P-Value
A p-value is a measure of the probability that an observed difference could have occurred just by random chance.
Smaller the p value, better are the chances of rejecting the Null Hypothesis, while bigger the p value, better are the chances of accepting Null Hypothesis.
Eg — If the P value is 0.05, it means that if we do the statistical tests ’n’ times, only 5% of the times we will get something other than the Null Hypothesis. Like for p = 0.05, if we do a statistical test 1000 times, 950 times I will land on Ho while 50 times, I will land on Ha( Alternative Hypothesis )
P-value has the benefit that we only need one value to make a decision about the hypothesis. We don’t need to compute two different values like critical value and test scores. Another benefit of using p-value is that we can test at any desired level of significance by comparing this directly with the significance level.
Level of Significance or Alpha
The alpha value is a criterion for determining whether a test statistic is statistically significant.
It is the P-Value for our Population on which the Null Hypothesis was made.
This is the metric with which we will compare our calculated P-value with whether to accept or reject Null Hypothesis.
If calc p value is less than or equal to Alpha, we reject Null Hypothesis
If calc p value is greater than Alpha, we accept Null Hypothesis
Confidence Level vs Confidence Interval
The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way.
The confidence interval is the actual upper and lower bounds of the estimate you expect to find at a given level of confidence.
For example, if you are estimating a 95% confidence interval around the mean proportion of female babies born every year based on a random sample of babies, you might find an upper bound of 0.56 and a lower bound of 0.48. These are the upper and lower bounds of the confidence interval. The confidence level is 95%. This means that 95% of the time, you can expect your estimate to fall between 0.48 and 0.56.
95 percent confidence intervals mean that there is a 95 percent chance that the true mean value is within the range.
Confidence Interval:
It is the range of values in which we are fairly confident our true value lies in.
Formula for Calculating the Confidence Interval Where:
X is the mean
Z is the chosen Z-value from the table above
s is the standard deviation
n is the number of observations
The value after the ± is called the margin of error
Empirical Rule The empirical rule, or the 68–95–99.7 rule, tells you where most of the values lie in a normal distribution:
Around 68% of values are within 1 standard deviation of the mean.
Around 95% of values are within 2 standard deviations of the mean.
Around 99.7% of values are within 3 standard deviations of the mean.
The empirical rule is a quick way to get an overview of your data and check for any outliers or extreme values that don’t follow this pattern.
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