Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in regression analysis, ANOVA, and designed experiments. In this blog post, I explain interaction effects, how to interpret them in statistical designs, and the problems you will face if you don’t include them in your model.

In any study, whether it’s a taste test or a manufacturing process, many variables can affect the outcome. Changing these variables can affect the outcome directly. For instance, changing the food condiment in a taste test can affect the overall enjoyment. In this manner, analysts use models to assess the relationship between each independent variable and the dependent variable. This kind of an effect is called a main effect. However, it can be a mistake to assess only main effects.

In more complex study areas, the independent variables might interact with each other. Interaction effects indicate that a third variable influences the relationship between an independent and dependent variable. This type of effect makes the model more complex, but if the real world behaves this way, it is critical to incorporate it in your model. For example, the relationship between condiments and enjoyment probably depends on the type of food—as we’ll see in this post!

## Example of Interaction Effects with Categorical Independent Variables

I think of interaction effects as an “it depends” effect. You’ll see why! Let’s start with an intuitive example to help you understand these effects conceptually.

Imagine that we are conducting a taste test to determine which food condiment produces the highest enjoyment. We’ll perform a two-way ANOVA where our dependent variable is Enjoyment. Our two independent variables are both categorical variables: Food and Condiment.

Our ANOVA model with the interaction term is:

Satisfaction = Food Condiment Food*Condiment

To keep things simple, we’ll include only two foods (ice cream and hot dogs) and two condiments (chocolate sauce and mustard) in our analysis.

Given the specifics of the example, an interaction effect would not be surprising. If someone asks you, “Do you prefer ketchup or chocolate sauce on your food?” Undoubtedly, you will respond, “It depends on the type of food!” That’s the “it depends” nature of an interaction effect. You cannot answer the question without knowing more information about the other variable in the interaction term—which is the type of food in our example!

That’s the concept. Now, I’ll show you how to include an interaction term in your model and how to interpret the results.

## How to Interpret Interaction Effects

Let’s perform our analysis. All statistical software allow you to add interaction terms in a model. Download the CSV data file to try it yourself: Interactions_Categorical.

The p-values in the output below tell us that the interaction effect (Food*Condiment) is statistically significant. Consequently, we know that the satisfaction you derive from the condiment *depends* on the type of food.

But, how do we interpret the interaction effect and truly understand what the data are saying? The best way to understand these effects is with a special type of graph—an interaction plot. This type of plot displays the fitted values of the dependent variable on the y-axis while the x-axis shows the values of the first independent variable. Meanwhile, the various lines represent values of the second independent variable.

On an interaction plot, parallel lines indicate that there is no interaction effect while different slopes suggest that one might be present. Below is the plot for Food*Condiment.

The crossed lines on the graph suggest that there is an interaction effect, which the significant p-value for the Food*Condiment term confirms. The graph shows that enjoyment levels are higher for chocolate sauce when the food is ice cream. Conversely, satisfaction levels are higher for mustard when the food is a hot dog. If you put mustard on ice cream or chocolate sauce on hot dogs, you won’t be happy!

Which condiment is best? It depends on the type of food, and we’ve used statistics to demonstrate this effect.

## Overlooking Interaction Effects is Dangerous!

When you have statistically significant interaction effects, you can’t interpret the main effects without considering the interactions. In the previous example, you can’t answer the question about which condiment is better without knowing the type of food. Again, “it depends.”

Suppose we want to maximize satisfaction by choosing the best food and the best condiment. However, imagine that we forgot to include the interaction effect and assessed only the main effects. We’ll make our decision based on the main effects plots below.

Based on these plots, we’d choose hot dogs with chocolate sauce because they each produce higher enjoyment. That’s not a good choice despite what the main effects show! When you have statistically significant interactions, you cannot interpret the main effect without considering the interaction effects.

Given the intentionally intuitive nature of our silly example, the consequence of disregarding the interaction effect is evident at a passing glance. However, that is not always the case, as you’ll see in the next example.

