Visualizing Data, Significance Level, T-test, Level of Measurement

In summary, the conversation revolved around several statistics questions, including identifying appropriate graphs for visualizing data, interpreting significance levels, and understanding different types of data. It also included a request for help with two additional questions about significant differences between groups and plotting relationships on a scatter graph.
  • #1
mmatusevici1
2
0
Hello. I was just wandering if anyone could help. I've been doing a couple of statistics questions, and when they ask for some questions, I am not sure if I have an appropriate understanding of what the right answer should be. I would really like to understand this material, so what I want to know is your opinions which are the right answers and why? Thank you.

0. Which one of these graphs is NOT an appropriate way of visualising the distribution of your data?

A. A box plot
B. A cumulative frequency curve
C. A scatter plot
D. A frequency histogram1. When setting the significance level at which to test your hypothesis, what does a probability level of 0.05 mean?

A.There is a 0.05% probability that your result could have occurred by chance
B.There is a 5% probability that your result could have occurred by chance
C. There is a 0.95% probability that your result could have occurred by chance
D. There is a 95% probability that your result could have occurred by chance

2. You have a dataset containing 10 values and conducted a one-sample t test against an expected mean value. Your test statistic (t) was 2.23 and the critical value of t at the 0.05 level with 9 degrees of freedom is 2.26. How would you interpret this result?

A. The difference is significant at the 0.05 level so do not reject the H0.
B. The difference is significant at the 0.05 level so reject the H0.
C. The difference is not significant at the 0.05 level so do not reject the H0.
D. The difference is not significant at the 0.05 level so reject H0.

3.You have measure the suspended sediment of water samples taken from a variety of sites along a stream. What TYPE of data is this?

A. Nominal
B.Ordinal
C.Interval
D.Ratio

Thank you. I would really appreciate your help.
 
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  • #2
Re: Statistics

0. They're all appropriate depending on what you want to learn on the distribution :confused:

- A is useful for visualizing mean and quartiles as well as outliers.
- B is useful if you want to work out the median or other related quantities.
- C is useful for graphically observing patterns in data.
- D is useful when you want to compare data points.

1. I believe B is the right answer. First, 0.05 is on a scale of 0 to 1, so it's not going to be A nor C. But I've generally seen this worded a bit more differently (since definitions are important here) as "In the long term, 95% of all measured [quantity you are measuring according to given distribution] will fall into [your confidence interval]".

2. Too rusty :confused:

3. Presumably you can measure these data points, and compare them to one another, so it can't be nominal. Now the difference between two measurements is meaningful, I suppose, so it can't be ordinal data. And, of course, this type of data has a natural zero point (measuring 0 means "no sediment"). Therefore this is ratio data.

That said I don't really know what is meant by "suspended sediment", so I assume it is some form of measurement (like rainfall in mm). If it isn't, the answer could be different.
 
  • #3
Re: Statistics

Thank you, Bacterius, it was very helpful.

Question 0 is very tricky, as all choices look appropriate for me as well :confused: Probably I would choose 'A box plot' because you have to read it, whereas in curves, scatter plots, and frequency histograms you can "see" the information, it's kind of "visualization". what do you think about my interpretation of answer? which answer would you choose?

In regards to Question 1, thank you, my answer would be the same as yours. I still can't solve the Question 2..

Thank you very much for Question 3, after your answer I did a further research on ratio data (before I thought it was ordinal), and I agree with you. Thanks. (flower)

There are two more things I would like to discuss to go through with statistics. Would you (or someone else) mind to help me to come up with solutions together?

4. In what situation are two groups most likely to have significant differences in their means?

A.When within-group variability is high and between-group variability is high
B.When within-group variability is high and between-group variability is low
C.When within-group variability is low and between-group variability is low
D.When within-group variability is low and between-group variability is high

5.You think that there total amount of precipitaton in a storm will influence the peak discharge in a river during the associated storm flow event. How would you plot this relationship on a scatter graph?

A.Peak discharge is the dependent variable so should be on the x axis, total precipitation is the independent variable so should be on the y axis.
B.Peak discharge is the dependent variable so shold be on the y axis, total precipitation is the independent variable so should be on the x axis
C.Peak discharge is the independent variable so should be on the y axis, total precipitation is the dependent variable so should be on the x axis.
D.Peak discharge is the independent variable so should be on the x axis, total precipitation is the dependent variable so should be on the y axis.
 

FAQ: Visualizing Data, Significance Level, T-test, Level of Measurement

What is visualizing data and why is it important in science?

Visualizing data is the process of representing data in a visual format, such as graphs or charts, to better understand patterns, relationships, and trends within the data. It is important in science because it allows researchers to communicate their findings in a clear and concise manner, making it easier for others to interpret and replicate their results.

What is significance level and how is it determined in statistical analysis?

Significance level, also known as alpha, is the probability of rejecting the null hypothesis when it is actually true. It is typically set at 0.05 or 0.01, but can vary depending on the study. It is determined by the researcher based on the level of risk they are willing to take in potentially making a Type I error (rejecting the null hypothesis when it is true).

How does a t-test work and when is it used in statistical analysis?

A t-test is a statistical test used to compare the means of two independent groups. It works by calculating the difference between the means of the two groups and taking into account the variability within each group. It is used when the data is normally distributed and the sample sizes are relatively small (typically less than 30).

What are the different levels of measurement and how do they impact data analysis?

The four levels of measurement are nominal, ordinal, interval, and ratio. Nominal data is categorical and cannot be ranked or compared. Ordinal data can be ranked, but the differences between values are not equal. Interval data has equal intervals, but has no true zero point. Ratio data has equal intervals and a true zero point. The level of measurement impacts data analysis because different statistical tests are used for each level and the type of data collected can influence the conclusions that can be drawn from the data.

How can data visualization be used to communicate the results of a t-test?

Data visualization can be used to display the results of a t-test by creating a graph or chart that compares the means of the two groups, such as a bar graph or box plot. This allows the reader to easily see the difference between the two groups and determine if it is statistically significant. Additionally, data visualization can be used to show the distribution of the data and any potential outliers that may have influenced the results of the t-test.

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