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Thread: Interpreting significance based on confidence interval

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    Interpreting significance based on confidence interval




    Hi Everyone,
    Could some of you help to interpret my results based on p values and confidence intervals? A little bit of background: I am trying to analyse the function of a gene during bacterial infection. So I have cell that express this gene, called naive and cell that do not express my gene, called mutant. Then I infect those cells with bacteria and after 24 hours I count the bacteria inside the cell to see whether the expression of this gene affects the bacteria growth. In this case, I ran the Mann-Whitnney test to detect statistical significance between the two groups and what I found was (p value: 0,0008; 95% CI 0,1040 to 0,3490). In term of statistics this is very significant. However, analyzing the data you do see that this difference is strictly small and insignificant. Here my question is: how the confidence interval could help me with this interpretation? In another experiment (called EXP IIa I got the following values (p value: < 0,0001; 95%CI 4,440 to 4,646). In this case, I do believe that significance is true because I have a drop of 5 logs on bacterial growth in the mutant group.
    Could anyone help me with those interpretations?
    Thank you
    Best
    Julian

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    Re: Interpreting significance based on confidence interval

    Wilcoxon-Mann-Whitney is considered the non-parametric analog of a t-test. It is typically used when there are normality concerns and skewed data. I am guessing this is why you used it.


    Also can you provide examples of the bacterial growth data. You say counts, but I would be interested in how you are formatting it. Also, what is your sample size.


    Lastly, what does your 95% CI represent, what value is it for. If it is for your growth variable that may be skewed, it may not be a good representation if your distributions are asymmetrical.
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    Re: Interpreting significance based on confidence interval

    Like hlsmith, I do not understand what the CI is actually referring to. It would also be helpful if you can tell us which software you are using.

    Mann-Whitney has indeed its "own" effect-size measures, like the Probability of Superiority and another one named "r". You could try and search on the web for those two.

    Further, you did not tell us about your sample size. It could be that you have a very large sample size, and therefore even a small (practically negligible) difference proves statistically significant. But, not knowing the details of your analysis and data, we (well, I) cannot tell you more.

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    Re: Interpreting significance based on confidence interval


    Hi,

    Thanks gianmarco and hlsmith for your comments.
    The software I use is Graphpad prism version 6. My sample size is 9 (three indenpendent experiments and 3 replicates each). When I say counts, I refers the yields of bacterial DNA quantified by qRT-PCR.
    Below the raw data of my statistical analysis.
    Thank you

    Best
    Experiment: Bacteria Internalization [/B]
    Table Analyzed STAT S aureus

    Column A MEF-wt
    vs. vs,
    Column B MEF-pprg-/-

    Mann Whitney test
    P value 0,0008
    Exact or approximate P value? Exact
    P value summary ***
    Significantly different? (P < 0.05) Yes
    One- or two-tailed P value? Two-tailed
    Sum of ranks in column A,B 121,0 , 50,00
    Mann-Whitney U 5,000

    Difference between medians
    Median of column A 6,176
    Median of column B 5,964
    Difference: Actual 0,2125
    Difference: Hodges-Lehmann 0,2266
    96.01% CI of difference 0,1040 to 0,3490
    Exact or approximate CI? Exact

    MEF-wt MEF-pprg-/-
    Number of values 9 9

    Minimum 5,964 5,737
    25% Percentile 6,090 5,835
    Median 6,176 5,964
    75% Percentile 6,246 6,035
    Maximum 6,313 6,086

    Mean 6,158 5,933
    Std. Deviation 0,1092 0,1169
    Std. Error of Mean 0,03639 0,03898

    Lower 95% CI 6,074 5,843
    Upper 95% CI 6,242 6,023

    Mean ranks 13,44 5,556


    Experiment Bacterial Growth

    Table Analyzed STAT S aureus

    Column A MEF-wt
    vs. vs,
    Column B MEF-pprg-/-

    Mann Whitney test
    P value < 0,0001
    Exact or approximate P value? Exact
    P value summary ****
    Significantly different? (P < 0.05) Yes
    One- or two-tailed P value? Two-tailed
    Sum of ranks in column A,B 126,0 , 45,00
    Mann-Whitney U 0,0

    Difference between medians
    Median of column A 7,181
    Median of column B 4,091
    Difference: Actual 3,091
    Difference: Hodges-Lehmann 3,097
    96.01% CI of difference 3,048 to 3,180
    Exact or approximate CI? Exact

    MEF-wt MEF-pprg-/-
    Number of values 9 9

    Minimum 7,121 3,751
    25% Percentile 7,153 3,998
    Median 7,181 4,091
    75% Percentile 7,213 4,124
    Maximum 7,234 4,142

    Mean 7,184 4,047
    Std. Deviation 0,03793 0,1259
    Std. Error of Mean 0,01264 0,04196

    Lower 95% CI 7,155 3,950
    Upper 95% CI 7,213 4,143

    Mean ranks 14,00 5,000

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