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How to give 'where' condition in select query while selecting the columns?

I want to give condition in a column selection while performing the select statement.

I want to perform average of TOTAL_TIMEONSITE, RENAME IT, and want to average it for the values existing in the month of Jun'20, Jul'20 and Aug'20 against a visitor.

Also the range of the whole query must be the month of Aug'20 only. So I want to put the constraint on TOTAL_TIMEONSITE so that it averages the values for the months of Jun'20, Jul'20 and Aug'20 against a visitor.

select FULLVISITORID AS VISITOR_ID,
VISITID AS VISIT_ID,
VISITSTARTTIME_TS,
USER_ACCOUNT_TYPE,
(select AVG(TOTAL_TIMEONSITE) AS AVG_TOTAL_TIME_ON_SITE_LAST_3M FROM "ACRO_DEV"."GA"."GA_MAIN" WHERE
 (cast((visitstarttime_ts) as DATE) >= to_date('2020-06-01 00:00:00.000') and CAST((visitstarttime_ts) AS DATE) <= to_date('2020-08-31 23:59:00.000'))
 GROUP BY TOTAL_TIMEONSITE),
CHANNELGROUPING,
GEONETWORK_CONTINENT
from "ACRO_DEV"."GA"."GA_MAIN"
where (FULLVISITORID) in (select distinct (FULLVISITORID) from "ACRO_DEV"."GA"."GA_MAIN" where user_account_type in ('anonymous', 'registered') 
and (cast((visitstarttime_ts) as DATE) >= to_date('2020-08-01 00:00:00.000') and CAST((visitstarttime_ts) AS DATE) <= to_date('2020-08-31 23:59:00.000')));

The issue is that it is giving me the 'select subquery for TOTAL_TIMEONSITE' as the resultant column name and the values in that column are all same but I want the values to be unique for visitors.

So for Snowflake:

So I am going to assume visitstarttime_ts is a timestamp thus cast((visitstarttime_ts) as DATE) is the same as `visitstarttime_ts::date'

select to_timestamp('2020-08-31 23:59:00') as ts
    ,cast((ts) as DATE) as date_a
    ,ts::date as date_b;

gives:

TS DATE_A DATE_B
2020-08-31 23:59:00.000 2020-08-31 2020-08-31

and thus the date range also can be simpler

select to_timestamp('2020-08-31 13:59:00') as ts
    ,cast((ts) as DATE) as date_a
    ,ts::date as date_b
    ,date_a >= to_date('2020-08-01 00:00:00.000') and date_a <= to_date('2020-08-31 23:59:00.000') as comp_a
    ,date_b >= to_date('2020-08-01 00:00:00.000') and date_b <= to_date('2020-08-31 23:59:00.000') as comp_b
    ,date_b >= '2020-08-01'::date and date_a <= '2020-08-31 23:59:00.000'::date as comp_c
    ,date_b between '2020-08-01'::date and '2020-08-31 23:59:00.000'::date as comp_d
TS DATE_A DATE_B COMP_A COMP_B COMP_C COMP_D
2020-08-31 13:59:00.000 2020-08-31 2020-08-31 TRUE TRUE TRUE TRUE

Anyways, if I understand what you want I would write it like using CTE to make it more readable (to me):

with distinct_aug_ids as (
    SELECT DISTINCT 
        fullvisitorid 
    FROM acro_dev.ga.ga_main
    WHERE user_account_type IN ('anonymous', 'registered') 
        AND visitstarttime_ts::date BETWEEN '2020-08-01::date AND '2020-08-31'::date
), three_month_avg as (
    SELECT 
        fullvisitorid
        ,AVG(total_timeonsite) AS avg_total_time_on_site_last_3m
    FROM acro_dev.ga.ga_main
    WHERE visitstarttime_ts::DATE BETWEEN to_date('2020-06-01 00:00:00.000') AND to_date('2020-08-31 23:59:00.000')
    GROUP BY 1
)
select 
    m.fullvisitorid as visitor_id,
    m.visitid as visit_id,
    m.visitstarttime_ts,
    m.user_account_type,
    tma.avg_total_time_on_site_last_3m,
    m.channelgrouping,
    m.geonetwork_continent
FROM acro_dev.ga.ga_main as m
JOIN distinct_aug_ids AS dai
    ON m.fullvisitorid = dai.fullvisitorid
JOIN three_month_avg AS tma
    ON m.fullvisitorid = tma.fullvisitorid
;

But if you want that to be sub-selects, they are the same:

select 
    m.fullvisitorid as visitor_id,
    m.visitid as visit_id,
    m.visitstarttime_ts,
    m.user_account_type,
    tma.avg_total_time_on_site_last_3m,
    m.channelgrouping,
    m.geonetwork_continent
FROM acro_dev.ga.ga_main as m
JOIN (
    SELECT DISTINCT 
        fullvisitorid 
    FROM acro_dev.ga.ga_main
    WHERE user_account_type IN ('anonymous', 'registered') 
        AND visitstarttime_ts::date BETWEEN '2020-08-01::date AND '2020-08-31'::date
) AS dai
    ON m.fullvisitorid = dai.fullvisitorid
JOIN (
    SELECT 
        fullvisitorid
        ,AVG(total_timeonsite) AS avg_total_time_on_site_last_3m
    FROM acro_dev.ga.ga_main
    WHERE visitstarttime_ts::DATE BETWEEN to_date('2020-06-01 00:00:00.000') AND to_date('2020-08-31 23:59:00.000')
    GROUP BY 1
)AS tma
    ON m.fullvisitorid = tma.fullvisitorid
;

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