Slovin Formula

Category: Statistics

Last Updated: 20 Jun 2022

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SAMPLE AND SAMPLING TECHNIQUE Sample ? Is a finite number of an item (or individual) taken from a population having identical characteristics with those of the population from which it was taken. ? A sample is considered biased if one or several of the items (or individuals) in the population are given a consistently better opportunity to be chosen than the others. ? A collection with specified dimension Sample size ? Random sampling, the larger the sample, the more accurately it represents the population from which it was taken. As the sample size decreases, the degree of representativeness becomes less. Size of sample depends on some factors: ? Degree of accuracy required ? Amount of variability inherent in the population from which the sample was taken ? Nature and complexity of the characteristics of the population under consideration Sample Strategy ? Common Misguided Approach ? decide what data to collect ? then undertake survey ? decide what analysis should be done wrong data collected ? data collected on wrong subjects ? insufficient data collected ? Desired analysis may not be possible or effective Key to Good Sampling ? formulate the aims of the study ? decide what analysis is required to satisfy this aims ? decide what data are required to facilitate the analysis ? collect the data required by the study Determine sample size ? Slovin Formula: ? n = N__ ? 1+NE? ? Where: n = sample size ? N = population size

E = margin of error * desired Example:What should be the representative sample size if the population from which the sample will be taken is 10,000 and the desired margin of error is 2%? Solution:To determine the sample size, use the formula; n = ___N__ 1+NE? n = 10,000 = 2,000 1+ (10,000) (0. 02)? The sample size is 2,000 This formula in finding the sample size cannot be used when the normal approximation of the population is poor or small. Margins of Error | |Population |± 1% |± 2% |± 3% |± 4% |± 5% |± 10% | |500 |* |* |* |* |222 |83 | |1500 |* |* |638 |441 |316 |94 | |2500 |* |1250 |767 |500 |345 |96 | |3000 |* |1364 |811 |517 |353 |97 | |4000 |* |1538 |870 |541 |364 |98 | |5000 |* |1667 |909 |556 |370 |98 | |6000 * |1765 |938 |566 |375 |98 | |7000 |* |1842 |959 |574 |378 |99 | |8000 |* |1905 |976 |580 |381 |99 | |9000 |* |1957 |989 |584 |383 |99 | |10000 |5000 |2000 |1000 |588 |385 |99 | |50000 |8333 |2381 |1087 |617 |387 |100 | Margin of Error Is the allowable error in percent due to the use of the sample, instead of the population ? * indicate that the assumption of normal approximation is poor and that the sample size formula does not apply. Guidelines with regards to the minimum number of items needed for a representative sample: ? Descriptive studies – a minimum number of 100 ? Co-relational studies – a sample of at least 50 is deemed necessary to establish the existence of a relationship ? Experimental and causal comparative studies – minimum of 30 per group ?

Sometimes experimental studies with only 15 items in each group can be defended if they are very tightly controlled ? If the sample is randomly selected and is sufficiently large, an accurate view of the population can be had, provided that no bias enters the selection process Sampling Error ? Is the error attributed to chance that is being made when selecting random samples to represent a given population under consideration. ? It is the expected chance difference, variation or deviation between a random sample and the population. ? Does not result from measurement or computation errors, although these errors also contribute to inaccuracy.

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