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Data analysis: hypothesis testing

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# 3 Alpha (α) levels

The level of statistical significance is the threshold at which you decide whether to reject the null hypothesis (to make a decision). A result is statistically significant when the situation described in the null hypothesis is highly unlikely to have occurred.

By using the concept of statistical significance, you can have a concrete way of examining the claim concerning the null hypothesis, using the data collected, to make a clear decision on when to reject the null hypothesis and when to leave it. In this way, you do not have to guess whether the test statistic is too high or too low.

How can you determine the appropriate level of statistical significance to use? In order to answer this question, you must introduce the concept of ‘level of confidence’ (C) – how confident are you in your decision to reject the null hypothesis? C is related to the concept of ‘confidence intervals’ that you may have seen elsewhere. C is usually set at 95% when establishing a confidence interval. Having determined C, you can calculate the level of statistical significance that you want to use as 1 − C.

If you choose the level of confidence (C) at 95%, then the level of statistical significance that you set up for your decision is equal to 1 − 95% = 5%.

The level of statistical significance is referred to as ‘alpha’ or ‘α’.

So, returning back to the question on caffè latte foam, is 1.5 cm average foam height, which was only slightly different from the expected value of 1 cm, significant enough to reject or fail to reject the null hypothesis (H0)? The researchers had to consider the alpha level to determine the appropriate course of action. The alpha level is a crucial factor in hypothesis testing and is used to determine the threshold for statistical significance. In other words, it helps to determine whether the results obtained are due to chance or if they represent a genuine difference between the expected and observed values.

Calculating the alpha level can be tricky, but it is a necessary step in hypothesis testing (you will discuss how to calculate the alpha level in later sections). Once the alpha level has been determined, it can be used to decide whether to accept or reject the null hypothesis based on the findings of Researcher 2. The decision of whether to reject or fail to reject H0 based on the findings of Researcher 2 will ultimately depend on the alpha level chosen, so the researchers will have to carefully consider this factor before drawing any conclusions from the study.

You will be tested on your understanding of how to transfer levels of confidence to alpha levels in the following activity.

## Activity 2 Level of alpha

Timing: Allow approximately 10 minutes to complete this activity

Imagine you are working as a marketing analyst for a new product launch, and you want to make sure that your market research is accurate and reliable. You need to determine the appropriate alpha level for your survey results, based on the desired confidence level.

Can you determine α?

Table 1 Level of alpha
Level of Confidence (C) α
90%
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95%
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99%
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### Comment

Table 1 Level of alpha (completed)
Level of Confidence (C) α
90% 10%
95% 5%
99% 1%

α is calculated as 1 − C.

1 − 90% = 10%

1 − 95% = 5%

1 − 99% = 1%

There is an inverse relationship between confidence levels and alpha levels, as increasing the confidence level leads to a decrease in the alpha level, and vice versa. It is important to carefully consider the appropriate alpha level and confidence level when conducting hypothesis testing to ensure that the appropriate level of risk and certainty are balanced.