Galaxy Hunter
A cosmic photo safari
Explore the Hubble Deep Fields from a statistical point of view.

Watch out for the booby traps of bias, the vagueness of variability, and the shiftiness of sample size as we travel on a photo safari through the Hubble Deep Fields (HDFs).

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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.

CLOSE

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.

CLOSE

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.

CLOSE

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.

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.
CLOSE

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?

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?

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.

You must choose at least one galaxy
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 membersâ€™ 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
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.
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
Astronomers counted and classified all the galaxies that could be counted and classified in each of the Deep Fields.
WHOLE POPULATION OF HDFS
Astronomers counted and classified all the galaxies that could be counted and classified in each of the Deep Fields.
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