{
 "question": "Is posting cadence associated with view-to-subscriber ratio once channel size is held roughly constant?",
 "inputs": [
  "channels.csv",
  "posts.csv"
 ],
 "caution": "Observational, one night, recent posts only. A negative rho means busier channels show lower ratios; it does not show that posting less would raise anyone's ratio. Each rho carries null_band_95, an approximate 95% band for zero correlation at that n.",
 "all_channels": {
  "channels": 325,
  "median_subscribers": 2149,
  "median_posts_per_day": 0.908,
  "median_gap_hours_between_posts": 10.6383,
  "spearman_posts_per_day_vs_ratio": -0.5418,
  "null_band_95": 0.109,
  "spearman_posts_per_day_vs_subscribers": 0.378,
  "spearman_median_gap_vs_ratio": 0.3839,
  "by_cadence_tercile": [
   {
    "tercile": 1,
    "channels": 108,
    "posts_per_day_min": 0.014,
    "posts_per_day_max": 0.331,
    "median_ratio": 0.7448,
    "median_subscribers": 431.5
   },
   {
    "tercile": 2,
    "channels": 108,
    "posts_per_day_min": 0.333,
    "posts_per_day_max": 2.667,
    "median_ratio": 0.2026,
    "median_subscribers": 2213.0
   },
   {
    "tercile": 3,
    "channels": 109,
    "posts_per_day_min": 2.724,
    "posts_per_day_max": 9056.604,
    "median_ratio": 0.05,
    "median_subscribers": 50836
   }
  ],
  "age_restricted": {
   "what_it_is": "channel ratio recomputed from posts aged 48h to 30 days only; channels with fewer than 3 such posts are left out",
   "channels_with_enough_aged_posts": 145,
   "channels_left_out": 180,
   "median_posts_per_day_left_out": 0.717,
   "median_posts_per_day_kept": 0.926,
   "spearman_posts_per_day_vs_ratio_2_to_30_days": -0.3078,
   "null_band_95": 0.163
  }
 },
 "partial_spearman_posts_per_day_vs_ratio_controlling_subscribers": -0.4199,
 "spearman_subscribers_vs_ratio": -0.667,
 "by_size_band": {
  "small (<1k)": {
   "channels": 134,
   "median_subscribers": 135.5,
   "median_posts_per_day": 0.359,
   "median_gap_hours_between_posts": 20.8842,
   "spearman_posts_per_day_vs_ratio": -0.4046,
   "null_band_95": 0.17,
   "spearman_posts_per_day_vs_subscribers": 0.07,
   "spearman_median_gap_vs_ratio": 0.2857,
   "by_cadence_tercile": [
    {
     "tercile": 1,
     "channels": 44,
     "posts_per_day_min": 0.014,
     "posts_per_day_max": 0.193,
     "median_ratio": 1.5799,
     "median_subscribers": 158.5
    },
    {
     "tercile": 2,
     "channels": 45,
     "posts_per_day_min": 0.195,
     "posts_per_day_max": 0.732,
     "median_ratio": 0.678,
     "median_subscribers": 104
    },
    {
     "tercile": 3,
     "channels": 45,
     "posts_per_day_min": 0.738,
     "posts_per_day_max": 9056.604,
     "median_ratio": 0.2721,
     "median_subscribers": 174
    }
   ],
   "age_restricted": {
    "what_it_is": "channel ratio recomputed from posts aged 48h to 30 days only; channels with fewer than 3 such posts are left out",
    "channels_with_enough_aged_posts": 50,
    "channels_left_out": 84,
    "median_posts_per_day_left_out": 0.23,
    "median_posts_per_day_kept": 0.663,
    "spearman_posts_per_day_vs_ratio_2_to_30_days": -0.174,
    "null_band_95": 0.28
   }
  },
  "mid (1k-50k)": {
   "channels": 100,
   "median_subscribers": 5707.5,
   "median_posts_per_day": 1.0125,
   "median_gap_hours_between_posts": 11.3192,
   "spearman_posts_per_day_vs_ratio": -0.4473,
   "null_band_95": 0.197,
   "spearman_posts_per_day_vs_subscribers": 0.1483,
   "spearman_median_gap_vs_ratio": 0.3957,
   "by_cadence_tercile": [
    {
     "tercile": 1,
     "channels": 33,
     "posts_per_day_min": 0.014,
     "posts_per_day_max": 0.331,
     "median_ratio": 0.2505,
     "median_subscribers": 2910
    },
    {
     "tercile": 2,
     "channels": 33,
     "posts_per_day_min": 0.333,
     "posts_per_day_max": 2.093,
     "median_ratio": 0.162,
     "median_subscribers": 7218
    },
    {
     "tercile": 3,
     "channels": 34,
     "posts_per_day_min": 2.415,
     "posts_per_day_max": 1371.429,
     "median_ratio": 0.0621,
     "median_subscribers": 11002.0
    }
   ],
   "age_restricted": {
