Which central tendency should i use

What is a t-score? What is a t-distribution? Is the correlation coefficient the same as the slope of the line? What do the sign and value of the correlation coefficient tell you?

What are the assumptions of the Pearson correlation coefficient? What is a correlation coefficient? How do you increase statistical power? There are various ways to improve power: Increase the potential effect size by manipulating your independent variable more strongly, Increase sample size, Increase the significance level alpha , Reduce measurement error by increasing the precision and accuracy of your measurement devices and procedures, Use a one-tailed test instead of a two-tailed test for t tests and z tests.

What is a power analysis? Sample size : the minimum number of observations needed to observe an effect of a certain size with a given power level. Expected effect size : a standardized way of expressing the magnitude of the expected result of your study, usually based on similar studies or a pilot study. What are null and alternative hypotheses? What is statistical analysis?

How do you reduce the risk of making a Type II error? How do you reduce the risk of making a Type I error? To reduce the Type I error probability, you can set a lower significance level.

Are ordinal variables categorical or quantitative? What is statistical power? How do I calculate effect size? What is effect size? A point estimate is a single value estimate of a parameter.

For instance, a sample mean is a point estimate of a population mean. An interval estimate gives you a range of values where the parameter is expected to lie. A confidence interval is the most common type of interval estimate.

What is standard error? How do you know whether a number is a parameter or a statistic? To figure out whether a given number is a parameter or a statistic , ask yourself the following: Does the number describe a whole, complete population where every member can be reached for data collection?

Is it possible to collect data for this number from every member of the population in a reasonable time frame? What are the different types of means? But there are some other types of means you can calculate depending on your research purposes: Weighted mean: some values contribute more to the mean than others.

Geometric mean: values are multiplied rather than summed up. Harmonic mean: reciprocals of values are used instead of the values themselves. How do I find the mean?

You can find the mean , or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set. What is multiple linear regression? Univariate statistics summarize only one variable at a time. Bivariate statistics compare two variables. Multivariate statistics compare more than two variables.

What are the 3 main types of descriptive statistics? Distribution refers to the frequencies of different responses. Measures of central tendency give you the average for each response. Measures of variability show you the spread or dispersion of your dataset. What is meant by model selection? What is a model?

How is AIC calculated? What is the Akaike information criterion? Some examples of factorial ANOVAs include: Testing the combined effects of vaccination vaccinated or not vaccinated and health status healthy or pre-existing condition on the rate of flu infection in a population.

Testing the effects of marital status married, single, divorced, widowed , job status employed, self-employed, unemployed, retired , and family history no family history, some family history on the incidence of depression in a population.

Testing the effects of feed type type A, B, or C and barn crowding not crowded, somewhat crowded, very crowded on the final weight of chickens in a commercial farming operation. How do you calculate a test statistic?

How is the error calculated in a linear regression model? MSE is calculated by: measuring the distance of the observed y-values from the predicted y-values at each value of x; squaring each of these distances; calculating the mean of each of the squared distances.

What is simple linear regression? What is a regression model? Can I use a t-test to measure the difference among several groups? What is the difference between a one-sample t-test and a paired t-test?

What does a t-test measure? Which t-test should I use? What is a t-test? What is statistical significance? What is a test statistic? Which measures of central tendency can I use? For a nominal level, you can only use the mode to find the most frequent value.

For an ordinal level or ranked data, you can also use the median to find the value in the middle of your data set. For interval or ratio levels, in addition to the mode and median, you can use the mean to find the average value. What is ordinal data? Ordinal data has two characteristics: The data can be classified into different categories within a variable. The categories have a natural ranked order. However, unlike with interval data, the distances between the categories are uneven or unknown.

What does it mean if my confidence interval includes zero? How do I calculate a confidence interval if my data are not normally distributed? If you want to calculate a confidence interval around the mean of data that is not normally distributed , you have two choices: Find a distribution that matches the shape of your data and use that distribution to calculate the confidence interval.

