Update grasping-longitudinal-studies-introduction-and-dataset-overvie…

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longitudinal-analysis/grasping-longitudinal-studies-introduction-and-dataset-overview.md

@@ -4,7 +4,7 @@ In clinical microbiome research, longtudinal studies haven been widely employed
 * **Task 1** (time effect analysis): Anlyze all time points to see if the microbiome composition shows consistent changes with the time.
 * **Task 2** (global null analysis)：Jointly analyze all time points (categorical) and test the global hypothesis that none of the time points is associated with a subject-level outcome. This analysis will allow the identification of taxa whose abundance variation is associated with the outcome in certain ways. The global test pools all time points and  could be more powerful than testing individual time points followed by multiple testing correction.  Task 3 and 4 will then help understand the details of the association for  taxa that reject the global null hypothesis.
 * **Task 3** (per time point analysis): Test the association of the microbiome at different time points with the outcome. This will help identify the particular time window where the association occurs or peaks.
-* **Task 4** (change analysis): Test the association of the microbiome changes with the outcome.  By using changes, it controls the large inter-subject variability in microbiome composition, and amplifies the association strength.  It is likely that task 4 finds more associations than Task 4 with larger strength. 
+* **Task 4** (change analysis): Test the association of the microbiome changes with the outcome.  By using changes, it controls the large inter-subject variability in microbiome composition, and amplifies the association strength.  It is likely that task 4 finds more associations than Task 3 with larger strength. 
 * **Task 5** (volatility analysis): It is possible that the average composition of the microbiome remains similar between conditions, but the variability differs by conditions.  Volatility analysis will help identify the taxa whose temporal variability ("volatility") is associated with the outcome.
 * **Task 6** (trend analysis): In the global null test (Task 2), we do not assume any temporal pattern such as linearly or monotonically increasing. If we have some prior knowledge about the temporal trend or the microbiome is more densely sampled longitudinally, we can model the temporal trend and test the association of the trend with the outcome.  This offers more power than Task 2 to identify the taxa associated with the outcome.