Day 5: STA205 - Introduction to Statistical Methods

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• Today: sampling
  • You have an IMath assignment (due Friday).
  • Your quiz is returned. Let's talk about it....
    • A couple of things about your normal:
      • They're centered at $\mu$
      • The standard deviation $\sigma$ is used to measure distance from $\mu$ -- and $\mu \pm \sigma$ occurs at the two (symmetric) points where the bell curve changes from an umbrella to a bowl.
      • By three standard deviations, the normal and the x-axis are basically indistinguishable. There's just a tiny little bit of area under the curve beyond three standard deviations.

    • Let's practice drawing one....
      • Draw a straight line. Buy yourself a ruler, if need be. Or use another straight edge, like a book.
      • Draw a symmetric umbrella above the line. Stop a little above the halfway point.
      • Mark off the points along the x-axis that correspond to the values $\mu \pm \sigma$.
      • Mark off the points along the x-axis that correspond to the values $\mu \pm 2\sigma$. Use equal spacing!
      • Mark off the points along the x-axis that correspond to the values $\mu \pm 3\sigma$.
      • Now draw two symmetric little bowls, off the umbrella, that taper off to the axis at about $\mu \pm 3\sigma$: there's almost no area beyond that.

  • Part b. The empirical rule in action.... 68, 95, 99.7.

• Now let's get back to Packet 2: Definitions, and Summarizing Categorical Data
  • If you don't have your Packet, just take out some paper and make notes that you can use to transfer to your packet when you DO get it printed out.

  • Today I read this, from The Guardian: Study links high levels of screen time to slower child development

    The journal article itself is available here.

    • How would researchers determine this?
    • Is it true for all children?
    • Is it true for all screen time?
    • Here's what they did:
      • Conclusion of the article: "Researchers in Canada say children who spent more time with screens at two years of age did worse on tests of development at age three than children who had spent little time with devices. A similar result was found when children's screen time at three years old was compared with their development at five years."

      • So they're studying children from ages 2-5 (not all children).

      • They studied 2441 mothers and children in Calgary, Alberta, Canada.

      • Participants included mothers and children from the All Our Families study, a large, prospective pregnancy cohort of 3388 mothers and children from Calgary, Alberta, Canada

      • They measured screen time at 2 years and 3 years.

      • Mothers indicated the range of time their child spent using particular electronic mediums on a typical weekday and weekend day. Mothers reported on the following devices and/or mediums: watch television programs; watch movies, videos, or stories on a VCR or DVD player; use a computer, gaming system, or other screen-based devices. A weighted weekly average of weekday and weekend screen time across mediums was calculated to yield screen time use in hours/week.

      • Child sex was coded as female (1) or male (0), and maternal and child age were recorded in years and months, respectively. When the child was 12 months, mothers indicated whether they "look at or read children's books to my child," coded as not very often (1), sometimes (2), or often (3). When the child was 24 months, mothers indicated the amount of time that the child engaged in physical activity on a typical weekday, ranging from none (1) to 7 hours or more (7), and completed the Center for Epidemiologic Depression Scale.

      • Finding (from their report): " In this cohort study of early childhood development in 2441 mothers and children, higher levels of screen time in children aged 24 and 36 months were associated with poor performance on a screening measure assessing chidren's achievement of development milestones at 36 and 60 months, respectively."

    • What might you have done differently?
    • What variables were collected, and are they quantitative or categorical?

• Links:
  • Statcrunch instructions for packet 2 (and IMath homework):
    • Load the Stop and Frisk Data for packet 2. Load it by "WWW address", and make sure to set the delimiter to "comma" (because this is a "csv" (comma-separated values) file.
    • Once the data is loaded, click on "Graph" or "Table".
    • Alternatively, you may want to join my "group" on Statcrunch. That way you can access the data more quickly. It's Sta205-Long, if you want to add yourself into that group.
    • For the IMath homework, you'll need the Bipolar Depression Study data. Same thing: Load it by "WWW address", and make sure to set the delimiter to "comma" (because this is a "csv" (comma-separated values) file (or get it from the group).