## Example of an Interaction Effect with Continuous Independent Variables

For our next example, we’ll assess continuous independent variables in a regression model for a manufacturing process. The independent variables (processing time, temperature, and pressure) affect the dependent variable (product strength). Here’s the CSV data file if you want to try it yourself: Interactions_Continuous.

In the regression model, I’ll include temperature*pressure as an interaction effect. The results are below.

As you can see, the interaction term is statistically significant. But, how do you interpret the interaction coefficient in the regression equation? You could try entering values into the regression equation and piece things together. However, it is much easier to use interaction plots!

**Related post**: How to Interpret Regression Coefficients and Their P-values for Main Effects

In the graph above, the variables are continuous rather than categorical. To produce the plot, the statistical software chooses a high value and a low value for pressure and enters them into the equation along with the range of values for temperature.

As you can see, the relationship between temperature and strength changes direction based on the pressure. For high pressures, there is a positive relationship between temperature and strength while for low pressures it is a negative relationship. By including the interaction term in the model, you can capture relationships that change based on the value of another variable.

If you want to maximize product strength and someone asks you if the process should use a high or low temperature, you’d have to respond, “It depends.” In this case, it depends on the pressure. You cannot answer the question about temperature without knowing the pressure value.

## Important Considerations for Interaction Effects

While the plots help you interpret the interaction effects, use a hypothesis test to determine whether the effect is statistically significant. Plots can display non-parallel lines that represent random sample error rather than an actual effect. P-values and hypothesis tests help you sort out the real effects from the noise.

The examples in this post are two-way interactions because there are two independent variables in each term (Food*Condiment and Temperature*Pressure). It’s equally valid to interpret these effects in two ways. For example, the relationship between:

- Satisfaction and Condiment depends on Food.
- Satisfaction and Food depends on Condiment.

You can have higher-order interactions. For example, a three-way interaction has three variables in the term, such as Food*Condiment*X. In this case, the relationship between Satisfaction and Condiment depends on both Food and X. However, this type of effect is challenging to interpret. In practice, analysts use them infrequently. However, in some models, they might be necessary to provide an adequate fit.

Finally, when you have interaction effects that are statistically significant, do not attempt to interpret the main effects without considering the interaction effects. As the examples show, you will draw the wrong the conclusions!

If you’re learning regression, check out my Regression Tutorial!

Neha says

Thank you for amazing posts. the way you express concepts is matchless.

Jim Frost says

You’re very welcome! I’m glad they’re helpful!

Mona says

what does it mean when I have a significant interaction effect only when i omit the main effects of the independent variables (by choosing the interaction effect in “MODEL” in SPSS). it is “legal” to report the interaction effect without reporting the main effects?

Jim Frost says

Hi Mona,

That is a bit tricky.

If you had one model where the main effects are not significant, but the interaction effects are significant, that is perfectly fine.

However, it sounds like in your case you have to decide between the main effects or the interaction effects. Models where the statistical significance of terms change based on the specific terms in the model are always difficult cases. This problem often occurs (but is not limited to) in cases where you multicollinearity–so you might check on that.

This type of decision always comes down to subject area knowledge. Use your expertise, theory, other studies, etc to determine what course of action is correct. It might be OK to do what you suggest. On the other, perhaps including the main effects is the correct route.

Jim

Apple says

what is the command for conintuous by continuous variables interaction plot in stata?

Thanks

Jim Frost says

Hi, I’ve never used Stata myself, but I’ve seen people use “twoway contour” to plot two-way interaction effects in Stata. Might be a good place to start!

Sol says

Hi Jim, thank you very much for your post. My question is how do you interpret an insignificant interaction of a categorical and a continuous variable, when the main effects for both variables are significant? For the sake of simplicity if our logit equation is as follows Friendliness = α + βAge + βDog + βAge*Dog. Where Friendliness and Dog are coded as dummy variables that take the values of either 1 or 0 depending on the case. So if all but the interaction term, βAge*Dog, is significant, does that mean the probability of a dog being friendly is independent of its age?

