I do not understand what you mean by 'paired t-tests do not take standard errors into account'. Maybe, it is from the software, but if you use PASS software program, the results will clearly show a standard error column which you may have to interpret. https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Paired_T-Test.pdf

You are correct, it's better to "compare the slopes". However, I would not calculate individual slopes and then compare them but use a model that fits the slopes depending on the cell type. The correlation structure (you have multiple values from the same plate, and different plates may behave differently; more importantly: the plate is your sampling unit) can be accounted for in a hierarchical model (i.e. by including random coefficients for the intercept and for the slope by plate). If some plates are processed in parallel (on the same day), and the experiment took several days, "day" is another factor in this correlation structure and you can include random coefficients for the intercept and slope by day, too).

But if you have not heard about hierarchical models, this may be too much.

If you always ran pairs of plated in parallel (1 wt, 1 ko), and always used the same time-points and always have the same number of values, you have a simpler option, that can be realized in some slightly different ways:

1) You can determine the slopes individually and the do a paired t-test for the slopes of wt and ko.

2) You determine the slopes like in 1, then manually calculate the differences for each pair, and use a one-sample t-test on these differences.

3) You use the data from each pair and fit a regression model depending on time and cell line (I think this is sometimes called an ANCOVA model, as there is one categorical [cell line] and one continuous [time] predictor). This model estimates the mean difference in slopes for each pair, and you can run a one-sample t-test on these differences.

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Regarding your problem that "a paired t-test does not take into account standard error of those doubling times":

Yes, that's correct, because it is completely irrelevant for the question how much the data between individual days vary. This variation (between-days) is removed and not considered by the paired t-test. It is removed by calculating the pair-wise differences. Since the day-specific effect is assumed the same in both plated measured on that particular day, this effect is cancelled out. The cost of that procedure is that you also loos the information about the between-plate variation of plates run at the same day, what means, in statistical terms, that you loose half of the degrees of freedom for the test.

I'm not sure where you found that t tests do not take into account standard errors of means. T-tests are based on the t statistic, which is the quotient of the mean difference and the standard error of the difference.

Do you mean that the t-test only take into account variability between growth curves of individual cells, but not the variability of each curve? T-tests assume that individual data point (in your case growth curve slopes) comes from a single measurement. One underlying assumption of t-tests is that measurement error is distributed normally, so the average measurement error will approach (or be) zero as the number of data point increases.

Marc-André Goulet Yup that was what I was looking for, I thought it would be something along those lines, but I wasn't sure and I couldn't find any confirmation online.

One more question

When I ran the paired T-tests on the slopes of Wt and KD, one cell line gave a p-value = 0.06208, which is very strange as this cell line (SEM) is the one with the clearest difference between KD and Wild-type.

Am I doing something wrong or is it because the difference is inconsistent that I get this unexpected p-value?

Cell line________WT____________KD

SEM 1___0,0004145144___0,0003107695

SEM 2___0,0005127009___0,0004560236

SEM 3___0,0004638400___0,0004186776