Perform a transformation on your data to make it fit a normal distribution, and then find the confidence interval for the transformed data. What is a standard normal distribution? What are z-scores and t-scores? How do you calculate a confidence interval? To calculate the confidence interval , you need to know: The point estimate you are constructing the confidence interval for The critical values for the test statistic The standard deviation of the sample The sample size Then you can plug these components into the confidence interval formula that corresponds to your data.

What is the difference between a confidence interval and a confidence level? What is nominal data? What are the main assumptions of statistical tests? Statistical tests commonly assume that: the data are normally distributed the groups that are being compared have similar variance the data are independent If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

What are measures of central tendency? Therefore the median is not that affected by the extreme value 9. The mean is a sensitive measure or sensitive statistic and the median is a resistant measure or resistant statistic. After reading this lesson you should know that there are quite a few options when one wants to describe central tendency. In future lessons, we talk about mainly about the mean. However, we need to be aware of one of its shortcomings, which is that it is easily affected by extreme values.

Unless data points are known mistakes, one should not remove them from the data set! One should keep the extreme points and use more resistant measures. For example, use the sample median to estimate the population median.

We will discuss methods using the median in Lesson What happens to the mean and median if we add or multiply each observation in a data set by a constant? What effect does this have on the mean and the median? The result of adding a constant to each value has the intended effect of altering the mean and median by the constant. For example, if in the above example where we have 10 aptitude scores, if 5 was added to each score the mean of this new data set would be Similarly, if each observed data value was multiplied by a constant, the new mean and median would change by a factor of this constant.

Returning to the 10 aptitude scores, if all of the original scores were doubled, the then the new mean and new median would be double the original mean and median.

As we will learn shortly, the effect is not the same on the variance! Why would you want to know this? One reason, especially for those moving onward to more applied statistics e.

For many applied statistical methods, a required assumption is that the data is normal, or very near bell-shaped. When the data is not normal, statisticians will transform the data using numerous techniques e.

We just need to remember the original data was transformed!! So, why have we called it a sample mean? This is because, in statistics, samples and populations have very different meanings and these differences are very important, even if, in the case of the mean, they are calculated in the same way. The mean is essentially a model of your data set.

It is the value that is most common. You will notice, however, that the mean is not often one of the actual values that you have observed in your data set. However, one of its important properties is that it minimises error in the prediction of any one value in your data set. That is, it is the value that produces the lowest amount of error from all other values in the data set. An important property of the mean is that it includes every value in your data set as part of the calculation.

In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.

The mean has one main disadvantage: it is particularly susceptible to the influence of outliers. These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. For example, consider the wages of staff at a factory below:. Staff 1 2 3 4 5 6 7 8 9 10 Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k. The mean is being skewed by the two large salaries. Therefore, in this situation, we would like to have a better measure of central tendency.

As we will find out later, taking the median would be a better measure of central tendency in this situation. Another time when we usually prefer the median over the mean or mode is when our data is skewed i. If we consider the normal distribution - as this is the most frequently assessed in statistics - when the data is perfectly normal, the mean, median and mode are identical.

Moreover, they all represent the most typical value in the data set. However, as the data becomes skewed the mean loses its ability to provide the best central location for the data because the skewed data is dragging it away from the typical value. However, the median best retains this position and is not as strongly influenced by the skewed values.

This is explained in more detail in the skewed distribution section later in this guide. Please find below some common questions that are asked regarding measures of central tendency, along with their answers. These FAQs are in addition to our article on measures of central tendency found on the previous page. There can often be a "best" measure of central tendency with regards to the data you are analysing, but there is no one "best" measure of central tendency.

Further considerations of when to use each measure of central tendency is found in our guide on the previous page. It is usually inappropriate to use the mean in such situations where your data is skewed.

You would normally choose the median or mode, with the median usually preferred. This is discussed on the previous page under the subtitle, "When not to use the mean". Yes and no.