Data can be categorized as either primary or secondary and as either qualitative or quantitative. Data can be classified as either primary or secondary. Primary data is original data that has been collected specially for the purpose in mind. This type of data is collected first hand.
Those who gather primary data may be an authorized organization, investigator, enumerator or just someone with a clipboard.
These people are acting as a witness, so primary data is only considered as reliable as the people who gather it. Research where one gathers this kind of data is referred to as field research. An example of primary data is conducting your own questionnaire. Secondary data is data that has been collected for another purpose. This type of data is reused, usually in a different context from its first use. You are not the original source of the data—rather, you are collecting it from elsewhere.
An example of secondary data is using numbers and information found inside a textbook. Knowing how the data was collected allows critics of a study to search for bias in how it was conducted. A good study will welcome such scrutiny. Each type has its own weaknesses and strengths.
Primary data is gathered by people who can focus directly on the purpose in mind. This helps ensure that questions are meaningful to the purpose, but this can introduce bias in those same questions. Stated another way, those who gather secondary data get to pick the questions.
Those who gather primary data get to write the questions. There may be bias either way. Qualitative data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description. Collecting information about a favorite color is an example of collecting qualitative data. Although we may have categories, the categories may have a structure to them. When there is not a natural ordering of the categories, we call these nominal categories.
Examples might be gender, race, religion, or sport. When the categories may be ordered, these are called ordinal categories. Categorical data that judge size small, medium, large, etc.
Attitudes strongly disagree, disagree, neutral, agree, strongly agree are also ordinal categories; however, we may not know which value is the best or worst of these issues. Note that the distance between these categories is not something we can measure. Quantitative data is a numerical measurement expressed not by means of a natural language description, but rather in terms of numbers.
Quantitative data always are associated with a scale measure. Probably the most common scale type is the ratio-scale. Observations of this type are on a scale that has a meaningful zero value but also have an equidistant measure i. For example, a 10 year-old girl is twice as old as a 5 year-old girl. Since you can measure zero years, time is a ratio-scale variable.
Money is another common ratio-scale quantitative measure. Observations that you count are usually ratio-scale e. A more general quantitative measure is the interval scale. Interval scales also have an equidistant measure. However, the doubling principle breaks down in this scale. Quantitative Data : The graph shows a display of quantitative data.
Statistics deals with all aspects of the collection, organization, analysis, interpretation, and presentation of data. It includes the planning of data collection in terms of the design of surveys and experiments. Statistics can be used to improve data quality by developing specific experimental designs and survey samples. Statistics also provides tools for prediction and forecasting.
Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences as well as government and business. Statistical methods can summarize or describe a collection of data. This is called descriptive statistics. This is particularly useful in communicating the results of experiments and research. Statistical models can also be used to draw statistical inferences about the process or population under study—a practice called inferential statistics.
Inference is a vital element of scientific advancement, since it provides a way to draw conclusions from data that are subject to random variation. Conclusions are tested in order to prove the propositions being investigated further, as part of the scientific method. Descriptive statistics and analysis of the new data tend to provide more information as to the truth of the proposition.
Summary statistics : In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible. It consists of five experiments, each made of 20 consecutive runs. When applying statistics to a scientific, industrial, or societal problems, it is necessary to begin with a population or process to be studied.
A population can also be composed of observations of a process at various times, with the data from each observation serving as a different member of the overall group. For practical reasons, a chosen subset of the population called a sample is studied—as opposed to compiling data about the entire group an operation called census. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting.
This data can then be subjected to statistical analysis, serving two related purposes: description and inference. Descriptive statistics summarize the population data by describing what was observed in the sample numerically or graphically.
Numerical descriptors include mean and standard deviation for continuous data types like heights or weights , while frequency and percentage are more useful in terms of describing categorical data like race. Inferential statistics uses patterns in the sample data to draw inferences about the population represented, accounting for randomness. Inference can extend to forecasting, prediction and estimation of unobserved values either in or associated with the population being studied.
It can include extrapolation and interpolation of time series or spatial data and can also include data mining. Statistical analysis of a data set often reveals that two variables of the population under consideration tend to vary together, as if they were connected. For example, a study of annual income that also looks at age of death might find that poor people tend to have shorter lives than affluent people.
The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation could be caused by a third, previously unconsidered phenomenon, called a confounding variable. For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. To use a sample as a guide to an entire population, it is important that it truly represent the overall population.
Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any random trending within the sample and data collection procedures.
There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population.
Randomness is studied using the mathematical discipline of probability theory. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method. In applying statistics to a scientific, industrial, or societal problem, it is necessary to begin with a population or process to be studied. Recall that the field of Statistics involves using samples to make inferences about populations and describing how variables relate to each other.
The concept of correlation is particularly noteworthy for the potential confusion it can cause. Statistical analysis of a data set often reveals that two variables properties of the population under consideration tend to vary together, as if they were connected. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a confounding variable.
The essential skill of critical thinking will go a long way in helping one to develop statistical literacy. Experts and advocates often use numerical claims to bolster their arguments, and statistical literacy is a necessary skill to help one decide what experts mean and which advocates to believe.
This is important because statistics can be made to produce misrepresentations of data that may seem valid. The aim of statistical literacy is to improve the public understanding of numbers and figures. For example, results of opinion polling are often cited by news organizations, but the quality of such polls varies considerably. Some understanding of the statistical technique of sampling is necessary in order to be able to correctly interpret polling results.
Sample sizes may be too small to draw meaningful conclusions, and samples may be biased. Along with measures of central tendency , measures of variability give you descriptive statistics that summarize your data. Variability is also referred to as spread, scatter or dispersion. It is most commonly measured with the following:. Table of contents Why does variability matter? Frequently asked questions about variability. While the central tendency , or average, tells you where most of your points lie, variability summarizes how far apart they are.
This is important because it tells you whether the points tend to be clustered around the center or more widely spread out. Low variability is ideal because it means that you can better predict information about the population based on sample data. Data sets can have the same central tendency but different levels of variability or vice versa.
Both of them together give you a complete picture of your data. Using simple random samples , you collect data from 3 groups:. All three of your samples have the same average phone use, at minutes or 3 hours and 15 minutes.
This is the x-axis value where the peak of the curves are. Although the data follows a normal distribution , each sample has different spreads. Sample A has the largest variability while Sample C has the smallest variability. Range The range tells you the spread of your data from the lowest to the highest value in the distribution. To find the range , simply subtract the lowest value from the highest value in the data set. The highest value H is and the lowest L is The range of your data is minutes.
See an example. The interquartile range gives you the spread of the middle of your distribution. The interquartile range is the third quartile Q3 minus the first quartile Q1. This gives us the range of the middle half of a data set. Multiply the number of values in the data set 8 by 0. Q1 is the value in the 2nd position, which is Q3 is the value in the 6th position, which is The interquartile range of your data is minutes. Just like the range, the interquartile range uses only 2 values in its calculation.
But the IQR is less affected by outliers: the 2 values come from the middle half of the data set, so they are unlikely to be extreme scores. Standard deviation The standard deviation is the average amount of variability in your dataset. It is used in several types of statistical tests to analyze the data for an underlying structure.
I hope that this post has helped you out; I look forward to seeing questions below. Happy statistics! John loves math and science to the point that his family buys him statistics and chemistry books as gifts for his birthday. While earning his Doctorate in Education from Western Kentucky University, he went full on geek for statistics and research methods. When he is not nerding out on science and math, John loves to face paint, write with fountain pens, and dote on his loving wife and family.
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