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Statistical analysis is the use of tools and techniques to collect and analyze numerical data to identify patterns and trends and discover meaningful insights used for decision-making.

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In this article, we discuss the types and advanced methods of statistical analysis and sampling methods.

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Statistical analysis is classified into two primary categories: Descriptive and inferential statistics. Descriptive statistics includes the condensation of data in the form of tables, their graphical presentations, and the calculation of numerical indicators of central tendency and variability. Inferential statistics uses a variety of tests and estimates to make conclusions about the larger population from which the sample was drawn. In this section, we discuss the subdivisions of these categories and advanced methods of statistical analysis.

(1). Descriptive Statistics

(a). Measures of Central Tendency

The measures of central tendency produce numbers or words that attempt to describe the middle or typical value of a distribution. Common measures are the mean, mode, and median. The mode reflects the value of the most frequently occurring score, the median shows the middle value when observations are ordered from the least to most, and the mean is the most common average, which is acquired by adding all digits and then dividing by the total number of scores.

Statisticians can compute two types of means: The sample and the population mean. This classification is based on whether the data is viewed as a sample (a subset of scores) or a population (a complete set of scores). Below are the formulas used to calculate both:

Sample mean: x̄ = ∑x/n

Population mean: μ = ∑x/N

Where:

x̄ is the sample mean.

∑x is the summation of all scores.

n is the sample size

N is the population size

(b). Variability

Variability is described by range, interquartile range, variance, and standard deviation. The range is the difference between the smallest and the largest scores. The variance is a measure of how far a set of numbers is spread out from the average value, and the standard deviation is the square root of the variance that describes the variability in the original units of measurement. Below are the formulas:

Variance: σ² = SS ⁄ N

Standard deviation: σ = √SS ⁄ N

Where:

σ is the standard deviation

σ² is the variance

SS is the sum of squared deviation scores

N is the number of scores

(c). Z Scores

A z score is a unit-free standardized score that, regardless of the original units of measurement, indicates how many standard deviations a score is above or below the mean of its distribution. Calculating the z score allows us to calculate the probability of a score occurring within the normal distribution. It is calculated using the formula:

Ζ= X-μ ⁄ σ

(d). Correlation

Correlation analysis is a method used to measure the strength of the linear relationship between two variables, whether positive or negative. It is usually presented by the correlation coefficient, which is normally designated as r. The correlation coefficient is a number between -1 and 1 that describes the relationship between pairs of variables.

(2). Inferential Statistics

(a). Hypothesis Testing

Hypothesis testing is a method in which samples are selected to learn more about the characteristics of a given population. It is a systematic way of testing claims and ideas about a certain group using a small representative of the population. There are four key steps in hypothesis testing. The first step is stating the null or alternative hypothesis. The second step involves setting the criteria for a decision, the third is computing the test statistic, and the fourth is decision-making.

(b). T-test

A t-test is a statistical measure used to evaluate the difference between the means of two groups. There are three different types of t-tests: One sample t-test, independent sample t-test, and paired sample t-test. The one-sample t-test compares a sample mean with a known reference mean, the independent sample t-test distinguishes the means of two independent groups, and the paired sample test differentiates the means of two dependent groups.

(c). Analysis of Variance (ANOVA)

The analysis of variance is an extension of the independent sample t-test. It is a technique used to test the claim that three or more population means are equal by examining the variance of the samples taken. ANOVA helps to calculate the ratio between within-group variability and between-group variability to determine if any of the groups have a significantly different mean.

(d). Sampling Methods in Statistics

Most inferential statistical procedures assume that you have a random sample. Randomization ensures that you obtain a sample that accurately represents your population. Outlined below are common sampling procedures in statistics:

(i). Simple Random Sampling

Simple random sampling is a method for obtaining an unbiased representative sample. In this procedure, all items in the population have an equal probability of being selected, and there is no connection between the researchers collecting data. The researcher usually has a list of the population and then randomly chooses participants from the list.

(ii). Stratified Sampling

Stratified sampling involves breaking down the population into strata and then from each stratum, using simple random sampling to acquire a fixed sample size. A stratum is a subpopulation whose members are relatively similar to each other in comparison to the broad population. This process ensures that the researcher has a specific number of observations per stratum, which produces precise estimates for all strata and facilitates comparison.

Advanced Methods in Statistical Analysis

Advanced statistical methods are used to analyze complex data sets.

(1). Principal Component Analysis

The principal component analysis is a technique used to display patterns in multivariate data. Other techniques for displaying multivariate data include cluster analysis, exploratory factor analysis, and MANOVA. Principal component analysis aims to display graphically the relative positions of data points in fewer dimensions and explore the relationships between dependent variables. It is a hypothesis-generating technique that describes the patterns in a data table rather than testing the formal hypothesis.

(2). Factor Analysis

Factor analysis is a technique for investigating whether several variables of interest are linearly related to a smaller number of unrelated factors. Using this analysis method, the researcher can distinguish the factors of interest from the errors.

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Summary

Statistical analysis is the use of tools and techniques to analyze numeric data to identify patterns and trends. It is broadly categorized into two key areas which are descriptive and inferential statistics. Descriptive statistics are further classified into the measures of central tendency, variability, z-scores, and correlation. Inferential statistics are categorized into hypothesis testing, t-tests, and ANOVA and multivariate statistical analysis such as MANOVA.

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