level

(noun)

The specific value of a factor in an experiment.

Related Terms

Examples of level in the following topics:

  • Randomized Design: Single-Factor

    • For example, if there are 3 levels of the primary factor with each level to be run 2 times, then there are $6!
    • An example of an unrandomized design would be to always run 2 replications for the first level, then 2 for the second level, and finally 2 for the third level.
    • To randomize the runs, one way would be to put 6 slips of paper in a box with 2 having level 1, 2 having level 2, and 2 having level 3.
    • $L$: 4 levels of that single factor (called 1, 2, 3, and 4)
    • $N$: 4 levels multiplied by 3 replications per level gives 12 runs

  • Level of Confidence

    • The proportion of confidence intervals that contain the true value of a parameter will match the confidence level.
    • The desired level of confidence is set by the researcher (not determined by data).
    • If a corresponding hypothesis test is performed, the confidence level is the complement of respective level of significance (i.e., a 95% confidence interval reflects a significance level of 0.05).
    • In applied practice, confidence intervals are typically stated at the 95% confidence level.
    • However, when presented graphically, confidence intervals can be shown at several confidence levels (for example, 50%, 95% and 99%).

  • Choosing a significance level

    • Choosing a significance level for a test is important in many contexts, and the traditional level is 0.05.
    • However, it is often helpful to adjust the significance level based on the application.
    • Is there good reason to modify the significance level in such an evaluation?
    • A slightly larger significance level, such as α = 0.10, might be appropriate.
    • Choose a small significance level, such as α = 0.01.

  • Between- and Within-Subjects Factors

    • In the "Smiles and Leniency" study, the four levels of the factor "Type of Smile" were represented by four separate groups of subjects.
    • When different subjects are used for the levels of a factor, the factor is called a between-subjects factoror a between-subjects variable.
    • In the "ADHD Treatment" study, every subject was tested with each of four dosage levels (0, 0.15, 0.30, 0.60 mg/kg) of a drug.
    • Age has three levels and gender has two levels.
    • When all combinations of the levels are included (as they are here), the design is called a factorial design.

  • Significance Levels

    • If a test of significance gives a $p$-value lower than or equal to the significance level, the null hypothesis is rejected at that level.
    • A fixed number, most often 0.05, is referred to as a significance level or level of significance.
    • If a test of significance gives a $p$-value lower than or equal to the significance level, the null hypothesis is rejected at that level.
    • The choice of significance level is somewhat arbitrary, but for many applications, a level of 5% is chosen by convention.
    • Different levels of cutoff trade off countervailing effects.

  • Factorial Experiments: Two Factors

    • A full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values (or levels), and whose experimental units take on all possible combinations of these levels across all such factors.
    • For the vast majority of factorial experiments, each factor has only two levels.
    • The strings have as many symbols as factors, and their values dictate the level of each factor: conventionally, $-$ for the first (or low) level, and $+$ for the second (or high) level .
    • The simplest factorial experiment contains two levels for each of two factors.
    • Each combination of a single level selected from every factor is present once.

  • Changing the Confidence Level or Sample Size

    • Suppose we change the original problem by using a 95% confidence level.
    • σ = 3 ; n = 36 ; The confidence level is 95% (CL=0.95)
    • Use the original 90% confidence level.
    • x = 68• σ = 3 ; The confidence level is 90% (CL=0.90) ; = z = 1.645
    • σ = 3 ; The confidence level is 90% (CL=0.90) ; = z .05 = 1.645

  • Statistical Literacy

    • A low level of HDL have long been known to be a risk factor for heart disease.
    • Taking niacin has been shown to increase HDL levels and has been recommended for patients with low levels of HDL.
    • You could randomly assign patients with low levels of HDL to a condition in which they received niacin or to one in which they did not.

  • Analysis of Variance Designs

    • Be able to identify the factors and levels of each factor from a description of an experiment
    • Since four types of smiles were compared, the factor "Type of Smile" has four levels.
    • Age would have three levels and gender would have two levels.

  • Factors Affecting Power

    • There is a trade-off between the significance level and power: the more stringent (lower) the significance level, the lower the power.
    • Figure 3 shows that power is lower for the 0.01 level than it is for the 0.05 level.
    • A one-tailed test at the 0.05 level has the same power as a two-tailed test at the 0.10 level.
    • A one-tailed test, in effect, raises the significance level.
    • The relationship between significance level and power with one-tailed tests: μ = 75, real μ = 80, and σ = 10