3-Experimental Error and Statistics-24

The specific data or information outlined in the table.

5.6 ± 4.0%.

Addition and Subtraction.

The margin of uncertainty associated with a measurement.

As a value with a plus-minus sign, e.g., 12.35 ± 0.02 ml.

Analyze samples of known composition.

Arithmetic mistakes, transposition of number errors, using the wrong scale, spilling solutions, and reversing signs.

Analyze blank samples.

The ion channel is closed and cations cannot enter the muscle cell.

The uncertainty associated with a measurement expressed as a percentage.

The curve becomes shorter and broader.

The middle number in a series arranged in increasing or decreasing order.

It represents the range within which approximately 99.7% of data points fall in a normal distribution.

To compare two sets of measurements to determine if they are 'the same' or 'different'.

21.64 ml.

21.62 ml.

Absolute error E = |true value - measured value|.

0.04/2.11 = 1.896%.

A standard deviation that combines data from two sets.

Use different analytical methods to measure the same quantity.

It signifies the range within which approximately 68% of data points fall in a normal distribution.

Constant errors and proportional errors.

It causes data to fluctuate around a central value, affecting precision.

Random errors.

Observational error, imperfect instrument calibration, and environmental interference.

12.6, 11.9, 13.0, 12.7, and 12.5 g of carbohydrate per 100 g of protein.

自由度是指樣本中獨立或能自由變化的數據的個數。

A range of values that is likely to contain the true parameter with a specified level of confidence.

± ts / √n.

x = (Σ xi) / n, where n is small (n < N).

Data points are close to the true value but vary widely from each other.

By using as large a sample as possible.

Not significant figures.

Errors that occur occasionally and cause results to be significantly high or low, affecting a single result in a set of replicate data.

It compares absolute uncertainty with its associated measurement.

As the standard deviation or as a confidence interval.

A value with an uncertainty of 0.02.

Variance (s²) = (Σ(Xi - X̄)²) / N.

By using (n1 + n2 - 2), where n1 and n2 are the sample sizes.

A systematic error, also called a determinate error, is a repeatable error that occurs consistently when measurements are taken in the same way.

Relative error E = (Absolute error / true value) x 100%.

s = √(Σ (xi - x)² / (n - 1)).

They vary in direction and magnitude from measurement to measurement.

Imperfections in measuring devices and instabilities in power supplies.

It relates the sample mean, t-value, standard deviation, and population mean.

Because gusts and changes in direction affect the value.

Constant errors become more serious as the size of the sample decreases.

Determine t calc using the formula with the 'true' mean and the measurement statistics.

How well we can read an instrument or experience with a particular method.

自由度等於獨立變量數減掉其衍生量數。

It indicates the range within which about 95% of data points fall in a normal distribution.

Use identical samples to analyze in several laboratories by other people and methods.

A Gaussian distribution.

By improving your experimental procedure.

Gross errors.

Because of the constraint that Σ (xi - x) = 0.

Air currents and changes in the specimen's water content.

Precision or probable error, and it measures the width of the distribution.

Carelessness, inattention, or personal limitations of the experimenter.

It was too great to be due to experimental error.

-0.1%.

The RSD is approximately 36%.

It ranges from -ts/sqrt(n) below x to +ts/sqrt(n) above x.

W. S. Gossett.

Systematic errors.

The distribution of a set of observations.

They affect a single result, leading to inaccuracies in the overall data set.

21.59 ml.

No, but it might be reduced by a better experiment.

By increasing the number of measurements.

The method measuring the average mass from air.

y = a^x, with standard deviation calculated as s_y/y = x(s_a/a).

The presence of interfering contaminants in the sample.

± 0.02 mL.

It accounts for the fact that one deviation is dependent on the others, thus providing an independent measure of precision.

When successive readings become consistently lower or higher over time, often seen in electronic equipment.

The relative error becomes -1.0%.

The null hypothesis is false, indicating that the means are different and something may be wrong with the experiment.

An operation containing subtraction and division.

A measure of the reproducibility of a result.

Data points are widely spread and far from the true value.

They become more serious.

Mean and standard deviation.

Visual judgment, temperature fluctuation, balance reading, and other uncontrollable variables.

Data points are closely clustered but far from the true value.

0.46% greater.

x approaches μ and s approaches σ.

The number of degrees of freedom or the number of independent data points.

The standard deviation is approximately 4.5.

