Statistical Analysis - Revision history

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-the science of collecting, exploring, and presenting large amounts of data to discover underlying patterns and trends. Statistics are applied every day – in research, industry, and government – to become more scientific about decisions that need to be made. For example:
+'''Statistical Analysis''' is the science of collecting, exploring, and presenting large amounts of data to discover underlying patterns and trends. Statistics are applied every day – in research, industry, and government – to become more scientific about decisions that need to be made. For example:
 *Manufacturers use statistics to weave quality into beautiful fabrics, to bring life to the airline industry, and to help guitarists make beautiful music.
 *Researchers keep children healthy by using statistics to analyze data from the production of viral vaccines, which ensures consistency and safety.

← Older revision		Revision as of 00:04, 7 December 2022
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	*[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5037948/ Basic statistical tools in research and data analysis]		*[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5037948/ Basic statistical tools in research and data analysis]
	*[https://www.worldscientific.com/worldscibooks/10.1142/5224 Statistical Methods of Analysis]		*[https://www.worldscientific.com/worldscibooks/10.1142/5224 Statistical Methods of Analysis]
		+
		+	__NOTOC__

@@ Line 1: / Line 1: @@
-the science of collecting, exploring and presenting large amounts of [[data]] to discover underlying patterns and trends. [[Statistics]] are applied every day – in research, [[industry]] and government – to become more scientific about decisions that need to be made. For example:
+the science of collecting, exploring and presenting large amounts of [[data]] to discover underlying patterns and trends. Statistics are applied every day – in research, [[industry]] and government – to become more scientific about decisions that need to be made. For example:
 *Manufacturers use statistics to weave [[quality]] into beautiful fabrics, to bring lift to the airline industry and to help guitarists make beautiful music.
 *Researchers keep children healthy by using statistics to analyze data from the production of viral vaccines, which ensures consistency and safety.

@@ Line 99: / Line 99: @@
 *More Advanced Analysis:Once you have calculated some basic values of location, such as mean or median, spread, such as range and variance, and established the level of skew, you can move to more advanced statistical analysis, and start to look for patterns in the data.
@@ Line 110: / Line 120: @@
 == See Also ==
+[[Big Data]]<br />
@@ Line 118: / Line 137: @@
 == Further Reading ==

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-== Uses of Statistical Analysis<ref>What is Statistical Analysis Used For? [https://www.statisticshowto.datasciencecentral.com/statistical-analysis/ Statistics How to]</ref> ==
+== Using Statistical Analysis<ref>How is Statistical Analysis Used? [https://www.statisticshowto.datasciencecentral.com/statistical-analysis/ Statistics How to]</ref> ==
 Statistical Analysis may be used to:
 *Summarize the data. For example, make a pie chart.
@@ Line 13: / Line 13: @@
 *Make future predictions based on past behavior. This is especially useful in retail, manufacturing, banking, sports or for any organization where knowing future trends would be a benefit.
 *Test an experiment’s hypothesis. Collecting data from an experiment only tells a story when you analyze the data. This part of statistical analysis is more formally called “Hypothesis Testing,” where the null hypothesis (the commonly accepted theory) is either proved or disproved.

