# Statistics Project

StatisticsProject

Todetermine the changing rate of short-term memory loss, an experimentwas conducted on human subjects of different ages. Considering thefact that short-term memory is experienced during one’s period ofconsciousness, a simple task was used as the ingredient for theexperiment. Flash cards were used, having pictures of differentcommon items printed on them. The printed items included leaves,apples, rocks and cups. They were placed face down on a table, andthe subjects were asked to sit next to them, picking up two at atime. If the two selected cards had similar pictures, they were putaside. If not similar, the two flashcards were placed back on thetable face down, and the subject would select a different match,trying to remember whether they had previously seen an image of acard. A timer was used to determine the average amount of time usedby the different age groups to complete the matching exercise. Theflashcards used had similar top patterns to ensure that one could notdistinguish one from another whenever they were placed face down.Although random picking of the flashcards was allowed, trying toremember where a certain drawn card was placed was the key to thesuccess of the experiment. The experiment was conducted in aconducive room, and within a short time in the early morning hoursfor all the subjects to ensure that exhaustion would not be blamedfor spending too much time trying to create the correct matches. Thesubjects of the experiment were also made to relax on a bench,ensuring that they were completely open-minded during theirparticipation. It was also communicated to them that they had tovolunteer and not feel pressured to participate, which would havecompromised the findings of the test. Data collected from theexperiment was recorded, comparing the different age groups and theamount of time they took to complete the test successfully.

Ahypothesis that was to be tested during the experiment was formulated(Edward, 1969). It stated that human beings lose some of theirshort-term memory abilities with age.

Toget the data that was to be analyzed to determine whether thehypothesis was true or null, a sample had to be determined. Thesample was from different age groups. There were people in the agebrackets of 10-19 years, 20-29 years, 30-39 years, 40-49 years, 50-59years, 60-69 years and above 70 years. 20 people from each age groupwere selected to participate in the experiment and an average of thematching times recorded in a table. Random sampling was used in theselection of participants of a certain age group. A standarddeviation of 0.5 and a margin of error of +/-5% were used to assistin the determination of the sample size. A confidence interval of 95was applied. Using a randomized test sequence (Edward, 1969) was thebest option although getting a large number of people over 70 yearsold did not have much of randomization since their population was lowin the area of study. It was, however, easier to get them toparticipate, with the oldest subject being 84 years old and theyoungest being 10 years old. Having volunteer participants ensuredthat the results generated were genuine and accurate, avoiding anydata collected under distress. The gender of the participants wasbalanced in terms of equal male and female participants in all agegroups, sometimes using married couples in the age groups above 50years of age.

Thetime taken by the different age groups in completing the matchingexercise was averaged and recorded in the table below:

 Age bracket (years) Average time (minutes) Over 70 25 60-69 11 50-59 7 40-49 5 30-39 4 20-29 2 10-19 2

Table1: Data collected

Table2: The data as entered in Minitab

Fromthe table, it can be seen that the age brackets of 10-19 years and20-29 years had an average time of 2 minutes to complete matching theflash cards. The Minitab table had the two columns in numeric formfor ease of analysis of the data, but the first column in agebrackets was in text format.

Thedescriptive statistics of age were as shown below, with a standarddeviation of 22.14:

Thedescriptive statistics of the average time taken to complete thematching exercise was as shown below, with a standard deviation of8.12:

Withthe above collected data, it was clearly visible that members of theoldest age group spent the most time in trying to get the correctmatching pair and this was contributed to by the fact that they couldnot quickly remember where they had previously seen a certain imageon a flash card. They would either pick up the wrong card or randomlymake another pair guess, which mostly turned out to be wrong. It wasobserved that the rate of getting the correct match was different butincreased with time for each age group. The increase was attributedto the level of remembrance of the individuals and also due to theelimination of several pairs of flash cards such that the probabilityof getting a matching pair also increased (Davis, 2009). Theparticipants also seemed jovial once they started getting the correctmatches, indicating that they were loving the exercise. The presenceof a timer made them make quick selections as they seemed to becompeting against time. The presence of a crowd around theparticipants did not affect their picking of the flashcards. Someeven enjoyed cheers that seemed to create a motivating atmosphere,prompting them to play first and to try assess where each card was.

Acorrelation was used to test for the level at which the change in ageaffected the length of time used in completing the matching exercise.It was done using Minitab, and the results were obtained as below:

Correlations: average age (years),average time (minutes)

Pearsoncorrelation of average age (years) and average time (minutes) = 0.821

P-Value= 0.024

Itcan be seen that the correlation between the two variables is 0.821,which is closer to one than to zero, indicating a higher dependencebetween the two.

Acorrelation with regression was plotted for more understanding of theresults and is shown below:

Figure1: Scatterplot of the average time against the average age

Thetrend line slopes positively, indicating a relationship between theaverage age and short-term memory.

Figure2:Residual plot for short-term memory loss

Theabove are residual plots for short-term memory loss. The individualvalue plot clearly indicates the constantly increasing duration oftime spent in deciding which pairs to choose and forgetting theposition in which a certain image lay face down. The second graph,the histogram, indicates the frequency with which a certain timeaverage was achieved. The biggest number of participants spent morethan 5 minutes in the matching exercise. The 10 minutes and 25minutes brackets on average were used up by equal number of players.The two youngest groups used an average of 2 minutes each. Theseaverages were roughly equal for both male and female participants,eliminating gender from affecting short-term memory. The ladies,however, managed to match images of beautiful brightly coloredobjects faster followed by cards with dull images, although theoverall time taken was generally the same for both sexes.

