# Inferential Statistics 101 — part 7

May 16, 2018 · 11 min read
• Calculate the test statistic for the sample data: Test statistic compares the sample data with the expected value of the population parameter which was hypothesised and helps us to make a decision in hypothesis testing. CLT plays a major role in calculating the test statistic. The test statistic in a Z-test indicates the distance between the sample mean and the hypothesis mean (H0) in terms of standard deviation. A Z score of 0.25 indicates that the sample mean is 0.25 standard deviations away from the hypothesized mean. A very high or a very low (negative) Z scores indicate that sample mean is very much different from hypothesized mean (H0). In other words, the sample mean has comes from a different distribution other than the null distribution.
• Calculate the p-value: It is a way to quantify the Z-score in terms of the probability. Given the null hypothesis is true p-value represents the probability of seeing a sample as extreme as the one which we have. So higher its value, higher is the probability that our null hypothesis is true.
• Making a decision: In order to make a decision i.e. either accepting the null hypothesis or failing to reject the null hypothesis we fix some levels of significance which is usually represented by α and is predefined. Typical values for α are 0.1, 0.05, and 0.01 depending on the application. The decision is then made by comparing the p-value with α,
• p-value > α (Decision: Fail to reject the null hypothesis)
• p-value < α (Decision: Reject the null hypothesis)
• As the sample size increases, t-distribution moves closer towards normal distribution.
• Cross-over trials in which individuals are randomized to two treatments and then the same individuals are crossed-over to the alternative treatment.
• Matched samples, in which individuals are matched on personal characteristics such as age and sex.
• Any circumstance in which each data point in one sample is uniquely matched to a data point in the second sample.

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