Flowchart Symbols Guide - Includes common flowchart icons such as process, terminator, and decision symbols for standard and non-standard uses. Use this guide when you explore Lucidchart's vast flowchart shape library. Sign up and try it for free! If more than the most basic flowchart symbols appear in your diagram, it is good practice to include a legend or symbol key. Most flowcharts should be built using only the Start/End and Action or Process symbols and should follow a very basic set of best practices. Sticking with these two primary flowchart symbols is the best way to ensure that.

In statistics, the logit (/ˈloʊdʒɪt/LOH-jit) function or the log-odds is the logarithm of the odds${\displaystyle \frac{p}{1-p}}$ where p is a probability.^[1] It is a type of function that creates a map of probability values from ${\displaystyle (0,1)}$ to ${\displaystyle (-\mathrm{\infty },+\mathrm{\infty })}$.^[2] It is the inverse of the sigmoidal'logistic' function or logistic transform used in mathematics, especially in statistics.

Definition[edit]

If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.

${\displaystyle \mathrm{logit}(p)=\log \left(\frac{p}{1-p}\right)=\log (p)-\log (1-p)=-\log \left(\frac{1}{p}-1\right).}$

The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used. The choice of base corresponds to the choice of logarithmic unit for the value: base 2 corresponds to a shannon, base e to a “nat”, and base 10 to a hartley; these units are particularly used in information-theoretic interpretations. For each choice of base, the logit function takes values between negative and positive infinity.

The “logistic” function of any number ${\displaystyle \alpha }$ is given by the inverse-logit:

${\displaystyle {\mathrm{logit}}^{-1}(\alpha )=\mathrm{logistic}(\alpha )=\frac{1}{1+\exp (-\alpha )}=\frac{\exp (\alpha )}{\exp (\alpha )+1}}$

The difference between the logits of two probabilities is the logarithm of the odds ratio (R), thus providing a shorthand for writing the correct combination of odds ratios only by adding and subtracting:

${\displaystyle \log (R)=\log \left(\frac{p_1/(1-p_1)}{p_2/(1-p_2)}\right)=\log \left(\frac{p_1}{1-p_1}\right)-\log \left(\frac{p_2}{1-p_2}\right)=\mathrm{logit}(p_1)-\mathrm{logit}(p_2).}$

History[edit]

There have been several efforts to adapt linear regression methods to a domain where the output is a probability value, ${\displaystyle (0,1)}$, instead of any real number ${\displaystyle (-\mathrm{\infty },+\mathrm{\infty })}$. In many cases, such efforts have focused on modeling this problem by mapping the range ${\displaystyle (0,1)}$ to ${\displaystyle (-\mathrm{\infty },+\mathrm{\infty })}$ and then running the linear regression on these transformed values. In 1934 Chester Ittner Bliss used the cumulative normal distribution function to perform this mapping and called his model probit an abbreviation for 'probability unit';.^[3] However, this is computationally more expensive. In 1944, Joseph Berkson used log of odds and called this function logit, abbreviation for 'logistic unit' following the analogy for probit. Log odds was used extensively by Charles Sanders Peirce (late 19th century).^[4]G. A. Barnard in 1949 coined the commonly used term log-odds;^[5] the log-odds of an event is the logit of the probability of the event.^[6]

Uses and properties[edit]

• The logit in logistic regression is a special case of a link function in a generalized linear model: it is the canonical link function for the Bernoulli distribution.
• The logit function is the negative of the derivative of the binary entropy function.
• The logit is also central to the probabilistic Rasch model for measurement, which has applications in psychological and educational assessment, among other areas.
• The inverse-logit function (i.e., the logistic function) is also sometimes referred to as the expit function.^[7]
• In plant disease epidemiology the logit is used to fit the data to a logistic model. With the Gompertz and Monomolecular models all three are known as Richards family models.
• The log-odds function of probabilities is often used in state estimation algorithms^[8] because of its numerical advantages in the case of small probabilities. Instead of multiplying very small floating point numbers, log-odds probabilities can just be summed up to calculate the (log-odds) joint probability.^[9][10]

Comparison with probit[edit]