Jim Frost says

If the Age variable is significant, then you know that friendliness

isassociated with age, and dog is as well if that variable is significant. A significant interaction effect indicates that the effect of one variable on the dependent variable depends on the value of another variable. In your example, lets assume that the interaction effect was significant. This tells you that the relationship between age and friendliness changes based on the value of the dog variable. In that case, it’s not a fixed relationship or effect size. (It’s also valid to say that the relationship between dog and friendliness changes based on the value of age.)Now, in your case, the interaction effect is not significant but the two main effects are significant. This tells you that there is a relationship between age and friendliness and a relationship between dog and friendliness. However, the exact nature of those relationships DO NOT change based on the value of the other variable. Those two variables affect the probability of observing the event in the outcome variable, but one independent variable doesn’t affect the relationship between the other independent variable and the dependent variable.

The fact that you have one categorical variable and a continuous variable makes it easier to picture. Picture a different regression line for each level of the categorical variable. These fitted lines display the relationship between the continuous independent variable and the response for each level of dog. A significant interaction effect indicates that the differences between those slopes are statistically significant. An insignificant interaction effect indicates that there is insufficient evidence to conclude that the slopes are different. I actually show an example of this situation (though not with a logistic model) that should help.

I hope that makes it more clear!

Luka says

Hello,

I am interested how to read for interaction effect if we just have a table of observations, for example

A B C

2 4 7

4 7 8

6 9 13

In the lecture I attended this was explained as “differences between differences” but I didn’t get what this refers to.

Thanks

Jim Frost says

Hi Luka, it’s impossible to for me to interpret those observations because I don’t know the relationships between the variables and there are far too few observations.

In general, you can think of an interaction effect as an “it depends” effect as I describe in this blog post. Suppose you have two independent variables X1 and X2 and the dependent variable Y. If the relationship between X1 and Y changes based on the value of X2, that’s an interaction effect. The size of the X1 effect depends on the value of X2. Read through the post to see how this works in action. The value of the interaction term for each observation is the product of X1 and X2 (X1*X2).

An effect is the difference in the mean value of Y for different values of X. So, if the interaction effect is significant, you know that the differences of Y based on X will vary based on some other variable. I think that’s what your instructor meant by the differences between differences. I tend to think of it more as the relationship between X1 and Y depends on the value of X2. If you plot a fitted line for X1 and Y, you can think of it as the slope of the line changes based on X2. There’s a link in this blog post to another blog post that shows how that works.

I hope this helps!

Syahmi says

Your explanation is really great! Thank you so much. I totally will recommend you to my friends

Jim Frost says

You’re very welcome! Thank you for recommending me to your friends!

Luka says

Thanks for help, I appreciate it!

Yeasin says

Great work Jim! People get very vague idea whenever they look at google to learn the basic about interaction in statistics. Your writing is a must see and excellent work that demonstrated the basic of interaction. Thanks heaps.

Jim Frost says

Hi Yeasin, thank you! That means a lot to me!

Tanikan says

Hi Jim,

Thank for the valuable tutorial.

I have 2 questions as follows:

1. In more complex study areas, the independent variables might interact with each other. What do you mean by complex area? Is it social science?

2. I have run Mancova and observed that results of two-way = interaction. I found that SPSS does not run post-hoc. Can I use the t-test after that?

My model is factorial design (2 levels of X1, 2 levels of X2, and 2 levels of X3) on Y.

I report in paper for two-way and three way interaction on below. Is it ok?

Two-way interaction

Among the X2 level 1 group, the mean of Y among subjects who viewed X3 level 2 (adjusted M = xxx, SE =xxx) is significantly higher than those who viewed X3 level 1 (adjusted M = xxx, SE = xxx) with t(xx) = xx, p < xx.

three-way interaction

Among the subjects who viewed the X3 level 2, the mean of Y of the subjects who expressed X1 level 2 (adjusted M = xxx, SE = xxx) is significantly greater than those who expressed X1 level 1 (adjusted M = xxx, SE = xxx) for those who had X2 level 1 [t(xx) = xxx, p < xxx].

Thank you in advance

Jim Frost says

Hi Tanikan,

Thanks for the great questions!

