# Comparing different sized samples, statistics help needed.

• earl_grey
In summary, The conversation discusses the use of statistics for a charity event, specifically looking at the number of volunteers per group and the relative contribution of each group. The data shows that Group A has the most volunteers, but when taking into account the size of each group, Group C has the highest percentage of volunteers. The conversation ends with a request for recommendations on further analysis or topics to study in the field of statistics.

#### earl_grey

It has been a long time since I've done any statistics, so apologies in advance if I'm asking elementary questions.

I wanted to do some nice statistics for a charity event that was held. The data I have is:

Group A, 20 volunteers (total people in group 100 people.)
Group B, 15 volunteers (total size of group 50 people.)
Group C, 10 volunteers (total size of group 30 people.)
Group D, 5 volunteers (total size of group 20 people.)

I have shown a breakdown of how many people volunteered per group.
e.g. # of volunteers / total # of volunteers,
Group A: 20/50 = 40% of volunteers were from Group A
Group B: 15/50 = 30% of volunteers were from Group B
Group C: 10/50 = 20% of volunteers were from Group C
Group D: 5/50 = 10% of volunteers were from Group D

This shows that Group A has contributed the most amount of volunteers. However, this doesn't take into account the size of the groups. So, I calculated the number of volunteers relative to size of the group.

Volunteers (relative to size of the group)
Group A, 20/100 = 0.2 (20% of people in this group volunteered)
Group B, 15/50 = 0.3 (30% of people in this group volunteered)
Group C, 10/30 = 0.33 (33% of people in this group volunteered)
Group D, 5/20 = 0.25 (25% of people in this group volunteered)

From this view, Group C has contributed the most amount of volunteers (per # of people.)

How can I represent this data?
There has been a total of (20+15+10+5) 50 volunteers, from 200 people (group A+B+C+D). So only 25% of people volunteered for the event.

I want to show statistics around this 25% of people, relative to the amount of people per groups.

Can you recommend other analysis that I should perform?

Any help (or reference to the types of topics that I should study) would be appreciated.

Thank you

earl_grey said:
I wanted to do some nice statistics for a charity event that was held.

The field of mathematical statistics can't tell you what you are trying to accomplish. Until you state some objectives, it isn't clear what kind of statistics should be used.

Perhaps you only want to "explore" or "get a feel" for the data. Then you should look into descriptive statistics.

Perhaps you want evidence for some theory. ( -for example, something about one group being more likely to volunteer than another.) This is the field of "hypothesis testing".

Perhaps you want to estimate a quantitative effect. For example, if the groups were determined by the size of their monetary donations or by their age, you might want a formula that predicts the probability of volunteering vs that quantity. This is the field of estimation, or statistical prediction.

## 1. What is the purpose of comparing different sized samples?

Comparing different sized samples allows us to determine if there are significant differences between groups or populations. This can help us understand patterns and relationships within our data.

## 2. How do you determine the appropriate sample size for comparison?

The appropriate sample size for comparison depends on the type of analysis being conducted and the desired level of precision. Generally, a larger sample size will provide more accurate results, but it also depends on the variability of the data and the effect size being measured.

## 3. How do you handle unequal sample sizes in statistical analysis?

Unequal sample sizes can be handled by using statistical techniques such as weighted means, unequal variance t-tests, and analysis of covariance (ANCOVA). These methods take into account the differences in sample sizes and adjust the analysis accordingly.

## 4. Can you compare different sized samples using the same statistical test?

Yes, you can compare different sized samples using the same statistical test as long as the assumptions of the test are met. However, it is important to note that the power of the test may be affected by unequal sample sizes.

## 5. What are some potential limitations of comparing different sized samples?

One potential limitation is that unequal sample sizes may affect the accuracy and generalizability of the results. Additionally, unequal sample sizes may also make it difficult to detect small differences between groups or populations. It is important to carefully consider the sample sizes and their implications when interpreting the results of a comparison.

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