Chi-square Test Graphpad Prism

[Daiana Parthemore]

Contingencytables are used to analyze count data across two or more experimental factors by separating the subjects into the appropriate categories. An example is comparing subjects with and without some risk factor (such as smoking/non-smoking) and further categorizing by whether they have a disease (such as lung cancer).

Unlike regression analysis or ANOVA, both of the factors are categorical (rather than numeric variables). A 2x2 table means that subjects are separated based on two factors (or questions) with two levels in each factor (groups 1 or 2 for the first factor and outcome 1 or 2 for the second factor). Each subject falls into one of the two levels for each factor, which results in four possible categories in all.

The goal is to determine if the factors are associated, for example, a subject in group 1 may be more likely to be part of the outcome 2 category. Be careful with interpretation, though, as a relationship does not necessarily imply causation!

Suppose you recruit a fixed number of people with and without lung cancer. Then you interview each subject and record whether they are smokers or not. Notice these are both factors with exactly two possibilities.

This study would correspond to a contingency table like the one below, where you could count the number of subjects in each of the four categories. Testing the differences between the observed and expected counts can help you quantify the relationship between smoking and lung cancer.

Chi-square tests compare the observed (O) and expected (E) frequencies of the subjects. With contingency table tests, the expected frequencies are calculated in the background based on the multiplication rule of probability. The idea is to use the row and column (marginal) totals to calculate the expected counts if there is no association between the variables. If the observed values vary significantly from the expected values (using a chi-square test), then there is statistical evidence of association.

Several methods exist to calculate Fisher's test, and this calculator uses the summing small P values method. Fisher's test is rarely calculated by hand and can be very intensive even for a computer.

Statistical tests for contingency tables evaluate whether the factors are associated. After you click calculate, the P value will be reported along with a sentence describing its statistical significance. For chi-square this will also include the chi-square test statistic and its degrees of freedom.

Although this calculator does not create a graphic of the relationship between the groups and outcomes, you might want to look at a grouped bar chart that compares your observed and expected counts. That will visually show you which categories vary from what would be expected if there was no association between the variables.

I am analyzing a questionnaire survey data about online learning receptibility across different age groups. I have 4 age groups, and each has its % acceptance of the online learning susceptibility. For example,

I did a contingency table analysis with Chi-square using GraphPad prism. P-value is 0.0185 and is significant. But The bar diagram clearly says receptibility of two age groups is low, but the other two are high.

Personally I'd probably be fine if somebody presented this to me and said, overall this is significant, and the bar diagram shows what is responsible for the significance, so I wouldn't require additional formal tests.

Problem with this (as generally with multiple testing) is that it loses some power. If you end up with p-values between 0.05 and 0.05/7, you may want to say that this is suspicious, though not significant. But if your data set is of a good size (i.e. not too small, and not so big that everything will always be significant) and the true situation is rather simple (in the sense that either something strong is going on or nothing), all tests or at least those you care for may well either be significant using 0.05/7 or insignificant even using 0.05.

Most universities require students to follow APA format in the reporting of statistics. APA (American Psychological Association) style was the first and most commonly used set of rules to report statistics. The medical field then came up with their own set of guidelines: the SAMPL guidelines.Reporting statistics in APA formatReporting statistics in APA styleSAMPL guidelines

Follow this link for an overview of the different types of tables in Prism. It is important to choose the right type of table for your data since graphs and especially analyses are linked strictly to specific table types. Graphs can be used for any table type but often they will not look good if you use a graph for a table type it is not intended for: the titles and the legend will be messed up. Analyses are only possible for a specific table type: you are not allowed to perform them on a table type they are not intended for!!

This is often done to improve normality of the data. Some statistical analyses are only allowed on normally distributed data. So when data values are not normal, you can transform them and check if the transformed values do show a normal distribution. If this is the case you can do the statistical analysis on the transformed data. The most common transformations are:log transformationsquare transformationsquare root transformationreciprocal transformation...

Categorical data are non numerical data and the values taken are usually names e.g. variable sex: male or female. The particular case of a categorical variable with only 2 categories, is a binary variable e.g. alive/dead or male/female.

For unranked categorical data you cannot calculate a mean or a median. Therefore, analyses on this type of data are based on comparing observed proportions to expected proportions. Each test subject is seen as a separate trial with a binary outcome. For instance, you check in 50 persons whether they carry a SNP in a gene that is linked to epilepsy. Each person becomes a trial with a binary outcome:Yes, the person carries the SNPNo, the persons is not a carrier of the SNPThe proportion of persons that carry the SNP is calculated and compared to the expected proportion using a binomial test. Click the title to see how to perform such a test in Prism.

When you have more than two categories, you also compare observed proportions with expected values, this time using a chi square test. The typical example is a crossing experiment, where you want to know if the outcome follows the Mendelian ratio. Click the title to see how to perform a chi-square test in Prism.

A special case of more than two groups is when the groups are defined by multiple grouping variables. Grouping variables define the groups and are called factors, e.g. gender, age, treatment, genotype, smoking behaviour... When you have two grouping variables, you can compare the groups that are defined by them using two-way ANOVA. Click the title for an example on comparing the means of six groups, defined by two factors: gender and genotype.

If one of the factors is quantitative (time, dose) do not choose two-way ANOVA.

Two-way ANOVA will treat the groups as a set of independent groups, without regarding the link/trend between the groups.

Instead, fit a curve to the data and calculate time to peak, peak level, slope or area under the curve and compare these values with one-way ANOVA.

Click the title to see an example in which we want to compare cell distributions between two groups: a mutant and a wild-type. We used a number of perforin-deficient and wild type mice and used flow cytometry to count T-cell subpopulations in these mice. We counted the number of CD8+ naive cells, CD8+ central memory T cells (TCM) and CD8+ effector memory T cells (TEM). All variables are nominal: wt/mutant and CD8+ naive/TCM/TEM. The question is: Is there an effect of the mutation on the distribution of CD8+ T cells?

Frequency distributions and histograms are by definition discrete:For discrete data values, the bins correspond to the valuesFor continous data values, discrete intervals or bins are created:

e.g. bin with center = 1 and width = 1 then all data values between 0.5 and 1.5 belong in this bin and the frequencies of all members of a bin are added to calculate and plot the bin frequency.Tips on graphing histograms

Exercise on how to individually color points of the same row on a dot plot.

In this example we have measured 6 mice before and after drug treatment. I now want to plot a bar chart with individual data points but I want to color the data points according to the mouse they come from.

In ELISA, plates are coated with an antigen. Then antibodies are added allowing to detect (the amount) of antigen on the plates. When you include a standard curve in the test (a serial dilution of a known, purified antigen) ELISA data can be used to precisely calculate the concentrations of antigen in samples.

Sometimes people subtract the OD readings of the empty wells (blanks) from the other readings. In most cases, like when interpolating unknowns against a standard curve or doing titrations this is not really necessary. For the sake of showing you how it can be done in Prism we will subtract the blank value.

Enzyme kinetics is the study of chemical reactions that are catalysed by enzymes. The rate (speed) of the reaction is measured and the effect of different conditions on the reaction rate is investigated.

Exercise on assessing the effect of two inhibitors on the kinetics of the enzyme lysozyme.

Your scientific data from experiments and observations are easy to organize, analyze and visualized with the help of the software GraphPad Prism. Even without previous knowledge, statistical tests can simply be executed and their results can easily be interpreted.

GraphPad Prism was originally developed for experimental biologists, medicine scientists and pharmacologists. Meanwhile Graphpad Prism is used throughout the life sciences sector. Many undergraduate and graduate students also use this statistical program.

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