Vocab
A measurement calculated for a population is called a _______________ (1) and for a sample they are called _______________ (2)
1) Population Parameter
2) Sample Statistic
This cannot be determined from observational studies.
Causation / Causal Relationships
Name 2 non random sampling methods?
Convenience Sampling
Voluntary Response Sampling
What is the difference between an observational study and an experiment? (Show me that you know what both entail).
An observational study observes and collects data without influencing the results. An experiment imposes treatments on the experimental units, then measures and compares the results.
When the difference in results of an experiment are unlikely to have occurred by chance alone, they are _______ ________.
Statistically Significant
An additional variable that may affect one or more variables in the study, and may display a false relationship between the explanatory and response variables.
Confounding Variables
What type of study collects data from a sample of people using questionnaires?
a survey
What type of bias occurs when participants choose to respond to a survey themselves?
Self Reported Response Bias
Name the 4 components of a well- designed experiment.
Comparison, Random Assignment, Control, Replication
To establish causation between variables this aspect needs to be present: _________________ (1).
To generalize results to a population this aspect needs to be present: _________________ (2).
1) Random assignment to treatment groups.
2) Random selection of individuals in the study. (otherwise representative of the population)
A systematic tendency to prefer a certain outcome over others.
Bias
Random Sampling
What type of bias occurs when some groups are left out of the sample frame?
Undercoverage Bias
A researcher tests two fertilizers on tomato plants. She applies Fertilizer A to 1 tomato plant and Fertilizer B to 3 other tomato plants, chosen completely at random, and compares the average number of tomatoes produced by the plants. The plants all received the same amount of water and were placed on the same window sill. Is this a well- designed experiment? Explain.
No, this experiment satisfies the comparison, control, and random assignment aspects, but does not satisfy replication. Treatment 1: Fertilizer A is only used on 1 tomato plant, which means that we cannot tell if the results are due to the treatment, or the plant itself.
Researchers randomly select 200 adults from across the country and record their daily caffeine intake and average sleep hours. They find that people who drink more caffeine tend to sleep fewer hours.
Can the researchers generalize their results to the population? Can they establish causation?
They can generalize to adults in the population (random sample), but cannot establish causation because it’s an observational study.
What is a condition imposed on experimental units?
Treatments
Describe a simple random sample for selecting a sample of size n=50 from a population of 1000.
1) Assign all member of the population a number 1-1000 inclusive.
2) Use a random number generator to select 50 unique random numbers from the population.
3) The individuals with those numbers now make up the sample.
A survey asks high school students if they have ever cheated on a test. Of the 200 students surveyed, 10% admit to cheating. Describe the bias in this study.
This is likely a case of self reported response bias. 10% proportion of students that have cheated on tests is likely an underestimate because students may be embarrassed or afraid of getting in trouble.
A teacher wants to test whether listening to classical music improves test performance. She has 40 student volunteers, 20 males and 20 females. Describe how you could design a randomized block experiment for this scenario.
Block by gender, then randomly assign half of each block to listen to classical music during the test and the other half to take the test in silence; compare performance within and across blocks. Possible method for random allocation:
By block, assign all students in each block a number from 1 through 20, and use a random number generator to select approximately 10 unique values. The selected values represent subjects assigned to a treatment.
A psychologist recruits 100 volunteers and randomly assigns half to practice mindfulness for 10 minutes daily and half to read quietly for 10 minutes daily. After two weeks, the mindfulness group reports lower stress levels. Can these results be generalized to the population? Can they establish causation?
They can establish causation (random assignment), but cannot generalize beyond the volunteers because it wasn’t a random sample.
Describe blocking in randomized block designs.
Blocking means to split all experimental units into homogenous (similar) groups by some variable that is related to the explanatory and response variables. Then conducting a randomized experiment within blocks.
What type of sampling method is this?
The population is divided into groups. Some groups are randomly selected and all individuals in the chosen groups are sampled.
Cluster Sampling
A university wants to estimate the proportion of students who regularly attend campus sporting events. A student researcher surveys 100 people outside the basketball arena right before a big game, and 78% say they attend games regularly. Describe the bias in this study.
There is likely bias present in the study because the university used a convenience sample of students at the game. This group of students is more likely to regularly attend games than a random sample. Because of this reason, 78% is most likely an overestimate of the true proportion of students that regularly attend games.
A researcher wants to compare two study techniques A and B) on test performance. She has 30 pairs of twins volunteer. How could a matched pairs design be used here?
Randomly assign one twin in each pair to use Technique A and the other to use Technique B, then compare scores within each twin pair.
Possible method for random assignment:
Assign heads or tails to each twin in a pair, then flip a coin. The twin selected will be assigned to study technique A and the other twin will be assigned to study technique B.
A nutritionist asks for volunteers to test whether drinking a new energy drink improves workout performance. The volunteers choose whether they want to drink the energy drink or not, and their workout times are compared after one week. Can these results be generalized to the population? Can they establish causation?
She cannot generalize because the participants were volunteers (not randomly sampled), and she cannot establish causation because the participants were not randomly assigned to treatments — personal choice creates confounding.