9.3: Reporting Results

In the previous chapter, we discussed how each stage of the scientific method (originally discussed in the first chapter) is applied in the Null Hypothesis Significance Testing process. This section provides a little more detail about the Write-Up step. Remember that when conducting statistics for the social sciences, the answer is never just the number. In the social sciences, we do the statistics to answer questions so the final answer needs enough information to answer that question, and to let other statisticians know a little bit about the sample and the calculations.

You’ll see a sample write-up below, but let’s introduce some pieces before you read through the sample.

• Provide the means first. That is, you can tell the reader something about what the data looks like before going on to describing the results of the test. In general, this is good practice: always remember that your reader doesn’t know your data anywhere near as well as you do. So unless you describe it to them properly, the statistical tests won’t make any sense to them, and they’ll get frustrated and cry.
• The description tells you what the research hypothesis being tested is. To be honest, writers don’t always do this, but we're going to practice this since it might be a long ways and a lot of time from when the research hypothesis was first presented. Also, notice that the research hypothesis is in words, not (just) in symbols. For help knowing how to write numbers in your paragraph, check out this page on Reporting Statistics in APA Style.
• A "statistical sentence" showing the results is included. When reporting the results of the test itself, the write-up won't just say that the result was not statistically significant, there's a “statistical sentence” (the dense mathematical-looking part in the parentheses in the sample below) which reports all the statistical results. For the t-test, the information that gets reported is the test statistic result (the calculated t-score), the information about the distribution used in the test (the "t"), the Degrees of Freedom (which helps understand the sample size), and then the information about whether the result was significant or not (in this case p>.05). The general principle is that you should always provide enough information so that the reader could check the test results themselves if they really wanted to. Writing t(4)=1.49 is essentially a highly condensed way of writing “the sampling distribution of the t-test statistic with degrees of freedom of 4, and the value of the calculated t-score is 1.49”. This page on Reporting Statistics in APA Style (website address: https://my.ilstu.edu/~jhkahn/apastats.html) also shows how to write these "statistical sentences."
• The results are interpreted. In addition to indicating that the result was significant, include an interpretation of the result about whether or not the research hypothesis was supported. If you don’t include something like this, it’s really hard for your reader to understand what’s going on.

Now that you have a sense of what a one-sample t-test analysis (from the previous section) and its write-up (from above) might look like, let’s review a writing up of the results of a scenario an example with playing a card game.

Scenario

Imagine this scenario: After playing a game of solitaire on my phone 10 times, I found that I won 6 times. I felt like I wasn't doing well, so I found that, on average, folks win solitary 43% of the time. To conduct a t-test, I asked my ten closest friends to play solitaire 10 times and let me know how many times they won. I guess I don't have 10 close friends, because only 4 people replied back. If I found the sample mean (\( \bar{X} = .55 \) (my friends and I won \(55\%\) of the time), my research hypothesis is that the sample had a higher win rate than the population (\( \bar{X} > \mu \)). With a standard deviation (say, s=0.18), I could conduct a t-test! We'll skip how to do that part for now, and move on to how to write up your results.

Write-Up

Here's a sample way to report this would be to write something like this:

The average win rate for the five participants in the experiment was 55% (\( \bar{X} = .55) \), while the population average win rate was 43% (\( \mu = .43) \). We hypothesize that the sample (Dr. Navarro and her five friends) would have a higher average win rate than the population (\(\bar{X} > \mu \nonumber\)). A one-sample t-test found that the sample's win rate is similar to the population's win rate. (\(t\)(3) = 1.49, \(p\) > 0.05). The research hypothesis that the sample would have a higher win rate than the population was not supported.

Anything Missing?

The section on write-ups in the previous chapter indicated that the following should be included; were they?

• Restating the research hypothesis and stating whether or not it was supported, and
• Providing the calculated results, which will probably include the actual means (with units) but will definitely include the calculated statistic.

Example \(\PageIndex{1}\)

1. Was the research hypothesis (re-)stated in the write-up?
2. Did the write-up include whether or not the research hypothesis was supported?
3. Were the means of each group shared? Were the units of what was measured for the means stated?
4. Was the calculated statistic include? In other words, was there a statistical sentence showing the results?

Solution

1. Yes, in both words and symbols as the write-up says “We hypothesize that the sample (Dr. Navarro and her five friends) would have a higher average win rate than the population (\( \bar{X} > \mu \)).”
2. Yes, as the write-up says “the research hypothesis that the sample would have a higher win rate than the population was not supported”.
3. Yes, the means for both groups were named in the sentence and in symbols.
4. Yes, the results of the statistical analysis were provided in a statistical sentence.

One thing to notice is that the null hypothesis and the critical value is NOT included. That information is for you to use to make the decision, but readers should be able to figure out what happened by seeing the p-value, and whether it's p>0.05 or p<0.05.

In Closing,

As with everything else, your overriding concern should be that you explain things to your reader. Always remember that the point of reporting your results is to communicate to another human being. Dr. Navarro cannot tell you just how many times she has seen the results section of a report or a thesis or even a scientific article that is just gibberish, because the writer has focused solely on making sure they’ve included all the numbers, and forgotten to actually communicate with the human reader.

In sum, write-ups should include:

• Research Hypothesis, including:
  • Re-state the RH (including the groups being compared, the DV, and the direction word), and
  • If the RH was supported or not.
• Calculation results:
  • Calculated statistical (statistical sentence):
    • t(df) = calculated t-score, p<.05
    • or
    • t(df) = calculated t-score, p>.05
  • Means, with units, of each group (name the groups)

To put it all together, let's do a full practice problem, with the calculations and the write-up and everything!

Contributors and Attributions

• Danielle Navarro (University of New South Wales)

• Dr. MO (Taft College)