    "what_it_is": "channel ratio recomputed from posts aged 48h to 30 days only; channels with fewer than 3 such posts are left out",
    "channels_with_enough_aged_posts": 56,
    "channels_left_out": 44,
    "median_posts_per_day_left_out": 0.303,
    "median_posts_per_day_kept": 1.3265,
    "spearman_posts_per_day_vs_ratio_2_to_30_days": -0.4387,
    "null_band_95": 0.264
   }
  },
  "large (50k+)": {
   "channels": 91,
   "median_subscribers": 384946,
   "median_posts_per_day": 4.203,
   "median_gap_hours_between_posts": 2.5267,
   "spearman_posts_per_day_vs_ratio": -0.2903,
   "null_band_95": 0.207,
   "spearman_posts_per_day_vs_subscribers": 0.104,
   "spearman_median_gap_vs_ratio": 0.252,
   "by_cadence_tercile": [
    {
     "tercile": 1,
     "channels": 30,
     "posts_per_day_min": 0.036,
     "posts_per_day_max": 1.351,
     "median_ratio": 0.0643,
     "median_subscribers": 315286.0
    },
    {
     "tercile": 2,
     "channels": 30,
     "posts_per_day_min": 1.887,
     "posts_per_day_max": 13.644,
     "median_ratio": 0.0415,
     "median_subscribers": 298560.5
    },
    {
     "tercile": 3,
     "channels": 31,
     "posts_per_day_min": 15.591,
     "posts_per_day_max": 502.618,
     "median_ratio": 0.0223,
     "median_subscribers": 822549
    }
   ],
   "age_restricted": {
    "what_it_is": "channel ratio recomputed from posts aged 48h to 30 days only; channels with fewer than 3 such posts are left out",
    "channels_with_enough_aged_posts": 39,
    "channels_left_out": 52,
    "median_posts_per_day_left_out": 19.827,
    "median_posts_per_day_kept": 1.053,
    "spearman_posts_per_day_vs_ratio_2_to_30_days": -0.0002,
    "null_band_95": 0.318
   }
  }
 },
 "bursts_within_channel": {
  "what_it_is": "posts 7-60 days old; views as a multiple of the median views of the same channel's posts in that window, by minutes since the previous post",
  "channels_used": 99,
  "buckets": [
   {
    "gap_since_previous_post": "under 10 minutes",
    "posts": 183,
    "channels": 54,
    "median_relative_views_over_posts": 1.02,
    "median_relative_views_over_channels": 1.034,
    "share_of_posts_below_0_75": 0.082
   },
   {
    "gap_since_previous_post": "10 to 60 minutes",
    "posts": 43,
    "channels": 29,
    "median_relative_views_over_posts": 1.0,
    "median_relative_views_over_channels": 1.0134,
    "share_of_posts_below_0_75": 0.1395
   },
   {
    "gap_since_previous_post": "1 to 6 hours",
    "posts": 102,
    "channels": 51,
    "median_relative_views_over_posts": 1.0,
    "median_relative_views_over_channels": 1.0,
    "share_of_posts_below_0_75": 0.0588
   },
   {
    "gap_since_previous_post": "over 6 hours",
    "posts": 736,
    "channels": 97,
    "median_relative_views_over_posts": 1.0,
    "median_relative_views_over_channels": 1.0,
    "share_of_posts_below_0_75": 0.1236
   }
  ]
 },
 "bursts_within_channel_by_gap_to_next_post": {
  "what_it_is": "posts 7-60 days old; views as a multiple of the median views of the same channel's posts in that window, by minutes until the next post",
  "channels_used": 104,
  "buckets": [
   {
    "gap_until_next_post": "under 10 minutes",
    "posts": 185,
    "channels": 56,
    "median_relative_views_over_posts": 0.9773,
    "median_relative_views_over_channels": 0.9728,
    "share_of_posts_below_0_75": 0.1676
   },
   {
    "gap_until_next_post": "10 to 60 minutes",
    "posts": 45,
    "channels": 31,
    "median_relative_views_over_posts": 0.8936,
    "median_relative_views_over_channels": 0.8936,
    "share_of_posts_below_0_75": 0.2667
   },
   {
    "gap_until_next_post": "1 to 6 hours",
    "posts": 106,
    "channels": 54,
    "median_relative_views_over_posts": 0.9866,
    "median_relative_views_over_channels": 0.9796,
    "share_of_posts_below_0_75": 0.0849
   },
   {
    "gap_until_next_post": "over 6 hours",
    "posts": 807,
    "channels": 104,
    "median_relative_views_over_posts": 1.005,
    "median_relative_views_over_channels": 1.0027,
    "share_of_posts_below_0_75": 0.0954
   }
  ]
 }
}