@@ Line 48: / Line 48: @@
-Statistical Analysis - Techniques for Summarizing Data
+== Statistical Analysis - Techniques for Summarizing Data<ref>Statistical Analysis - Techniques for Summarizing Data [https://www.skillsyouneed.com/num/simple-statistical-analysis.html Skills You Need]</ref> ==
 Some of the most common techniques for summarising your data, and explains when you would use each one.
 *Summarising Data: Grouping and Visualising: The first thing to do with any data is to summarise it, which means to present it in a way that best tells the story. The starting point is usually to group the raw data into categories, and/or to visualise it. For example, if you think you may be interested in differences by age, the first thing to do is probably to group your data in age categories, perhaps ten- or five-year chunks. One of the most common techniques used for summarising is using graphs, particularly bar charts, which show every data point in order, or histograms, which are bar charts grouped into broader categories.
 An example is shown below, which uses three sets of data, grouped by four categories. This might, for example, be men, women, and ‘no gender specified’, grouped by age categories 20–29, 30–39, 40–49 and 50–59.
 An alternative to a histogram is a line chart, which plots each data point and joins them up with a line. The same data as in the bar chart are displayed in a line graph below.
 It is not hard to draw a histogram or a line graph by hand, as you may remember from school, but spreadsheets will draw one quickly and easily once you have input the data into a table, saving you any trouble. They will even walk you through the process.
 The important thing about drawing a graph is that it gives you an immediate ‘picture’ of the data. This is important because it shows you straight away whether your data are grouped together, spread about, tending towards high or low values, or clustered around a central point. It will also show you whether you have any ‘outliers’, that is, very high or very low data values, which you may want to exclude from the analysis, or at least revisit to check that they are correct.
@@ Line 63: / Line 66: @@
 It is always worth drawing a graph before you start any further analysis, just to have a look at your data.
-You can also display grouped data in a pie chart, such as this one. Pie charts are best used when you are interested in the relative size of each group, and what proportion of the total fits into each category, as they illustrate very clearly which groups are bigger.
+You can also display grouped data in a pie chart, such as the one below.
-As a result, researchers sometimes use the median instead. This is the mid-point of all the data. The median is not skewed by extreme values, but it is harder to use for further statistical analysis.
+[[File:Statistical_Analysis_-_Pie_Chart.png|300px|Statistical Analysis - Pie Chart]]<br />
-The mode is the most common value in a data set. It cannot be used for further statistical analysis.
+Pie charts are best used when you are interested in the relative size of each group, and what proportion of the total fits into each category, as they illustrate very clearly which groups are bigger.
-The values of mean, median and mode are not the same, which is why it is really important to be clear which ‘average’ you are talking about.
+*Measures of Location: Averages: The average gives you information about the size of the effect of whatever you are testing, in other words, whether it is large or small. There are three measures of average: mean, median and mode.When most people say average, they are talking about the mean. It has the advantage that it uses all the data values obtained and can be used for further statistical analysis. However, it can be skewed by ‘outliers’, values which are atypically large or small. As a result, researchers sometimes use the median instead. This is the mid-point of all the data. The median is not skewed by extreme values, but it is harder to use for further statistical analysis. The mode is the most common value in a data set. It cannot be used for further statistical analysis. The values of mean, median and mode are not the same, which is why it is really important to be clear which ‘average’ you are talking about.
-Measures of Spread: Range, Variance and Standard Deviation: Researchers often want to look at the spread of the data, that is, how widely the data are spread across the whole possible measurement scale.
+*Measures of Spread: Range, Variance and Standard Deviation: Researchers often want to look at the spread of the data, that is, how widely the data are spread across the whole possible measurement scale. There are three measures which are often used for this:
+**The range is the difference between the largest and smallest values. Researchers often quote the interquartile range, which is the range of the middle half of the data, from 25%, the lower quartile, up to 75%, the upper quartile, of the values (the median is the 50% value). To find the quartiles, use the same procedure as for the median, but take the quarter- and three-quarter-point instead of the mid-point.
-There are three measures which are often used for this:
+**The standard deviation measures the average spread around the mean, and therefore gives a sense of the ‘typical’ distance from the mean. To calculate the standard deviation, take the square root of the variance.
+**The variance is the square of the standard deviation. They are calculated by:
-The range is the difference between the largest and smallest values. Researchers often quote the interquartile range, which is the range of the middle half of the data, from 25%, the lower quartile, up to 75%, the upper quartile, of the values (the median is the 50% value). To find the quartiles, use the same procedure as for the median, but take the quarter- and three-quarter-point instead of the mid-point.
+***calculating the difference of each value from the mean;
+***squaring each one (to eliminate any difference between those above and below the mean);
-The standard deviation measures the average spread around the mean, and therefore gives a sense of the ‘typical’ distance from the mean.
+***summing the squared differences;
+***dividing by the number of items minus one.
 This gives the variance.
-To calculate the standard deviation, take the square root of the variance.
+*Skew: The skew measures how symmetrical the data set is, or whether it has more high values, or more low values. A sample with more low values is described as negatively skewed and a sample with more high values as positively skewed. Generally speaking, the more skewed the sample, the less the mean, median and mode will coincide.
-More Advanced Analysis
+*More Advanced Analysis:Once you have calculated some basic values of location, such as mean or median, spread, such as range and variance, and established the level of skew, you can move to more advanced statistical analysis, and start to look for patterns in the data.

