Q1 : How do we verify the in-dependency of the samples?
We are the one who knows our data and data collection setup better
If the values in one sample affect the values in the other sample, then the samples are dependent.
If the values in one sample reveal no information about those of the other sample, then the samples are independent.
Q2: What does the red line in the normal distribution curve of the t Test signify
A2 : The red line indicate the “mean difference”
Q3 : Why is the DF in decimal 17.98 and not a whole number?
A3 : For “Unequal variance”, the t test using the formula below , so DF might not a whole number
Q4 : If using hypothesis testing, is your conclusion "d unlikely lower or equal to f"? Non-overlapping H0 and H1.
The two groups’ mean are significantly different, and “Y_f” > “Y_d”
You can restate your own H0, H1 based on what’s you are going to prove / test
Q5 : What is the difference between t-ratio and p-value that we normally use?
The t-value measures the size of the difference relative to the variation in your sample data, using the difference between the means, and then divided this difference by the standard error of the difference
Probability (which I assume is the P value you normally refer to) is based on the accumulative plot of t distribution -- CDF plot, to be simple, translate into T table
Traditional way, need: DF, alpha- α, t value, looking for probability à is 0.0074 for demo case
So p value range during [0,1] while t value can be any
Q6: I have a DOE, for which I make 3 repeat measurements for each point. How can I compare these as three independent data sets?
3 repeat is 3 replication set of data point, the purpose of replication is make your result is reliable
They should be dependent as using same experiment setup
Q7: Will t-test work even if the distribution is not normally distributed?
It is recommended to follow the pre-requirement to using t test
In practice, T test might still work in certain situation where it is not that perfectly normally distributed