Regarding more and less complex study areas, in the context of this post, I’m simply referring to subject matter where only main effects are statistically significant as being simpler. And, subject areas where interaction effects are significant as more complex. I’m calling them more complex because the relationship between X and Y is not constant. Instead, that relationship depends on at least one other variable. It’s just not as simple.

I would not use t-tests for that purpose. I’m surprised if SPSS can’t perform post-hoc tests when there are interaction effects–but I use other statistical software more frequently. With your factorial design, there will be multiple groups based on the interactions of your factors. As you compare more groups, the need for controlling the family/joint/simultaneous error rate becomes even more important. Without controlling for that joint error rate, the probability that at least one of the many comparisons will be a false positive increases. T-tests don’t control that joint error rate. It’s important to use a post hoc test.

At least for the two-way interaction effects, I highly recommend using an interaction plot (as shown in this post) to accompany your findings. I find that those graphs are particularly helpful in clarifying the results. Of course, that graph doesn’t tell you which specific differences between groups are statistically significant. The post hoc tests for those groups will identify the significant differences.

I hope this helps!

Alicia says

Hi, Jim!

I have a sort of somehow interaction-related question, but I didn’t know where to post it, so this entry seemed the most adequate to me.

I work with R and I would like to use an ANCOVA to evaluate the effect of a factor (age, for example, with two levels, adult and subadult) in the regression of body length (log transformed, logLCC) and weight (log transformed, logweight). This regression measures body condition of an individual (higher weights at same lenghts indicate a better condition, that is, sort of “fluffyness”).

So, when I run the analysis:

aov(logweight~logLCC*age)

I obtain a significant interaction between logLCC:age (p=0.0068). I understand this means that slopes for each age class are not paralell. However, the factor age alone it’s not significant (p=0.2059).

What does this mean? How is it interpreted?

I have tried deleting the interaction from the model, but it loses a lot of explicative power (p=0.0068). So, what should I do? I am quite lost with this issue…

Thank you so much in advance,

Alicia

Jim Frost says

Hi Alicia!

First, before I get into the interaction effect, a comment about the model in general. I don’t know if you’re analyzing human weight or not. But, I’ve modeled Percent Body Fat and BMI. While I was doing that, I had to decide whether to use Height, Weight, and Height*Weight as the independent variables and interaction effect or should I use body mass index (BMI). I found that both models fit equally as well but I went ahead with BMI because I could graph it. I did have to include a polynomial term because the relationship was curvilinear. I notice that you’re using a log transformation. That might well be just fine and necessary. But, I found that I didn’t need to go that route. Just some food for thought. You can read about this BMI and %body fat model.

Ok, so on to your interaction effect. It’s not problematic at all that the main effect for age is not significant. In fact, when you have a significant interaction you shouldn’t try to interpret the main effect alone anyway. Now, if it had been significant and you wanted determine the entire effect of age, you would’ve had to assess both the main effect and the interaction effect together. Now, you just need assess the interaction effect alone. But, it’s always easiest to interpret interaction effects with graphs, as I do in this blog post.

In the post, I show examples of interaction plots with two factors and another with two continuous variables. However, you can certainly create an interaction plot for a factor * continuous variable. For your model, this type of graph will display two lines–one for each level of the age factor. Because you already know the interaction term is significant, the difference between the two slopes is statistically significant. (If the main effect had been significant, the interaction plot would have included it in the calculations as well–but it is fine that it’s not significant.)

It sounds like you should leave the interaction effect in the model. Some analysts will also include the main effects in the model when they are included in a significant interaction effect even if the main effect is not significant by itself (e.g., age). I could go either way on that issue myself. Just be sure that the interaction makes theoretical/common sense for your study area. But, I don’t see any reason for concern. The insignificant main effect is not a problem.

I hope this helps!

Alicia says

Hi Jim,

first of all… thank you very much for your early response!

And after that… I am so sorry! I forgot to explain that I work with lizards, not with humans. My measurement of body length (logLCC) corresponds to the log-transformed Snout-Vent Length (logSVL, whose acronym in spanish, given that it’s my mothertongue, is LCC; I forgot to translate it!). The relationship among these two variables tend to be linear.

