for a sample of 100 investors:

Annual Return (in $ per $1000)
Sample Standard Deviation,	15.8187
Sample Mean,	40.15
Sample Size,	100

Therefore,

90% Confidence Interval

Degrees of freedom

For a 90% confidence level, and -value is computed as 1.6604 (using technology: an online calculator)

Also, 90% CI Margin of Error,             

Thus, the 90% confidence interval estimate for mean annual return per $1000 investment can be obtained as:

Lower limit

Upper limit

Hypothesis Testing

Significance level = 5% (assumed), that is,

It is required to determine if the average annual return per $1000 investment is above $30. For this purpose, a right-tailed (directional) -test is performed at a significance level of 5%.

Note: -statistic is used instead of -statistic as the population standard deviation is unknown. It is further assumed that the variable ‘return per $1000’ data is approximately having a normal distribution.

The hypotheses are stated as:

Null hypothesis  

Alternative hypothesis  

Here, is the hypothesized mean annual return investment per $1000 for the investor population. The appropriate test statistic is computed as:

Substituting values gives:

Degrees of freedom

Using a -table, the corresponding right-tailed -value is obtained as

Since the -value, the null hypothesis can be rejected, thus concluding that there is sufficient evidence (at a significance level of 0.05) to claim that the average return per $1000 investment is above $30. 

Based on the above analysis and results, it can be concluded that, on average, female are investing less than males. Fundamentally, this difference can be subjected to poor risk-taking abilities of female investors, not because the inability to do so, but likely because women are more secured with their finances than males are. Moreover, female investors prefer to invest in safer options like ‘property/asset building’, saving accounts’, ‘government bonds’ etc. It is also that, in general, the financial goals of male and female investors differ significantly.

However, the investment gap also can be highly influenced by people’s own perception of investing and confidence. And therefore, there is a possibility (though, not very likely) that the above conclusion is wrong. The error in the output results can be due to a number of factors (survey bias, inappropriate sampling, wrong target population, etc.), that would have made the sampled data inappropriate to the research study in concern.

The main aim of this report was to identify any significant relationships or differences between different data variables for the investor data test of XYZ Investment Advisors; in order to better understand the investment preferences of associated investors (customers). Based on the above analyses and results, following conclusions are made:

• The mean amounts invested by male and female investors are significantly different from each other. On average, males invest higher than females. This conclusion is in line with the statement made in Section 2 of this report.The variation in investment levels can be likely explained by disparate risk-taking abilities of male and female investors.
• The mean return per $1000 investment is $40.15 and is expected to lie (with 95% confidence) within the range $(37.52, 42.78) for the broader investor population. Further, it was concluded that this mean value is significantly higher than the hypothesized mean return value of $30 per $1000 investment.

The research can further be advanced to investment differences between age groups specific to the gender of the investor. Adding this factor to the analyses will help us draw more accurate inferences about particular segments of the investor’s population.

References

Hitchings, C. (2017). Invest like a woman: the gender investment gap in the UK. Momentum UK. Retrieved 1 June 2017, from https://www.momentum.co.uk/features/invest-like-a-woman-the-gender-investment-gap-in-the-uk/