A range of values within which there is a specified probability of finding the true mean.

The shape of the curve is influenced by the number of observations.

Range = max - min.

If the calculated t is greater than the tabulated t at the 95% confidence level.

The probability, P, as a function of the measurement x, the 'true' mean (μ), and the 'true' standard deviation (σ).

y = a + b - c, where the standard deviation is calculated as s_y = √(s_a² + s_b² + s_c²).

By summing the measured values and dividing by the number of measurements.

It arises from non-ideal chemical or physical behavior of the analytical system.

y = log10(a), with standard deviation calculated as s_y = s_a/(a ln(10)).

Proportional errors that occur when using different measuring tapes, such as a new cloth tape versus an older, stretched one.

It may give accurate readings within a certain temperature range but become inaccurate at higher or lower temperatures.

0.5 kg.

50% and 90% confidence intervals.

The absolute maximum difference between the largest and smallest values.

對 N 個隨機樣本而言，自由度為 N - 1。

How close a measured value is to the 'true' value.

Limitations of instruments, environmental factors, and slight variations in procedure.

Constructing an experimental calibration.

A discrepancy between two different methods of measuring the density of nitrogen.

An error caused by not setting an instrument to zero prior to its use.

They increase or decrease in proportion to the size of the sample taken for analysis.

σ = √(Σ (xi - μ)² / N), when N → ∞.

The distribution is wider and the data is less precise.

Find the square root of the variance, which is the average of the squared differences from the mean.

Standard deviation (s) = √(Σ(x_i - x̄)² / n).

-10.0%.

RSD = 100% x (s / x), where s is the standard deviation and x is the mean.

It gives smaller confidence intervals.

Reading the value from a different angle each time.

μ = (Σx_i) / N.

Add all the measurements together and divide by the number of measurements.

When they fall between marks on a scale or when considering the thickness of measurement markings.

The variation from the reported value is greater than expected from random error alone.

The number of observations.

A value of 0.62 with a relative uncertainty of 3%.

Indeterminate error.

23.75 ml.

Systematic errors affect the accuracy of results.

Relative uncertainty = (standard deviation / mean) x 100%.

21.63 ml.

It gives the probability that an individual measurement will differ from the 'true' mean by a given amount due to random error.

y = ab/c, with standard deviation calculated as s_y/y = √((s_a/a)² + (s_b/b)² + (s_c/c)²).

Because two quantities must be extracted from a set of data, and only N-1 deviations provide an independent measure of precision.

An error that is independent of the size of the sample.

RSD = (Standard Deviation / Mean) x 100%.

It is taken from the Student's t distribution table.

自由度為 1，因為 b 值受 a 值影響。

The channel opens, cations enter the cell, and muscle action is initiated.

Limitations on our ability to make physical measurements and natural fluctuations in the quantity being measured.

The magnitude of the error does not depend on the size of the quantity measured.

Positioning yourself slightly differently each time can lead to different weight readings.

A contaminant on a balance pan that always causes measured weights to be too high.

The desired confidence level and the number of degrees of freedom in the calculation of s.

It will always result in an inaccurate reading, consistently low or high depending on the angle of the reading.

The height and time at which the measurement is taken.

By considering the uncertainty in each reading.

The mean is 12.5.

The current is represented by a Gaussian distribution.

It indicates the magnitude of uncertainty in relation to the measurement.

21.62 ml.

Data points are closely clustered and near the true value.

Overestimate, by 0.46%.

By using as large a sample as possible.

The volume remains the same regardless of the total volume of reagent required, leading to increased relative error as the total volume decreases.

To express confidence intervals and to compare results from different experiments.

x̄ = (Σx_i) / N.

They are often small and not positively identified or measured.

It gives different results due to thermal expansion of the material.

No, it does not diminish the significance of the error.

You compare t calc to t table from the table of Student's t values for a specific confidence level and degrees of freedom.

The measured standard deviation.

μ = (Σ xi) / N, when N → ∞.

Minor changes in posture can lead to different height readings.

The distribution is narrower and the data is more precise.

y = anti log10(a), with standard deviation calculated as s_y = s_a * 10^a * ln(10).

Mean (x) = (Σx_i) / n.

The measured mean.

The null hypothesis is true, meaning the two means are not different at the chosen confidence level.

Systematic errors, random errors, and gross errors.

The uncertainty associated with every measurement.