Midterm 1 EBIO 1010

sampling error

two important sources of error; random sampling error and systematic sampling error. It is a statistical difference between a sample’s result and the true value of the entire population being studied. It can occur naturally because a sample only includes a subset of a population rather than every single individual.

random sampling error

always exists when a subset of a population is sampled. Occurs purely due to random chance in selecting participants. It is unpredictable and neutral and flucuates in all directions. It can cause a sample average to be slightly higher or lower than the true population average, but it does not consistently skew results in one direction.

systematic sampling error

frequently called sampling bias. It occurs when an inherent flaw or flaw in methodology skews the sample in a specific direction. It is consistenly over representing or under representing. It skews the results away from the true population value, leading to biased outcomes. Increasing the sample size does not reduce systematic sampling error. It can only be fixed by correcting the sampling method or research design.

uncertainty

refers to the degree of doubt or lack of exact knowledge about a measurment, estimate or outcome. Because researchers rarely collect data from an entire population, statistical calculations rely on samples, which creates a gap between the sample estimate and the true population vote.

how to measure uncertainty

standard error

standard error

how accurate your sample estimate is to the true parameter. In other words, it measures how accuratly a sample mean represents the true population mean. It is calculated by dividing the standard deviation (s) by the square root of the sample size.

example of standard error

Imagine taking the test scores for a class of 30 students. Standard error would be: “If i picked another random class of 30 students, how close would their average score be to this class’s average. (Measures the precision of your average) Overall, it is the precision of the calculated mean. Another example: say the average sample score is 86, and there is a standard error of 1.87. This indicates that if you were to draw repeated samples of 5 students, the sample average would typically vary around the true class average by 1.87 points.

standard deviation

realistic measure of spread within the sample. In more words, it measures variation among individuals or things. It describes the variability within a single sample. Tells how far individual data points are spread out from the sample average. spread of individual data points. also standard deviation IS a parameter value and is not affected by sampling from a population.

small standard deviation

individual numbers are packed tightly around the sample average.

large standard deviation

individual numbers are spread far away from the average. (human data vs. computer)

parameter

always a value that describes the entire population, it is never calculated directly from a sample. The parameter can be the true mean of an entire population, but it is usually unknown because measuring everyone is impossible.

example of parameter

if you want to know the average height of every high school student in the US, you have to find the exact average height of all high school students, not just a sample.

estimate

refers to a value calculated from a sample of data that serves as your best approximation of an unknown population parameter.

point estimate

a single amount calculated from sample data used as a direct guess for the parameter. Limitation: it is rarely exact because sample data varies naturally.

what makes a good statistical estimate?

Unbiasedness (does not consistently over or underestimate the population parameter). And efficiancy (the estimates are tightly clustered together across different sample, the estimate has a low variance of standard error)

statistic

summary value of a sample taken from a population. Always a number describing a sample. used because gathering data from an entire populaton is usually too expensive, time consuming or impossible

variation

measuring spread within a sample (squared untis)

independent variable

cause. the variable that the researcher intentionally changes or manipulates to test its effect. Set or changed by researcher, on the x axis.

dependent value

the variable that is measured or observant. The effect (the y axis)

example of dependent and independent variables

a student wants to see how jumping jacks impacts pulse rates. independent variable is the anount of exercise. (0 min, 1 min, 3 min) and dependent variable (effect) is the heart rate, measured in beets per min

null hypothesis

there is no significant difference, relationship, or effect between 2 variables or groups

biological hypothesis

a proposed, testable explanation for a specific phenomenom obersvation or scientific question within the study of biology.

P-value

between 0 and 1. Shows significance of data

low p value

a low p value of below < 0.05 means there is a very small probability that your results happened by chance there you CAN reject the null hypothesis. It is statitiscally significant. There IS a difference between groups

high p value

>0.05. results could have easily have happened just by random variation in the data. you CANNOT reject the null hypothesis

confidence interval

measure of uncertaintiy. Calcluated by difference in means ± 2 * SE. If the study is repeated many times, 95% of the time the parameter estimate will be within the 95% confidence interval. If it DOES include zero you cannot reject the null hypothesis.

T test

specific test for comparing the means between 2 groups for a quantitive variable

T-statistic

difference in means divided by uncertainty. Basically, how far the difference in means is from expectation of the null hypothesis. If the T-value is far from zero, it means there is a statistical significance, even if its negative.

f- statistic

variation across all groups. The bigger the F value is, the more confident you can be that the groups are different from each other.

F>1

reject the null hypothesis. the difference between the group averages are way bigger than the random scatter within the group.

equation for linear model

y = B0 + B1 *x + error. (B0 is y intercept, B1 is slope)