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Sampling Techniques for Inference and Hypothesis Testing

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Added on  2020-03-28

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The use of p values becomes important as they tell us the probability of rejecting a null hypothesis. But a simple value like this depends on variability in the sampling distribution value which is used to determine the p value. It is advisable to explain p in terms of where ‘the confidence interval falls in relation to the null hypothesised value.’ (Cummings, D.

Sampling Techniques for Inference and Hypothesis Testing

   Added on 2020-03-28

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Sampling techniques are often used for inferences and hypothesis testing. It is convenient when wehave large populations that can cost a lot in terms of money and/or time. But the use of samples doesnot come free- a cost in terms of precision has to be paid. In simple words, we can never make anyconclusion with 100% confidence with the use of a sample. Higher confidence comes at the cost /loss ofprecision. The use of samples is associated with the use of a distribution that describes the statistic that we areconsidering. Since every sample has a different statistic value we can draw a sampling distribution forthe statistic. The spread of this value is called the variability of the sampling distribution. This variabilitydeclines as we use larger sample. As per (Frost, 2011)‘Increasing the sample size is like increasing the resolution of a picture of the populations. With just afew samples, the picture is fuzzy ...if we collect a very large sample, the picture becomes sharp enough’.The largest possible size is the population itself, which implies that the least variation is found in apopulation. Since we do not use the population we are saddled with higher variability. ‘As the samplesize increases, the chance of observing extreme values decreases and the observed values for thestatistic will group more closely around the mean of the sampling distribution’(Sampling in StatisticalInference). Thus, more datapoints allow greater precision. We can be 100% sure that the mean of apopulation lies between the maximum and minimum values, but such an estimate has zero precision. Tonarrow our interval estimate we need to lose some confidence, giving us narrow intervals. Probability and frequency are related through the relative frequency approach in statistics. The relativefrequency of an event becomes its probability as we allow the experiment to continue till infinity. This isakin to saying that the sample size is very large. In 50 tosses we may get only 30 heads and 20 tails, but ifwe toss the coin 1000 times we are likely to get close to 500 heads. Thus, as we increase the size of oursample (number of tosses) the relative frequency approaches the true probability value of an event. The use of p values becomes important as they tell us the probability of rejecting a null hypothesis.But a simple value like this depends on variability in the sampling distribution which is used todetermine the p value. It is better to use estimates of confidence intervals rather thanhypothesis tests using p values. It is advisable to explain p in terms of where ‘the confidenceinterval falls in relation to the null hypothesised value.’ (Cumming, 2010). Comparing p valuewith significance level is incorrect as it ignores the variability in sampling distribution, which is
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