The most likely outcome is 9 plusses with a probability of roughly 0.175: if we'd draw 1,000 random samples instead of 1, we'd expect some 175 of those to result in 9 plusses. Our null hypothesis dictates that each case has a 0.5 probability of doing so, which is why the number of plusses follows the binomial sampling distribution shown below. Of our 18 cases, between 0 and 18 could have a plus (that is: rate ad1 higher than ad3). However, for those who are curious, we'll go into a little more detail now. “a sign test didn't show any difference between the two medians, exact binomial p (2-tailed) = 0.24.” More on the P-Value Although p-values can easily be calculated from it, we'll add something like When reporting a sign test, include the entire table showing the signs and (possibly) ties. It's not included now because our sample size n <= 25. SPSS omits a continuity correction for calculating Z, which (slighly) biases p-values towards zero. (2-tailed)”, an approximate p-value based on the standard normal distribution. In many cases the output will include “Asymp. Our finding doesn't contradict our hypothesis is equal population medians. This means there's a 24% chance of finding the observed difference if our null hypothesis is true. (2-tailed) refers to our p-value of 0.24. Can we reasonably expect this difference just by random sampling 18 cases from some large population? Output - Test Statistics TableĮxact Sig. It turns out this holds for 12 instead of 9 cases. Since we've 18 respondents, our null hypothesis suggests that roughly 9 of them should rate ad1 higher than ad3. The percentage scales of our variables -fortunately- make this much less likely. This may be an issue with typical Likert scales. Output - Signs Tableįirst off, ties (that is: respondents scoring equally on both variables) are excluded from this analysis altogether. NPAR TESTS /SIGN=ad3 WITH ad1 (PAIRED) /MISSING ANALYSIS. SPSS Sign Test SyntaxĬompleting these steps results in the syntax below (you'll have one extra line if you included the exact test). If it's absent, just skip the step shown below. Whether your menu includes the E xact button depends on your SPSS license. We'll do so by reversing the variable order. We prefer having the best rated variable in the second slot. They're related (rather than independent) because they've been measured on the same respondents. The 2 Re lated samples refer to the two rating variables we're testing. The most straightforward way for running the sign test is outlined by the screenshots below. A very different distribution is unlikely under H0 and therefore argues that the population medians probably weren't equal after all. If our null hypothesis is true, then the plus and minus signs should be roughly distributed 50/50 in our sample. respondents who rated ad1 ad3 get a plus sign.We'll examine this by creating a new variable holding signs: Sign Test - Null Hypothesisįor some reason, our marketing manager is only interested in comparing median ratings so our null hypothesis is thatįor our 2 rating variables. We'll therefore exclude this variable from further analysis and restrict our focus to the first and third commercials. The mean and median ratings for the second commercial (“Youngster Car”) are very low. means ad1 to ad3 /cells count mean median. *Run descriptive statistics with medians in nice table. DESCRIPTIVES may seem a more likely option here but -oddly- does not include medians - even though these are clearly “descriptive statistics”. We'll use MEANS for inspecting the medians of our 3 rating variables by running the syntax below. The adratings data look fine so we'll continue with some descriptive statistics. Whenever you start working on data, always start with a quick data check and proceed only if your data look plausible. It holds data on 18 respondents who rated 3 car commercials on attractiveness. We'll use adratings.sav throughout this tutorial. For comparing means rather than medians, the paired samples t-test and Wilcoxon signed-ranks test It can be used on either metric variables or ordinal variables. Also see SPSS Sign Test for One Median - Simple Example It's really very similar to the test we'll discuss here. There's also a sign test for comparing one median to a theoretical value. The sign test for two medians evaluates if 2 variables measured on 1 group of cases are likely to have equal population medians. SPSS Sign Test for Two Medians – Simple Example
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