## Analysis

If you've decided to conduct some analysis of your data, it's time to read the story the stars have been trying to tell you. Statistics will be the tool that you will use to understand the story. Generally, the study of statistics is divided into two parts: descriptive and inferential. Descriptive statistics describes number sets, such as how many numbers, the middle number, and the spread of the numbers. Inferential statistics uses some of these descriptions to make inferences or guesses about an entire population based upon a sample of the data. You will use both to analyze the data that you produce from observing variable stars.

Two types of information can be collected in statistical studies: qualitative and quantitative data. Quantitative data consists of measures or quantities that can be put into an order or ranked in some way, such as estimates of star brightness or time between outbursts. Qualitative data is not comparable by arithmetic relations; for example, how much fun you're having observing variable stars or how tired you feel at 3 o'clock in the morning.

An additional distinction exists among quantitative data. Quantitative data is defined as either discrete or continuous data. Discrete data is measured in exact, or discrete, numbers. Data that can assume any value within an interval, or between two numbers, is an example of continuous data. Individual variable-star magnitude estimates are considered discrete data and each individual estimate that you make will consist of one discrete number. However, variable-star brightness

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R Leo

Long Period Variable (Mira type)

Beginning date (JO): 50010239 Ending date (JD): 51544 312

Minimum magnitude: Maximum magnitude:

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¡CALCULATION SECTION

JD mag epoch period et I o ci i or os cycle phis? cd dn Sid Ph*se

61073 303 68

51090 326 66

51095 325 60

51106 326 62

51109 319 63 51111272 51111 329

51114 266 51127 325 72

RMdy

50010.239 50010 239 50010 239 60010 239 50010 239 60010 239 50010 239 50010 239 50010 239

309 250 309 260 309250 309 260 309250 309 260 309 260 309 250 309 260

0 025 3 637

3000 0 637 ~liL

OUTPUT SECTION

Ol 02 Mag Sid Phis* 9 10

CU <fcv

58 66

0 463 0518 0 334 0.576 05» 0.525 0 586 0 595 0631 _1

66 70

72 76

3891

'inoar

I Hfl can assume any number, between a maximum and a minimum, and is therefore considered continuous.

Your goal as a variable-star observer is to estimate the brightness of a star, at a particular time, and describe that estimate as an accurate discrete measurement. Later, by using many accurate discrete measurements taken over a period of time, you will be able to construct a model of the continuous data that represents the star's variations over time. In other words, you will be able to develop a predictive model of some characteristic of the star, in this case the variability of the brightness of the star, and prediction is one of the fundamental goals of science. It's also fun.

Take a close look at Figure 13.1. The data shown is provided by the Variable Star Network (VSNET) and relates to the star R Leo, a Mira-type variable. The first column is the Julian date (2,400,000 +). The second column contains the magnitude estimates.

This arrangement is an example of the data collected by a variable-star observer or a group of observers. The date of each observation is a Julian date but you will notice that it has been truncated or shortened. It has been shortened by recording only the last five date digits. The full Julian date for the beginning of this data

Figure 13.1.

Observation dota for Ihe Mira type variable, R Leo. Dato provided by

VSNET.

figure 13.2. Light curve of R Leo produced from the observation data. Oata provided by VSNET

51050 5110051150 512005125051300 51350 51400

is 2451,073.303. It's a common practice among variable-star observers to shorten the Julian date and use only the last five or four numbers of the date. Care must be taken when using old data since the last four digits of a Julian date will eventually recur in a relatively short period of time. To determine the actual Julian date for any of the records shown here, just add 2400,000 to the date. The decimal portion of the date is the time element.

This table of data may look interesting and ordered, but reading the story that is concealed within will require a bit of work on your part. You're going to need to use a different language to read this story than you are using to read this book. Now is when the language of mathematics, specifically statistics, becomes important.

If we were to graph the data' provided in Figure 13.1, we would be able to see each data point representing a single estimate of magnitude (star brightness) placed in chronological sequence (date of observation). You can see that over a time period of about 300 days, this star has varied in brightness by a little less than five magnitudes (Figure 13.2).

Supposing that the data is correct, it's obvious that this star is varying in brightness. That piece of information is valuable in its own right but there is a deeper, more interesting story here. Before we learn to read the story, let's look at some of the things that hide or distort the real story that you are trying to read.

'To learn how to construct a graph similar to the one shown, refer to Appendix C, "Spreadsheets using Microsoft Excel".

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