So, in these animals, the regression of logSVL and logweight is a common and standardized method to assess body condition. Residuals from this regression are used to assess body condition; if they’re positive the animal is more “chubby” (better condition) and, if they’re negative, the animal is more “skinny” (worse condition). The aim of my ANCOVA is to compare the effect of age on this regression.

Anyway, following your advice I created an interaction plot which displays two lines, one for each level of the age factor. The two lines cross in a certain middle point, diverging prior and after that point. Thanks to your detailed answer, I understand that this means that age interacts somehow with body length (what sounds logical, as lizards grow together with aging), but I still don’t know how to interpret this in relation to body condition (regression).

Thanks again for your detailed, kind and early response!

Jim Frost says

You’re very welcome! And, subject area knowledge and standards definitely should guide your model building. I always enjoy learning how others use these types of analysis. And, that’s interesting actually using the residuals to assess a specimen’s health!

If you can, and are willing, post the interaction plot, I can take a stab at interpreting it. (I know I can post images in these comments but I’m not sure about other users.) Basically, the relationship between body length and weight depends on the age factor. Or, stated another way, you can’t use body length to predict weight until you know the age.

Alicia says

Hi, Jim!

Thank you again for your willingness! Unfortunately, I can’t /don’t know how to post the plot in the comments… If you are willing, you can contact me by email so I can send it to you, plus the results of the regression or whatever information that could be helpful.

Thank you!

Shruti says

Hi Jim,

Thanks for your explanation! It was really useful. I have a couple of follow-up questions. Let’s suppose a situation with 2 regression models, both of which have the exact same variables, except the second model has an additional interaction term between two variables already in the first model.

1. Now comparing the 2 regression equations, why do coefficients of other variables (apart from the interaction term and the 2 variables used to create the interaction term) change?

2. How do we compare and interpret the change in coefficients of variables which were used to create the interaction term in the first and second models?

Let me know in case it’s better for me to explain with an example here.

Thanks!

Jim Frost says

Hi Shruti,

I think I understand your questions.

1) Any time you add new terms in the model, the coefficients can change. Some of this occurs because the new term accounts for some of the variance that was previously accounted for by the other terms, which causes their coefficients to change. So, some change is normal. The changes can tend to be larger and more erratic when the model terms are correlated. The interaction term is clearly correlated with the variables that are included in the interaction. When you include an interaction term, you can help avoid this by standardizing your continuous variables.

2) I have heard about cases where analysts try to interpret the changes in coefficients when you add new terms. My take on this is that the changes are not very informative. Let’s assume that your interaction term is a valuable addition to the model. In that case, you can conclude the model without the interaction term is not as good of a model and it’s coefficient estimates might well be biased. Consequently, I wouldn’t attribute much meaning to the change in coefficient values other than your new model with the interaction term is likely to better.

However, one caveat, I believe there are fields that do place value in understanding those changes. I’m not sure that I agree, but if your field is one that has this practice, you should probably check with an expert.

I hope I covered everything!

Susanne says

Hello Jim!

Thanks for making such very clear posts. I tutor students with stats and its really tough to find good easy to follow material that EVERYONE can get. So to stumble on such a clear explanation is a breath of fresh air 😀

Now I recently saw in one of my students powerpoints that they are taught they have to redo the ANOVA analysis without the interaction if the interaction is not significant. Maybe i’ve always missed something but I have never heard of this before. Does this sound familiar to you and if so can you explain to me why this is?

thanks!

Susanne

Jim Frost says

Hi Susanne, thanks so much for your kind words. They mean a lot to me–especially coming from a stats tutor!

I have always heard that you should not include the interaction term when it is not significant. The reason being is that when you include insignificant terms in your model, it can reduce the precision of the estimates. Generally, you want to leave as many degrees of freedom for the error as you can.

Courtney Barrs says

Hi Jim,

Thankyou for this post, I found it incredibly helpful.

I am having trouble interpreting my own results of a two-way repeated ANOVA and was wondering if you could help me out.

Participants were exposed to two different videos, controlled with a counter balance. Video 1 consisted of a comedy sketch, while video 2 was of a nature documentary. Every 2 mins the participants had to indicate on a likert scale how Bored they felt at the time. For the analysis I averaged the boredom score over the first and second half of the video.

