in a classic study of problem solving, katona demonstrated that people whoa re required to figure out a problem on their own will learn more than people who are given the solution. One group of participants is presented with a series of problems that hey must figure out. second group sees the same problems but gets an explanation of the solutions. Later both groups are given a new set of similar problems and their problem-solving scores are as follows:
On their own
n=10
M=78
SS=1420
Given Solutions
n=15
M=66
SS=2030
ss stands for sum of squares
To find the significance of the difference between two means, we need to divide this difference by the standard error of the difference between means.
To find the standard error of the difference between means, we need to know the standard deviation (SD) of both groups.
To get the standard SD, you need both sum of squares (ΣX^2) and the sum of the scores squared ([ΣX]^2). You only give me one of these terms.
We need more information — or the corect information.
I hope this helps. Thanks for asking.
In the classic study conducted by Katona, participants were divided into two groups. One group was required to figure out a series of problems on their own, while the second group was given explanations of the solutions. Later, both groups were given a new set of similar problems, and their problem-solving scores were measured.
For the group that had to figure out the problems on their own:
- Sample size (n): 10
- Mean (M) of problem-solving scores: 78
- Sum of squares (SS): 1420
For the group that was given the solutions:
- Sample size (n): 15
- Mean (M) of problem-solving scores: 66
- Sum of squares (SS): 2030
The sum of squares (SS) is a statistical measure that indicates the variability or dispersion of the scores in a dataset. In this study, it helps quantify the differences in problem-solving scores between the two groups.
In this classic study conducted by Katona, the goal was to investigate the effects of problem-solving methods on learning. The study consisted of two groups of participants who were presented with a series of problems.
The first group of participants was required to figure out the problems on their own, without any specific guidance or solutions provided. This group was referred to as the "On their own" group.
The second group, known as the "Given Solutions" group, was presented with the same set of problems but received explanations of the solutions along the way.
After completing the initial set of problems, both groups were given a new set of similar problems to solve. The scores obtained by each group on these new problems were as follows:
On their own:
- Sample size (n): 10
- Mean (M): 78
- Sum of Squares (SS): 1420
Given Solutions:
- Sample size (n): 15
- Mean (M): 66
- Sum of Squares (SS): 2030
In statistical analysis, the sum of squares (SS) is a measure of the total variation or dispersion within a set of data. It quantifies how much each individual score deviates from the mean. The sum of squares is typically used to calculate variance and other statistical measures.
Based on these results, we can see that the group of participants who figured out the problems on their own (On their own group) had a higher mean score (M = 78) compared to the group that received solutions (Given Solutions group with M = 66). However, it is also important to consider the sample size, as the On their own group had fewer participants (n = 10) compared to the Given Solutions group (n = 15).
This study suggests that individuals who are required to figure out problems on their own may have a higher potential for learning compared to those who are provided with the solutions. The difference in problem-solving scores between the two groups indicates that independent problem-solving can lead to better learning outcomes.