# Statistical test design question

I have condition as such mouse liver and spleen data. So in liver I have WT (Wild Type) and KO (knock out) as well as in spleen WT (Wild Type) and KO (knock out).

I have to compare the parasite load in WT and KO condition in both liver and spleen.

In terms of data points what I got is this:

• 10 mice for WT, 6 mice for KO in case of liver
• 10 mice for WT, 5 mice for KO in case of spleen.

WT 20 8 21 9 22 10 23 11 24
KO 12 25 26 27 28


So far what I know is I have to perform a parametric test.

But I'm not sure if I have to go for a paired t-test or an unpaired t-test.

Because here I'm comparing with between two groups, only so I don't have to go for anova if I'm not wrong. Secondly there is a difference in number of observation that is available for WT as compared to KO. So would that affect my choice of test as well.

Suggestion would be highly appreciated

• Please take some time to clarify your question. It's unclear what you're ultimately asking. And your description of the data is unclear as well. For example, what you mean by days? Is this temporal data (WT parasite load at 1, 2, ..., 10 days), or 10 WT replicates for (in which case the significance of "days" is unclear). Jul 17 '19 at 19:20
• sorry will edit the question give me a moment
– kcm
Jul 17 '19 at 19:24
• edited the question and given you a sample scenario
– kcm
Jul 17 '19 at 19:31
• Your edits help, but the post is still very verbose and unclear. How/Why do you know you have to perform a parametric test? What do you want your test to tell you? Jul 17 '19 at 19:41
• ". How/Why do you know you have to perform a parametric test?" i guess if the data is normally distributed then parametric if not then non-parametric . "What do you want your test to tell you" I want to see there is difference in the parasitic load between WT and KO cases one in the liver and other in the spleen
– kcm
Jul 17 '19 at 19:47

If the samples are not matched, e.g. by time point, then it will be unpaired. You need a way to say sample 1 KO and sample 1 WT are uniquely matched to be paired, sample 2 KO and sample WT will be paired etc ... pairing is great for a time series. If you have replicates within the paired groups then ANOVA is the way to go, particularly if the sample sizes are uneven.

Note: in your case the sample sizes are uneven, you cannnot perform a paired T-test between two uneven sample sizes. HOWEVER you appear to a natural pairing, but I don't know whether this is biologically justified, i.e. liver and spleen. So you appear to have a biological pairing with uneven sample sizes. If this is correct it suggests a 1-way ANOVA is a better idea than a T-test.

Parametric test: check for normality in each data set, e.g.

• A Q-Q plot against the normal distribution (a cool way to do this)
• Homogeneity of variances is Hartley's Fmax test (good for T-test and ESSENTIAL for 1-way ANOVA)
• 68% of the data should be less than ±1 standard deviation around the mean, 95% less than ±2 standard deviation and 99% less than ±3
• Kolmogorov-Smirnov and/or Shapiro-Wilk test
• Skewness & kurtosis magnitudes < 1.96 respectively

Note if you combine liver and spleen data sets and find a nice normal distribution, and one or both is not normal by itself, then you would need to consider the biological justification for combining the data sets.

If the data passes all those tests, you are good to go. If not .... gets complicated,

• Normalisation, this is where you transform the data, in your case I'm not sure, but typically log transformation and then perform the checks for normality above. There are lots of ways to normalise data.
• Repeat the T-test/1-way ANOVA with normalised data
• Ignore it - yup its top level statistical advice, it is context specific and never a universally shared idea ... I suspect that is where the advice "just use a parametric test" came from. Please be aware if you do this, someone could turn around and sau "you've done it wrong". The statistical arguments about why this assumption can be valid get complicated.
• Use a non-parametric test, orthodox statistical advice, in this case it is the Mann-Whitney U test and Kruskal–Wallis test if you have paired replicates (i.e. non-parametric version of 1-way ANOVA).

Non-parametric tests often lack power and I suspect for this sample size that will be the case. Personally I would try and ignore all this advice :-) - okay I would definately check for normality and investigate avenues towards normality - then I would perform a general linear model (GLM). The reason is that it is a much more powerful method for identifying whether the two gropus are different. Performing a single GLM with two paired groups is not trivial, so I would have to give serious consideration to 1-way ANOVA, or KW-test, which would be a cleaner solution - but could miss a critical part of the data.

• "i.e. liver and spleen." after discussing i found biologically it would be more relevant to compare Liver WT and Liver KO and same goes with spleen .Meanwhile i will check the normality of the data which i never used to do because lack of basic stat concept . So to make it more clear since i have sample size uneven in number .so if it passes the normality criteria i can go with unpaired t test ?
– kcm
Jul 18 '19 at 7:09
• What you are saying is you want to do 2 unpaired T-tests, okay fine. I would much prefer to do one test with 2 groups (liver and spleen) using 1-way ANOVA. It might also give you more statistical power. You can always try it with 2 t-tests and 1 one-way ANOVA test. Obviously if you can combine liver and spleen, its a single unpaired T-test.
– M__
Jul 18 '19 at 7:20
• "would much prefer to do one test with 2 groups (liver and spleen) using 1-way ANOVA. It might also give you more statistical power. You can always try it with 2 t-tests and 1 one-way ANOVA test." thank you for your valuable insight
– kcm
Jul 18 '19 at 9:16

So far what i know is i have to perform a parametric test .

How did you determine this?

But im not sure if I have to go for a

Paired t-test or Unpaired t-test

If you can't tell the difference between when to do a paired t-test and an unpaired one, you need to stop and talk to someone who can teach you basic statistics. Throwing statistical tests at numbers when you don't understand them is a recipe for disaster.

• well "difference between when to do a paired t-test and an unpaired one" this part i know when to do. But my doubt as i have difference in sample number for WT vs KO cases .Here in this case it would be unpaired which i tried and there is no difference but when i ran it with paired it shows significance. Thats why i would like to know if im doing it right or not
– kcm
Jul 17 '19 at 20:25
• You can't run what you know is the wrong test just because you like the p-value! Jul 17 '19 at 20:28
• "You can't run what you know is the wrong test just because you like the p-value" .perhaps yes
– kcm
Jul 17 '19 at 20:35