IV1: Video (Comedy vs Nature)

IV2: Time (Time 1 vs Time 2)

DV: Boredom score

My analysis output reveals a significant main effect of video p<.000, and non significant effect for time p=.192. However I have an effect of interaction for video*time, p<.000.

How would you go about interpreting these results?

Thanks in advance!

Jim Frost says

Hi Courtney,

I’m happy to hear that you found this post helpful!

The first thing that I’d recommend is graphing your results using an interactions plot like I do in this post. That’s the easiest way to understand interactions. It’s great that you’ve done the ANOVA test because you already know that whatever pattern you see in the plot is, in fact, statistically significant. Given the significance, I can conclude the lines on your plot won’t be parallel.

For your results, you can state them one of two ways. Both ways are equally valid from a statistical standpoint. However, one way might make more sense than the other given your study area or what you’re trying to emphasize.

1) The relationship between Video and Boredom depends on Time. Or:

2) The relationship between Time and Boredome depends on Video.

For the sake of illustration, let’s go with #2. You might be able to draw the conclusion along the lines of: As subjects progress from time 1 to time 2, the average boredom score increases more slowly for those who watch comedy compared to those who watch a nature documentary. Of course, you’d have to adapt the wording to match your actual results. That’s the type of conclusion that you can draw, and you’re able to say that it is statistically significant given the p-value for the interaction term.

Given that the interaction term is significant, you don’t need to interpret the main effects terms at all. And, it’s no problem that one of the main effects is not significant.

I hope this helps!

Courtney says

Hi Jim,

Thankyou so much for your quick and helpful response, it really means a lot!

This is what initially confused me when it came to interpreting my results, looking at my interaction graph there was no cross over. Both conditions are more or less parallel with one another, the gradient between time 1 and time 2 for comedy is almost 0. However, there is quite the drop for the nature video in the boredom rating at time 2.

Because the interaction graph does not cross over, does this mean that only in the Nature video does the boredom decrease significantly at Time 2? Will I need to conduct a t-test to check this?

Many thanks!

Courtney

Courtney Barrs says

Hi Jim,

Thankyou for such a quick and helpful response!

Graphing the interaction effect is actually what confused me when it came to interpretting my results. The conditions are actually parallel to one another, there is no cross over. The gradient for the comedy condition is almost zero, whereas, there is a dramatic drop in rating of boredom between time 1 and time 2 for the nature video.

With this in mind does the interpretation then mean: A difference in boredom is found across time depending on condition. Therefore, only if you are watching the nature video will you become significantly more bored at time 2. Will I need to conduct a t-test to conform this?

Many thanks!

Courtney

Jim Frost says

Hi Courtney,

You bet! 🙂

Technically, a significant interaction effect means that the difference in slopes is statistically significant. The lines don’t actually have to cross on your graph–just have different slopes. Well, having different slopes means that the lines must cross at some point theoretically even if that point isn’t displayed on your graph.

As for the interpretation, the zero slope for comedy indicates that as time passes, there is no tendency to become more or less bored. However, for nature videos, as time passes, there is a tendency to become more bored. (I’m assuming that the drop in rating that you mention corresponds to “becomes more bored”.) This difference in tendencies is statistically significant. The significant interaction indicates that the relationship between the passage of time and boredom depends on the type of video the subjects watch.

Again, an interaction effect is an “it depends” effect. Do the subjects become more bored over time? It depends on what type of video they watch! You can’t answer that question without knowing which video they watch.

So, the interaction tells you that the difference in slopes is statistically significant, which is different than the whether the difference between group means are statistically significant. To identify the specific differences between group means that are statistically significant, you’ll need to perform a post hoc test–such as Tukey’s test. These tests control the joint error rate because as you increase the number of group comparisons, the chance of a Type I error (false positive) increases if you don’t control it. I don’t have a blog post on this topic yet but plan to write one.

The interaction term tells you that the relationship changes while the post hoc test tells you whether the difference between specific group means is statistically significant.

