What statistical methods a researcher can use to determine if weights of the children in pounds are normally distributed or not?
To determine if the weights of children in pounds are normally distributed, a researcher can use various statistical methods. Here are a few commonly used techniques:
1. Histogram: Plotting a histogram of the weights can provide a visual representation of the distribution. If the histogram resembles a bell-shaped curve, it suggests a normal distribution. However, keep in mind that histograms can be subjective, so it's important to complement this method with other statistical tests.
2. Shapiro-Wilk Test: This is a statistical test that assesses the normality of a distribution. The test calculates a test statistic (W-value) and compares it to critical values. If the calculated W-value is close to 1, it indicates that the data is normally distributed. However, this test is most effective for large sample sizes.
3. Anderson-Darling Test: Similar to the Shapiro-Wilk test, the Anderson-Darling test determines the presence of a normal distribution. It calculates a test statistic (AD-value) and compares it to critical values. If the AD-value is less than the critical value, it suggests a normal distribution. This test is more powerful for smaller sample sizes.
4. QQ plot: A quantile-quantile (QQ) plot is used to compare the distribution of the observed data to the theoretical normal distribution. If the points on the QQ plot fall along a diagonal line, it indicates a good match with normal distribution. Deviations from the line suggest departures from normality.
It's important to note that no single statistical method can definitively determine the normality of data. It is often recommended to use a combination of these methods to draw more accurate conclusions.