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Bias

Sample Size

HDF-N vs HDF-S

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The Ultimate Outback

Billions and billions of

galaxies

populate the universe. The Hubble Space Telescope has unmasked many of them in two of the clearest, most distant views ever obtained, called the Hubble "Deep Fields" (HDFs). One view peers northward, the other, southward.
Scientists have used mathematics to unlock many galactic secrets hidden in these two views. Ahead, we'll use sample statistics based on actual HDF data to unravel some cosmic mysteries

Meet the Hubble Deep Fields

What do we mean by "Deep"?

What is deep?

In the Hubble Deep Field views,

DEEP = FAINT = DISTANT = EARLIER IN TIME

A ‘deep’ survey detects faint objects, whether far or near. For the HDFs, the telescope was aimed at spots in the sky with few nearby objects, so most of the faint objects in the Deep Fields are also far away — 2 to 10 billion

light-years (LY)

.
Since the light travels so far and takes so long to reach us, we see the galaxies as they appeared 2 to 10 billion years ago in the early universe.
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Meet HDF-North

Introducing the

Hubble Deep Fields

Hubble Deep Fields

Meet HDF-South

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Hubble Deep Field North

The Hubble Deep Field North (HDF-N) is one of the deepest, sharpest, multi-color images of the faintest universe in visible light. The image was made by aiming the Hubble Space Telescope at one seemingly empty point in the northern sky near the Big Dipper for 10 days in December 1995. About a thousand never-before-seen galaxies are visible in this view of the universe.

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Hubble Deep Field South

Turning its sharp eye toward the southern constellation Tucana, the Hubble Space Telescope captured another dazzling assortment of never-before-seen galaxies. The Hubble Deep Field South (HDF-S) complements the original Hubble Deep Field (HDF-N) taken in late 1995. The constellation Tucana can only be viewed from the southern hemisphere. The 10-day-long observation, in October 1998, doubled the number of far-flung galaxies available to astronomers for deciphering the history of the universe.

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Bias

Sample Size

HDF-N vs HDF-S

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Hubble Deep Field North

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Hubble Deep Field South

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OOPS, That's Biased!

Samples picked by humans are always susceptible to bias. Unconsciously, we base our choices on a trait or quality of the sample member.

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Oops! Computer-generated sample: Unbiased

Selection of samples by computers is considered unbiased.

In the database sampling, each galaxy would be assigned a number. The computer would collect a sample of galaxies by randomly picking numbers.

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That's Right! Computer-generated sample: Unbiased

Selection of samples by computer is considered unbiased.

In the database sampling, each galaxy would be assigned a number. The computer would collect a sample of galaxies by randomly picking numbers.

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That's Right! Picking with eyes closed: biased

Though it seems unbiased, you introduce bias when you open your eyes and decide which galaxy your finger has chosen.

Your fingertip is huge compared to the galaxy images in the HDF; it could cover or point to several galaxies at once. When you decide which galaxy your finger is on or pointing to, you are introducing the possi-bility for bias.
Or, you might use your mental image of the picture to try to move your finger to differ- ent locations, in an attempt to avoid intro-ducing bias. This, too, would be biased. The very act of trying to avoid bias utilizes

human intention

, which introduces the potential for bias.
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OOPS! Picking with eyes closed: biased

Though it seems unbiased, you introduce bias when you open your eyes and decide which galaxy your finger has chosen.

human intention

, which introduces the potential for bias.
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Sorry!

Sorry,

your sample size was too small to be reasonable.
While it is statistically possible to get represen- tative results from such a sample, that sample size will not consistently yield good results.
Want to try again?

Skip

That's right

That's right,

your sample size was too small to be reasonable.
While it is statistically possible to get represen- tative results from such a sample, that sample size will not consistently yield good results.
Want to try again?

Skip

Oops!

To find the smallest reasonable sample, look for the smallest size that keeps the natural variability of results about as low as could be obtained by sampling much more of the population.

Here, the total number of galaxies in your HDF is slightly over 1,000. But a sample of 40-50 adequately represents this population because it yields about as low a variability as a sample of almost 1,000.

Try again or let us choose an appropriate sample size of 45 for you.

TRY AGAIN

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You must choose at least one galaxy

OK

Light-Years (LY)

The distance traveled by light in a full year — some 10 trillion kilometers (about 6 trillion miles).
To calculate one light-year, multiply the speed of light (300,000 km/sec, or 186,000 miles/sec) by the length of a year expressed in seconds:
(300,000 km/sec) (31,536,000 sec) or (186,000 miles/sec) (31,536,000 sec)

Inevitable Human Bias

Samples picked by humans are always susceptible to bias. Unconsciously, we base our choices on a trait or quality of the sample member.

Range

Range is the simplest measure of dispersion. It is the interval between the highest-valued (largest) piece of data and the lowest-valued (smallest) one, expressed as the difference between them.

MIN/MAX PLOT

A visual representation of the range. It shows the dispersion of the data by using a line to connect the lowest-valued (smallest) piece of data to the highest-valued (largest) one, as shown in the example below:

MEASURES OF CENTRAL TENDENCY

Numerical values that are located, in some sense, in the middle of a sample or population. These include the mean, median, and mode.

MEAN

The average value found by adding the values for all the members of the sample and dividing by the number of members.

MEDIAN

The middle value when the members of the sample are ranked in order according to size.
When there is an odd number of members, the median is the exact middle piece of data. If there is an even number of members, the median is the number halfway between the middle two members’ values.

Galaxy

An enormous collection of stars held together by gravitational attraction. Galaxies can be large or small and come in many shapes — elliptical, spiral or irregular.

SMALLEST REASONABLE SAMPLE SIZE

Statisticians look for the smallest sample that is "reasonable." The smallest sample minimizes time and costs. A "reasonable" sample is one that is unbiased and large enough to adequately represent the population it's derived from.

SMALLEST REASONABLE SAMPLE SIZE

Statisticians look for the smallest sample that is "reasonable." The smallest sample minimizes time and costs. A "reasonable" sample is one that is unbiased and large enough to adequately represent the population it's derived from.

SMALLEST REASONABLE SAMPLE SIZE

Statisticians look for the smallest sample that is "reasonable." The smallest sample minimizes time and costs. A "reasonable" sample is one that is unbiased and large enough to adequately represent the population it's derived from.

SMALLEST REASONABLE SAMPLE SIZE

Astronomers' Result

Astronomers counted and classified all the galaxies that could be counted and classified in each of the Deep Fields.

Astronomers' Result

Astronomers counted and classified all the galaxies that could be counted and classified in each of the Deep Fields.

Astronomers' Result

Astronomers counted and classified all the galaxies that could be counted and classified in each of the Deep Fields.

WHOLE POPULATION OF HDFS

WHOLE POPULATION OF HDFS

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