Saheeda says

This is one of the best explanations I have read to explain ‘interactions’. Thanks!

Jim Frost says

Thanks so much, Saheeda! Your kind words mean a lot to me! I’m glad it was helpful.

Bill says

Hello. Jim. Thank for your great article.

Sorry in advance for my English. Moreover, my understanding for SPSS and stat is quite limited so some question might be silly.

I’m doing 4×5 factorial ANOVA. One of the test has Sig. interaction effect but I don’t know what exact method should I interpret it. Some told that I need to do simple main effect test, some told that Post Hoc is enough so I’m quite confused.

Another test the graph shown some cross-over line (because there are a lot of levels of iv) but the sig. value is 0.069 = not significant interaction effect right?. However I’ve read that if the line crossed, the interaction is exist. So how should I summarize?

I’m willing to send the information for you if u need.

Thank you.

Bill

Jim Frost says

Hi Bill,

You have some excellent questions!

When you have a significant interaction effect, you know you can’t interpret the main effects without considering the interaction effects. As I show in the post, interaction effects are an “it depends” effect. The interpretation for one factor depends on the value of another factor. If you don’t assess the interaction effect, you might end up putting ketchup on your ice cream!

Assessing the Post Hoc test results can be fine by itself as long as you include the interaction term in the ad hoc test. Taking that approach, you’ll see the groupings based on the interaction term and know which groups are significantly different from each other. I also like to graph the interaction plots (as I do in this post) because it provides a great graphical overview of the interaction effect.

There’s an important point about graphs. They can be very valuable in helping you understand your results. However, they are not a statistical test for your data. An interaction plot can show non-parallel lines even when the interaction effect is not significant. When you work with sample data, there’s always the chance that sample error can produce patterns in your sample that don’t exist in the population. Statistical tests help you distinguish between real effects and sample error. These tests indicate when you have sufficient evidence to conclude that an effect exists in the population.

When you have crossed lines in an interaction plot but the test results are not statistically significant, it tells you that you don’t have enough evidence to conclude that the interaction effect actually exists in the population. Basically, the graph says that the effect exists in the sample data but the statistical test says that you don’t have enough evidence to conclude that it also exists in the population. If you were to collect another random sample from the same population, it would not be surprising if that pattern went away!

I hope this helps!

Bill says

Thanks for your help. I really appreciate.

Might need your help again after I finished the post hoc.

Hope you okay with that. Haha.

Again, THANK YOU.

Sincere,

Bill

Hakim says

Thank Jim, your explanation is very nice to follow, by the way, i have a model e.e. growth=average year of schooling +political stability+average year of schooling*political stability. the stata output gives individual coefficient positive while interactive coefficient negative. unfortunately i been asked by the reviewer to explain why interaction sign is negative any statistical or theoretical explanation please.

Jim Frost says

Hi Hakim, it’s difficult to interpret the coefficients for interaction terms directly. However, I can tell you that there is nothing at all odd about having a negative sign for an interaction term. Interaction terms modify the main effects. Sometimes it adds to them while other times it subtracts. It all depends on the nature of what you’re studying.

I’d suggest creating interaction plots, like I do in this post, because they’re much easier to understand than the interaction coefficients. Look through the plots to see whether they make sense given your understanding of the subject-area. These plots are a graphical representation of the interaction terms. Therefore, if the plots make sense, your model is good to go. If they don’t, then you need to figure out what happened. I think the reviewers will find the plots easier to understand than the coefficient.

I hope this helps!

Hakim says

Thanks Jim for your quick response and comprehensive explanation..

Ting-Chun Chen says

Hi Jim,

May I ask what reference about interaction effect do you suggest to study?

I want to know more about interaction effect in clinical trial.

Thank you.

Sincere,

Ting-Chun

Jim Frost says

Hi Ting-Chun, most any textbook about regression analysis, ANOVA, or linear models in general will explain interaction effects. My preferred source is Applied Linear Regression Models. That’s a huge textbook of 1400 pages, but that’s why I like it! I don’t have reference specific to interaction effects, but would recommend something that discusses linear models in all of its aspects.

I hope this helps!

Jim