Describe the primary types of measures of central tendency and variability used in quantitative research. How can these be used to test statistical hypotheses?
Before to describe the primary types of measure of central tendency and variability 'we firstly try to know that what is quantitative research?' In natural and social sciences, and sometimes in other fields, quantitative research is the systematic empirical investigation of observable phenomena via statistical, mathematical, or computational techniques. The objective of quantitative research is to develop and employ mathematical models, theories, and hypotheses pertaining to phenomena.
Primary types of measures of central tendency and variability which is used in quantitative research are defined as-
Measures of central tendency: which allows us to summarize an entire data set with a single value(midpoint). Generally there are three primary measures of central tendencies. Mean, Median and Mode.
Mean: the arithmetic average: directly considers every score in a distribution.
Median: the point (score) which divides the data set in 1/2. It implies that half of the data set is above the median value and half of the data set is below the median value.
Mode: which occurs most number of times in the given data set.
Measure of variability: These describe the dispersion of data around some sort of mean.
Range: the lowest and highest score of a given interval.
Percentile: the percentage band in to which score the falls.
Deviation: distance between an observed score and the mean score.
Variance: deviation squared.
Standard deviation: square root of variance.
Standard error: this is an estimate of spread of samples around the population mean.
In the second part of question we have to describe that how to use these measures in statistical hypotheses. Well, measure of central tendencies play an vital role in statistical hypotheses. When we use the large sample test-statistic then mean is frequently used in testing procedure and more or less we use the mean during formulating the null and alternative hypothesis. Apart from that when we use test statistic for small sample then we also use the mean. The Median test is used in non-parametric statistical hypothesis testing. Mode is also used during hypothesis testing. Because in some testing situation, at the place of mean we use the mode value according to the given conditions.
In statistical hypothesis, measures of variability is used as-
Sometimes we don't know the population mean - we only know the sample mean and the standard deviation for the given sample, but if the standard deviation is large, the sample mean may be rather far from the population mean. How far is it? The standard error can estimate this.
Standard Error (SE) = Standard Deviation(SD) / square root or n
The variability among sample means will be increased if there is a wide variability of individual data and sometimes small samples. Standard Error is used to calculate the confidence interval.
Hence, we can say that the measure of central tendencies and variability plays vital role in quantitative research and frequently used in statistical hypothesis.
Describe the primary types of measures of central tendency and variability used in quantitative research. How...
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