# Quick Tips on Writing with Statistics

## Simple and useful tips on writing with statistics

- Never use or calculate a statistical procedure that you do not fully understand. If you do not understand a procedure and you need to use it, you should learn how to use it correctly or consult someone to show you how to use it
- Never interpret or attempt the results of a statistical procedure that you do not understand fully. Talk to a statistician or a professional to help you understand the interpretation correctly if you need to interpret a particular statistic
- Consider your audience if you are using statistics in a paper. It involves trying to know if they will understand the statistics you are using. If they would not understand, you will need to explain in details the procedure you are using. The best way to ensure your audience understands your procedure is by including a lot of information rather than little details. Use footnotes, appendix or directly in the text o show your explanations depending on your field of study
- Write as much information as needed to allow the reader to make their interpretation appropriately. Giving your reader, a lot of information helps them to reconstruct your argument from your statistics. Not providing enough information will make people conclude that you are deceptive hence damaging your credibility since it is hard to convince someone you already believe that you are misleading them
- Use tables and graphics. Using visuals such as tables and graphics displays a lot of information which is also easy to understand
- For standard deviation, you can include measures of variability or calculate it if it is applicable.
- When using statistics from non-peer-reviewed places, be wary. It includes places such as magazines that usually use wrong statistics. Their samples are usually persons who choose to respond to online queries instead of properly selecting a good representation from all persons and genders in the population. They then generalize their results to the entire population. Some statistics may be generalizable while others may not. Do not use statistics which the source is unreliable.
- Include more information about the sources of your statistics. Be wary of statistics that seem to have no source. Your audience should know the exact place where your statistics came from for example: According to the Kenya census 2009. Showing your source help the audience to check for themselves in the cite you provided if they do not believe your statistics. It also shows that your statistics come from a reputable source hence increasing your credibility
- Show how you did your calculation if you calculated your statistic. In most fields, you need to show and explain how you did your calculation though this does not apply to all areas. For instance, in some fields such as the field of psychology, you do not need to explain your calculation
- Show clearly to what population(s) your statistic is meant to generalize to. If your statistic was calculated from a specific population, for example, the males in a population, you should not imply that your sample generalizes to the entire population which includes male and females
- Put the statistic at the end of the sentence and speak as plainly as possible if you are basing on inferential statistics

## Examples of statistics and how they are done

The following are the examples of statistics and how to do statistics:

### Arithmetic mean

It is the value at the center of a discrete set of numbers. It is data values divided by the number of the given values. It is denoted by x bar

### Population mean

It is the measure of the central tendency either the random variable or probability distribution which is characterized by that distribution. For a population that is finite, the population mean is the same as the arithmetic mean of the given property while considering each member of the population.

### Sample mean

It is an estimator of the population mean and population covariance whereby the population is the set from which the sample was obtained

### Sample median

In calculating the sample median, if the number of observation is low, arrange all the observations in order.

Make the total number be n

If n is odd, the median (M) = value of ((n+1)/2)th item term

If n is even, the median (M) = value of [(n/2)th item term+(n/2+1)th item term]/2

### Sample variance

It is the expectation of the squared deviation of a random variable from its mean

### Standard deviation

It is a measure used to quantify the amount of dispersion or variation of a set of data values

### Quantiles

It is a cut point that divides the range of probability distribution into intervals which are contiguous and have equal probabilities

It includes dividing observations the same way in a sample

### Median

It is a value that separates the lower half from the higher half in a data sample

### Percentile

It is a measure that indicates the value below which a percentage of observations in a group of observations given falls into. For example, the 30th percentile is the score or value below which 30% of the observations fall into

### Quartile

It is a type of quantile and is defined as the number at the middle between the smallest number in a data set and the median of that data set

### Test statistics

such as t statistics, chi-squared statistics, f statistics. A test statistic is a quantity that is derived from a sample that is used to test a hypothesis in statistics

-t statistic is a type of test statistics which is defined as the ratio of the departure of a value estimated in a parameter from its hypothesized value to its standard error

It is used to estimate the population mean from sample means in a sampling distribution where the population’s standard deviation is not known

-chi-squared statistic defined as any hypothesis test in statistics where the sampling distribution of the statistical test is a chi-squared distribution when the hypothesis (null hypothesis) is true

-f statistics

It is a type of test statistics whereby the test statistic consists of an F-distribution under a null hypothesis

### Order statistics

It is the kth-smallest value in a statistical sample and is among the most essential tools in inference and non-parametric statistics

### Sample moments and functions

It includes kurtosis and skewness. A moment in statistics is a measure which is specific and quantitative of the shape of a set of different points.

-Kurtosis is a measure of a probability distribution of a random variable which is real-valued

-skewness is an either negative, positive or undefined value which is a measure of the asymmetry of a probability distribution of a random variable which is real-valued about its mean

### The empirical distribution function

It is a cumulative distribution function is a step function which jumps up by 1/n at each of the n data points. Its value is a fraction of the observations in the variables measured and those variables must be equal to or less than the specified value. Note that in census statistics data is collected from the whole population rather than a sample of the population while statistic population the total set of observations which are made for example when studying the height of children, the population is the set of heights of children in an area.

## Statistic quotes

Statistics is known as the mathematical language of scientific experimentation hence it involves framing of key questions, analysis of data, designing of experiments and interpretations of various results. Different statisticians and professionals in the field of statistics have come up with some quotes over the years.

**These quotes include:**

- “Statistics is the science of variation”

Douglas M. Bates (~1985)

- “Statistics is the grammar of science”

Karl Pearson

- “79.48% of all statistics are made up of spot”

John Paulos, Professor of Math

- “Statistics is a body of methods for learning from experience”

Lincoln Moses

- “Statistics are the triumph of the quantitative method, and the quantitative method is a victory of sterility and death”

Hilaire Belloc

- “An approximate answer to a problem is better than an exact answer to an approximate problem”

John Turkey

- “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”

H.G. Wells

- “Numerical quantities focus on expected values, graphical summaries on expected values

John Turkey”

### How to cite statistics keys

When using numerical data or a prepared statistical table, it is essential to cite here the information was retrieved from.

The following shows how to cite statistics:

Note that information is arranged according to the citation style you are using:

- Write the name of the author. It includes the person(s) or organizations which created the dataset
- Write the date of publication. It is the year the dataset was published or released to the public
- Write the title or description. Write a complete title. Also, write a brief description of the data
- Write the publisher. It is the entity (database, organization, journal, archive) which is responsible for hosting the data
- Write the URL. Write the URL if the source of your information is online