← Older revision		Revision as of 19:35, 15 July 2019
Line 46:		Line 46:
	**the estimation of parameter(s) and		**the estimation of parameter(s) and
	**testing of statistical hypotheses.		**testing of statistical hypotheses.
		+
		+
		+	Statistical Analysis - Techniques for Summarizing Data
		+	Some of the most common techniques for summarising your data, and explains when you would use each one.
		+	*Summarising Data: Grouping and Visualising: The first thing to do with any data is to summarise it, which means to present it in a way that best tells the story. The starting point is usually to group the raw data into categories, and/or to visualise it. For example, if you think you may be interested in differences by age, the first thing to do is probably to group your data in age categories, perhaps ten- or five-year chunks. One of the most common techniques used for summarising is using graphs, particularly bar charts, which show every data point in order, or histograms, which are bar charts grouped into broader categories.
		+
		+	An example is shown below, which uses three sets of data, grouped by four categories. This might, for example, be men, women, and ‘no gender specified’, grouped by age categories 20–29, 30–39, 40–49 and 50–59.
		+
		+	An alternative to a histogram is a line chart, which plots each data point and joins them up with a line. The same data as in the bar chart are displayed in a line graph below.
		+
		+	It is not hard to draw a histogram or a line graph by hand, as you may remember from school, but spreadsheets will draw one quickly and easily once you have input the data into a table, saving you any trouble. They will even walk you through the process.
		+
		+
		+	The important thing about drawing a graph is that it gives you an immediate ‘picture’ of the data. This is important because it shows you straight away whether your data are grouped together, spread about, tending towards high or low values, or clustered around a central point. It will also show you whether you have any ‘outliers’, that is, very high or very low data values, which you may want to exclude from the analysis, or at least revisit to check that they are correct.
		+
		+	It is always worth drawing a graph before you start any further analysis, just to have a look at your data.
		+
		+	You can also display grouped data in a pie chart, such as this one. Pie charts are best used when you are interested in the relative size of each group, and what proportion of the total fits into each category, as they illustrate very clearly which groups are bigger.
		+
		+	Measures of Location: Averages: The average gives you information about the size of the effect of whatever you are testing, in other words, whether it is large or small. There are three measures of average: mean, median and mode.When most people say average, they are talking about the mean. It has the advantage that it uses all the data values obtained and can be used for further statistical analysis. However, it can be skewed by ‘outliers’, values which are atypically large or small.
		+
		+	As a result, researchers sometimes use the median instead. This is the mid-point of all the data. The median is not skewed by extreme values, but it is harder to use for further statistical analysis.
		+
		+	The mode is the most common value in a data set. It cannot be used for further statistical analysis.
		+
		+	The values of mean, median and mode are not the same, which is why it is really important to be clear which ‘average’ you are talking about.
		+
		+	Measures of Spread: Range, Variance and Standard Deviation: Researchers often want to look at the spread of the data, that is, how widely the data are spread across the whole possible measurement scale.
		+
		+	There are three measures which are often used for this:
		+
		+	The range is the difference between the largest and smallest values. Researchers often quote the interquartile range, which is the range of the middle half of the data, from 25%, the lower quartile, up to 75%, the upper quartile, of the values (the median is the 50% value). To find the quartiles, use the same procedure as for the median, but take the quarter- and three-quarter-point instead of the mid-point.
		+
		+	The standard deviation measures the average spread around the mean, and therefore gives a sense of the ‘typical’ distance from the mean.
		+
		+	The variance is the square of the standard deviation. They are calculated by:
		+
		+	calculating the difference of each value from the mean;
		+	squaring each one (to eliminate any difference between those above and below the mean);
		+	summing the squared differences;
		+	dividing by the number of items minus one.
		+	This gives the variance.
		+
		+	To calculate the standard deviation, take the square root of the variance.
		+
		+	Skew
		+	The skew measures how symmetrical the data set is, or whether it has more high values, or more low values. A sample with more low values is described as negatively skewed and a sample with more high values as positively skewed.
		+
		+	Generally speaking, the more skewed the sample, the less the mean, median and mode will coincide.
		+
		+	More Advanced Analysis
		+	Once you have calculated some basic values of location, such as mean or median, spread, such as range and variance, and established the level of skew, you can move to more advanced statistical analysis, and start to look for patterns in the data.
		+

@@ Line 16: / Line 16: @@
 == Types of Statistical Analysis<ref>Types of Statistical Analysis [http://intellspot.com/types-statistical-analysis/ Intellspot]</ref> ==
-The two main types of statistical analysis are descriptive and inferential. However, there are other types that also deal with many aspects of data including data collection, prediction, and planning.
+The two main types of statistical analysis are descriptive and inferential (see next section Descriptive Statistics Vs. Inferential Statistics). However, there are other types that also deal with many aspects of data including data collection, prediction, and planning.
 *Predictive Analytics: If you want to make predictions about future events, predictive analysis is what you need. This analysis is based on current and historical facts. Predictive analytics uses statistical algorithms and machine learning techniques to define the likelihood of future results, behavior, and trends based on both new and historical data. Marketing, financial services, online services providers, and insurance companies are among the main users of predictive analytics. More and more businesses are starting implementing predictive analytics to increase competitive advantage and to minimize the risk associated with unpredictable future. Predictive analytics can use a variety of techniques such as data mining, modeling, artificial intelligence, machine learning and etc. to make important predictions about the future.
 *Prescriptive Analytics:Prescriptive analytics is a study which examines data to answer the question “What should be done?” It is a common area of business analysis dedicated to identifying the best movie or action for a specific situation. Prescriptive analytics aim to find the optimal recommendations for a decision making process.  It is all about providing advice. Prescriptive analytics is related to descriptive and predictive analytics. While descriptive analytics describe what has happened and predictive analytics helps to predict what might happen, prescriptive statistics aims to find the best options among available choices. Prescriptive analytics uses techniques such as simulation, graph analysis, business rules, algorithms, complex event processing, recommendation engines, and machine learning.
@@ Line 34: / Line 34: @@
 [[File:Statistical_Analysis_-_Types.png|300px|Types of Statistical Analysis]]<br />
 source: Intellspot
@@ Line 42: / Line 54: @@
 Among some of the more popular statistical analysis software services are IBM's SPSS, SAS, Revolution Analytics' R, Minitab and Stata.