Closely related to the logit function (and logit model) are the probit function and probit model. The logit and probit are both sigmoid functions with a domain between 0 and 1, which makes them both quantile functions – i.e., inverses of the cumulative distribution function (CDF) of a probability distribution. In fact, the logit is the quantile function of the logistic distribution, while the probit is the quantile function of the normal distribution. The probit function is denoted ${\displaystyle {\mathrm{\Phi }}^{-1}(x)}$, where ${\displaystyle \mathrm{\Phi }(x)}$ is the CDF of the normal distribution, as just mentioned:

${\displaystyle \mathrm{\Phi }(x)=\frac{1}{\sqrt{2\pi }}{\int }_{-\mathrm{\infty }}^x{e}^{-\frac{y^2}{2}}dy.}$

As shown in the graph on the right, the logit and probit functions are extremely similar when the probit function is scaled, so that its slope at y = 0 matches the slope of the logit. As a result, probit models are sometimes used in place of logit models because for certain applications (e.g., in Bayesian statistics) the implementation is easier.

See also[edit]

• Sigmoid function, inverse of the logit function
• Discrete choice on binary logit, multinomial logit, conditional logit, nested logit, mixed logit, exploded logit, and ordered logit
• Daniel McFadden, a Nobel Prize in Economics winner for development of a particular logit model used in economics^[3]
• Ogee, curve with similar shape
• Probit, another function with the same domain and range as the logit
• Arcsin (transformation)

References[edit]

1. ^'LOG ODDS RATIO'. nist.gov.
2. ^'Logit/Probit'(PDF).
3. ^ ^abJ. S. Cramer (2003). 'The origins and development of the logit model'(PDF). Cambridge UP.
4. ^Stigler, Stephen M. (1986). The history of statistics : the measurement of uncertainty before 1900. Cambridge, Massachusetts: Belknap Press of Harvard University Press. ISBN978-0-674-40340-6.
5. ^Hilbe, Joseph M. (2009), Logistic Regression Models, CRC Press, p. 3, ISBN9781420075779.
6. ^Cramer, J. S. (2003), Logit Models from Economics and Other Fields, Cambridge University Press, p. 13, ISBN9781139438193.
7. ^'Archived copy'. Archived from the original on 2011-07-06. Retrieved 2011-02-18.CS1 maint: archived copy as title (link)
8. ^Thrun, Sebastian (2003). 'Learning Occupancy Grid Maps with Forward Sensor Models'. Autonomous Robots. 15 (2): 111–127. doi:10.1023/A:1025584807625. ISSN0929-5593.
9. ^Styler, Alex (2012). 'Statistical Techniques in Robotics'(PDF). p. 2. Retrieved 2017-01-26.
10. ^Dickmann, J.; Appenrodt, N.; Klappstein, J.; Bloecher, H. L.; Muntzinger, M.; Sailer, A.; Hahn, M.; Brenk, C. (2015-01-01). 'Making Bertha See Even More: Radar Contribution'. IEEE Access. 3: 1233–1247. doi:10.1109/ACCESS.2015.2454533. ISSN2169-3536.

Further reading[edit]

• Ashton, Winifred D. (1972). The Logit Transformation: with special reference to its uses in Bioassay. Griffin's Statistical Monographs & Courses. 32. Charles Griffin. ISBN978-0-85264-212-2.

Commercial patterns can be hard to interpret, what with the triangles, circles, and arrows scattered all over the pattern pieces. What do these symbols mean? Let’s find out!

• Lines

The outer edge of the pattern is where you’re supposed to cut. It’s usually marked with a solid black line. If the pattern is multi-sized, each size will have its own type of line—usually dashes of varying lengths.

• Dashed Lines

It’s rare for commercial patterns to mark the stitching line or seam allowance, but you’ll sometimes find this on vintage or independent patterns. The line will be narrow and dashed, always running parallel to the edge of the pattern. It tells you exactly where to sew, when you’re stitching two pieces together.

Stitching Lines

• Double Lines

Many patterns have a set of double lines running across the width of the piece, usually marked, “Lengthen or Shorten Here.” If you need to shorten the pattern (for a petite size), or lengthen it (for a taller size), these lines mark the best place to do so. Fold along the lines to shorten the pattern, or cut between them and add extra tissue to lengthen the pattern.