Theindividual value plot is easy to comprehend and can be interpretedcorrectly without the need for complex calculations. By observation,one can deduce from the individual value plot the fact that ageaffected the time taken to complete the matching exercise. Thevertically arranged dots on this graph indicate the different timesused by the different age brackets participating in the experiment.Two dots on the same horizontal position indicate that the averagetime spent by two different age brackets was the same. In this case,participant of the age brackets of 10 to 19 years and 20 to 29 yearsspent two minutes each on average, all other errors held constant.

Theindividual value plots display every value involving the data and itsinterpretation. With these plots, one can identify misplaced valuesand therefore easily notice errors in data manipulation. They alsotell the distribution of data by viewing the position of the pointson the graph. Some points can be clustered while others can bedistributed. These plots are also useful in comparing data ofdifferent groups because they can all be plotted on the same graphand are easily distinguishable by their mere positions on the graph.Their vertical arrangement enables one to plot values of many groupsalong on one plane of the graph, and viewing all this data at a go isuseful in the analysis (Edwards, 1969).

Acombined boxplot of average years of the participants and the averagetime taken in completion of the experiment was also plotted to give aclear understanding of the data ranges used. The boxplot is as shownbelow. This indicates that the data collected from the experiment canbe analyzed in terms of age and time and a comparison of the twomade. The lines cutting across the center of the boxes indicate themedian of the data. From these boxplots, it is clear that the agedifference of the participants had a great influence on the results,indicating that there is a relatively huge dependence of the rate ofshort-term memory loss on age.

Figure3: Boxplot of average age and average time

Ageneral linear model ANOVA test was carried out to show thesignificance of aging in studying short-term memory loss, and theresults are shown below:

General Linear Model: average time(minutes) versus average age (years)

ANOVA,or the analysis of variance, is used to analyze group means and theirdifference. It also checks on variation in the means. ANOVAs are thebest means of testing two or more variables and compare the variancesof these variables as contributed to by different sources ofvariation. In the testing of a hypothesis, ANOVA is used to analyzeexperimental data. It is used in the testing of the null hypothesis,such as the one used in this experiment stating that human beingslose some of their short-term memory abilities with age. When theanalysis is done, decisions have to be made as to whether the nullhypothesis holds or is to be rejected. It mostly involves the designand result manipulation parts of the experiment being carried out aspart of a research or testing of a hypothesis. In the short-termmemory loss rate experiment, ANOVA was used to show the variances ofthe means obtained from the different age brackets. The errorsinvolved in the experiment were considered and factored into theANOVA analysis and data interpretation. By using Minitab to analyzestatistical data, it is easy to get the correct ANOVA analysis of thedata collected and eliminate the complex calculations that come withthe manual calculation of ANOVA analysis results, especially in caseswhere multiple group are being compared.

Ageneral linear model ANOVA analysis was used in this experiment. Thegeneral linear model is basically an extension of the linear multipleregression when looked at in terms of a single dependent variable. Inthis experiment, regression was used to show the correlation of theaverage time spent to complete the matching exercise and the averageage of the people used as subjects in the experimental procedure. Aline of the perfect fit was used to show the slope of the curve,indicating the dependence of short-term memory loss on age of thesubjects. The multiple regression and general linear models differ interms of the number of statistically analyzable dependent variables.Independent variables are not used in this analysis and applyingANOVA on such would bring up variance errors.

Conclusionand Recommendation

Theexperiment was successfully carried out and tested the hypothesis asrequired. It was thus concluded that indeed human beings lose some oftheir short-term memory abilities with age. The hypothesis can,therefore, be coined as a theory and used in the understanding ofhuman being’s memory capacity and its degradation with time. It canhowever not be stated that age is the only factor behind short-termmemory loss. Illness, nutrition and genetic composition of a persongreatly affect the generation of brain cells and their activity.

Theabove results in terms of graphs and other statisticalrepresentations were an average of the whole sample used. Somesubjects, however, did not give the expected results, with a15-year-old boy completing the matching exercise in 12 minutes. Suchcase were treated as special cases, and deeper scrutiny into thebackground of the young boy indicated that he had recently sufferedfrom severe blood infection and was under medication at the time ofthe experiment. Assumptions were made that the infection had probablyinterfered with the functioning of his brain or the drugsadministered to him were impairing his short-term memory ability.

Astudy on nutritional exposure (Smith, 2007) and genetic compositionthat would change the rate of short-term memory loss with age wasrecommended as part of future work. Moreover, research on thepossibilities of preserving the brain in a youthful state should alsobe carried out to determine whether the hippocampus can be saved fromnormal aging effects.

WorksCited

Edwards,Allen Louis. StatisticalAnalysis.3d ed. New York: Holt, Rinehart and Winston, 1969.

Davis,Tom, and Al. Franken. Thirty-nineYears of Short-term Memory Loss.New York: Grove, 2009

Smith,Tom. Copingwith Age-related Memory Loss.London: Sheldon, 2007.