Whether shortening or lengthening, you’ll probably need to redraw the outer cutting line, just to make sure it’s straight and accurate.

• Dashed-and-Dotted Lines

To mark the center front and center back of a garment, the pattern may have a dashed-and-dotted line. This is helpful when you’re fitting a pattern, as you’ll know exactly where the center front or back is meant to be. It may be labeled with “CB” for center back and “CF” for center front.

Dashed & Dotted Lines

Chh Stock Quote

• Dashed & Solid Lines

When a pattern shows a short dashed line beside a short solid line (or two short solid lines) with an arrow pointing from one to the other, it’s indicating where to fold pleats. Pinch and fold the fabric in the direction of the arrow, then pin or baste it in place.

• Barred Lines

These look like extra-long capital I’s. Their purpose is to mark the placement of buttonholes.

Buttonhole Lines

Symbol For Choice

• X’s

A small X marks where to place buttons.

• Double-Headed Arrows

The long double-headed arrow running down the middle of the pattern is the grainline arrow. It shows you which direction the pattern should be oriented. The grain of the fabric should always run parallel to the grainline arrow.

Grainline Arrow

• Bent Double-Headed Arrows

Sometimes, there’s a double-headed arrow that’s bent at the ends, with the arrowheads pointing sideways. These arrows always point toward the edge of the pattern, which means that edge goes on the fold. Instead of placing the pattern piece somewhere in the middle of the fabric, place it right up against the folded edge. When the fabric is opened up, you’ll have one large piece.

• Small Triangles (or Diamonds)

Most patterns have small triangles (or diamonds) placed every so often along the outer edges. Their appearance can vary—they might be solid or outlined, thick or thin, etc. Either way, they’re called notches, and they’re meant to be matched up. In other words, when you pin two pattern pieces together, the notches on each piece should line up with each other. If they don’t, you have a problem. There’s four possible explanations:

• #1. You’re trying to match up the wrong pattern pieces.
• #2. Your pattern pieces simply aren’t aligned properly.
• #3. Your fabric has stretched or distorted.
• #4. You didn’t copy the notches accurately.

Sometimes, there are clusters of two or three notches, or in very complex garments, four or more. The number of notches usually increases as you move toward the back of the garment. If a pattern has a triple-notch, that seam probably goes in the back, while the double-notches go on the sides, and the single notches go in front. Knowing this can help you tell the front from the back, which is useful if your pieces look similar and you forgot to label them.

So long as you always match corresponding notches together, you’ll be fine.

Notches

Healthy Choice Symbol

• Diamonds or Giant Triangles

If you see a large triangle that stretches from the bust to the waist, or a diamond that extends from the bust to the hips, it’s a dart. (Usually, the lines are dashed, but occasionally you’ll see one that’s drawn with solid lines.) Darts are sewn to add three-dimensionality to a garment, so it will fit the curves of your body.

Many darts are marked with dots at the tip and at the seam allowances. Some also have a thin, solid line running down the center, which shows you where to fold the fabric prior to sewing the dart. If there is no fold-line, fold the dart so the seam allowance dots line up, and then sew along the dashed lines.

• Crossed Circles

A circle with a cross or X through it is used to mark the center bust point—the apex of the bust, which generally falls at the middle of your breast. (About where your nipple is, provided you’re wearing a decent bra.) Sometimes, the same symbol is used to mark the waistline and hipline, too. Use these symbols to help you fit the pattern correctly.

X’d Circle

• Dots, Squares, Etc.

Dots, squares, and other small shapes are used as match points, much like notches, or they’re used to indicate where to start and stop sewing. For example, a dot halfway up the center back of a skirt pattern probably indicates where you should stop sewing to leave room for the zipper. The square on a sleeve head is going to line up with a corresponding square on the armscye, so you can attach the sleeve properly. Dots on the side of a pants pattern will indicate where the in-seam pockets go.

While these symbols are fairly universal, some independent patterns have their own unique symbols. If you aren’t sure what a symbol is for, check the pattern directions. There’s usually a key that will tell you what everything means.

~~*~~

Looking for more sewing advice? Try the Sewing Basics menu for a list of beginner-friendly articles. Also, check out the Tutorials,Articles, andSewing Diaries.